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National Radio Day: The History of Our Stations
posted by Mason Black - Aug 20, 2018
There are 5 total stations that are apart of the iHeartRadio cluster in north Alabama. You have 102.1 WDRM, 100.3 The River, WBHP-AM, 106.1 WTAK, and 106.5 KissFM! Despite that being how you know these stations now, that may not have always been the case. Below is a brief history of all five of our stations throughout the years
102.1 WDRM
Today you know WDRM as being "#1 for New Country" but it hasn't always been that way. WDRM started out as WHOS-FM in 1951 but didn't settle in on the 102.1 frequency until 1959 and a little bit later became WDRM. Throughout the late 70's and early 80's WDRM focused on rock by day, urban by night, and even top 40 sprinkled in with an attitude of 'not following the rules'.
Fast forward to 1984 when WDRM flipped to a country format. Nearly 35 years after switching to country, WDRM is still '#1 for New Country' broadcasting all over north Alabama and south Tennessee. Be sure and listen to Dan&Josie during your mornings, Stuart Langston on your middays, Tige&Daniel while you're killing time in the afternoons or Mason on the nights!
WBHP-AM
WBHP started out back in 1931 as WBHS (World's Best Hardware Store) before going off air in 1933 due to financial strains of the Great Depression. The station returned to air in 1937 as WBHP (named after longtime owner Wilton "Buster" Harvey Pollard) and played country music all the way up until 1997 when it switched to an all-news format. There was an hour on Sunday's in the 1960's called the "German Hour" that played classical music which catered to Wernher von Braun's German rocket scientist. Now WBHP-AM can be heard on 800/1230AM, 102.5 FM, and 102.1 HD-2 in the Huntsville area. Tune in for Toni&Gary in the mornings, Glenn Beck from 8am to 11am, Dave Ramsey 11am to 2pm, Sean Hannity 2pm to 5pm, and Michael Berry 5pm to 7pm!
106.1 WTAK
WTAK got it's start on the AM band playing Top 40 hitsvthrough the 70's. WTAK debuted it's new call letters in the 80's on the AM dial as Huntsville's only Rock station and is one of the top rated radio station in the Huntsville Market! The broadcast tower is located on Brindlee Mountain with signal spread all over the central Tennessee Valley. Of course now you can hear WTAK on 106.1.
If you love classic rock, you'll love WTAK! Check out the The Big Show with John Boy and Billy in the mornings, Deano on your midday, Johnny Maze while you're rocking through an afternoon or Big Rig during you night!
100.3 The River (WQRV-FM)
There's a reason "We Play Anything"! WQRV actually started out as WVNA-FM back in 1962. Just like today, there was a wide variety in the genre's being played ranging from easy listening tunes, rock music, variety and even country music when the call letters changed to WLAY-FM in 2000.
In 2006 the callsign was changed to WQRV and became the station you know and love today! Along with playing all your favorite tunes; we also have Rick&Bubba during your mornings, John Malone on your middays, and Erich West keeping you company in the afternoons! When football rolls around, be sure and listen in to the Auburn football games every Saturday which this year will also be streaming on 1003theriver.com and the iHeartRadio app!
106.5 KissFM (WQRV-HD)
KissFM plays all the newest and biggest hits! Whether you listen at 100.3 HD-2 or you've got it tuned to 106.5 FM, get ready to sing along. Catch The Elvis Duran Morning Show on your drive in, Josie Lane while you're working through your midday, Ryan Seacrest on the ride home in the afternoons, or Billy the Kidd on your nights! Don't forget about DJ Ozone's 'Rocket City Remix' everyday at 5pm!
As always, thanks for listening!


So #SMWMusicAfrica day happened on Wednesday and I thought I'd let you know that if you're all about music, you missed!
We had a panel discuss the Future of Live Music; it was as funny and real as it gets.
Frankly, I'm super excited about where African music is headed. The future is gonna be lit!


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The Mule ist ein Krimi-Drama aus dem Jahr 2018. Regie führte Clint Eastwood, der auch die Hauptrolle spielt. Der Film kam am 14. Dezember 2018 in die US-amerikanischen und am 31. Januar 2019 in die deutschen Kinos.

Handlung
Der fast neunzigjährige Earl Stone muss Insolvenz anmelden, sein Haus soll zwangsversteigert werden. Sein ganzes Leben lang hat er Taglilien gezüchtet und verkauft, dabei aber seine Familie vernachlässigt. Seine Frau Mary hat sich von ihm getrennt, und seit er zwölf Jahre zuvor die Hochzeit seiner Tochter verpasst hat, redet diese nicht mehr mit ihm.

Auf der Verlobungsfeier seiner Enkeltochter erhält er ein Jobangebot eines ihm unbekannten Gastes: Er soll mit seinem angejahrten Pick-up in die Montagehalle eines Reifenhandels fahren. Dort warten einige bewaffnete Mexikaner auf ihn, legen ihm eine Sporttasche auf die Ladefläche und nennen ihm ein Hotel als Zieladresse. Er führt den Auftrag reibungslos aus und findet als Bezahlung ein ansehnliches Bündel Dollarnoten im Handschuhfach vor. Was er transportiert hat, weiß er nicht, es war für ihn eine einmalige Sache. Doch um den Erhalt seines Grundstücks, die Renovierung seines halb abgebrannten Lieblingslokals und einen neuen, schwarzen Pick-up Lincoln Mark LT finanzieren zu können, unternimmt er weitere Fahrten.

Derweil hat Colin Bates von der DEA Ermittlungen aufgenommen und Luis Rocha als Spitzel beim Drogenkartell angeworben. Dieser versorgt Bates und seinen Partner mit Informationen über Drogenumschlagplätze, Routen und Fahrer. Earl hat mittlerweile herausgefunden, dass er Kokain transportiert, und sich zu einem der zuverlässigsten Drogenkuriere des Kartells entwickelt. Als hochbetagter und bislang polizeilich vollkommen unauffälliger Weißer fällt er aus Ermittlersicht durch alle Raster. Da er allerdings entgegen seiner Vorgaben unterwegs Pausen einlegt, Umwege fährt oder Freunde besucht, setzt Kartell-Boss Laton den Spitzel Julio auf ihn an, der ihn überwachen soll und zunächst Härte zeigt, aber schon bald von Earls gutmütigem Wesen eingenommen ist. Schließlich ist es Earls sorgloses Verhalten, das ihn so erfolgreich macht. Nach einer besonders einträglichen Fahrt wird Earl auf Latons Hacienda eingeladen und dort verwöhnt.

Wenig später wird Laton auf Initiative seiner "rechten Hand" Gustavo erschossen, der seine Stelle einnimmt. Gustavo zieht die Zügel im Kartell schärfer an und duldet insbesondere Earls Extratouren nicht mehr. Zwei Schläger Gustavos fahren mit Earl in einen abgelegenen Wald und schüchtern ihn ein. Sie zeigen ihm einen Toten im Kofferraum: Das geschehe mit Leuten, die sich nicht an die Anweisungen hielten.

Die DEA fahndet mit Hochdruck nach dem mysteriösen Kurier, der regelmäßig große Drogenmengen transportiert, dessen Identität sie aber nicht kennen. Sie können nur nach einem schwarzen Pickup suchen und verdächtigen daher oftmals unbeteiligte Leute. Am Morgen nach einer dieser Aktionen treffen Bates und Earl sich unbekannterweise beim Frühstück in einem Diner. Bates hat seinen Hochzeitstag vergessen. Earl erzählt ihm, dass er selbst Meister im Vergessen von Familienterminen sei und schärft ihm ein, die Familie wichtiger zu nehmen.

Kurz darauf erfährt Earl von seiner Enkelin, dass seine Exfrau im Sterben liegt. Trotz der Warnung besucht er sie und verbringt eine Woche dort, ohne vom Kartell gefunden zu werden. Dabei söhnt er sich nicht nur mit ihr aus, sondern auch mit seiner Tochter. Auf Marys Frage, woher er in letzter Zeit so viel Geld habe, erzählt er ihr schließlich die Wahrheit, die sie jedoch nicht glaubt.

Als er nach Marys Beerdigung weiterfährt, wird er von den Leuten des Kartells aufgespürt und verprügelt. Nur weil er zusagt, die Tour noch zu Ende zu bringen, und weil Julio mittlerweile eine so hohe Meinung von ihm hat, bleibt er am Leben. Die DEA hört die Telefonate mit und fängt Earl mit einer Straßensperre auf dem Highway ab.

Während der Gerichtsverhandlung schneidet Earl seiner Verteidigerin das Wort ab und plädiert zum Erstaunen der Richterin selbst auf "schuldig". Zum Schluss sieht man ihn im Gefängnis bei der Pflege von Taglilien.

Biografisches
Der Film wurde von einer wahren Geschichte inspiriert. Leonard Sharp, auch bekannt unter den Namen Leo Sharp und El Tata, war ein US-amerikanischer Weltkriegsveteran und Drogenhändler für einen Arm des mexikanischen Sinaloa-Kartells, für das er Drogen über die Grenze schmuggelte, bis er 2011 von den Fahndern der DEA mit einer Ladung Kokain im Wert von drei Millionen Dollar erwischt wurde. Vor Gericht erreichte Sharps Anwalt ein recht mildes Urteil von drei Jahren Haft, indem er die Demenz seines Mandanten als mildernden Umstand anführte. Der Fall Sharp geriet 2014 durch einen Artikel der New York Times in den Fokus der Öffentlichkeit.

Produktion
Nachdem ursprünglich Ruben Fleischer dafür vorgesehen war, führte Clint Eastwood bei dem Film nicht nur Regie, sondern produzierte diesen gemeinsam mit Dan Friedkin, Jessica Meier, Tim Moore, Kristina Rivera und Bradley Thomas auch. Zudem übernahm Eastwood die Hauptrolle von Earl Stone, einem 90-jährigen Drogenkurier, dessen Figur auf der Lebensgeschichte von Leo Sharp basiert. Ein erster Drehbuchentwurf stammte von Nick Schenk, der von Dave Holstein überarbeitet wurde.

Bradley Cooper übernahm die Rolle des Ermittlers Colin Bates. Laurence Fishburne spielt seinen Vorgesetzten bei der DEA, Alison Eastwood übernahm die Rolle von Stones Tochter Iris, Taissa Farmiga die seiner Enkelin Ginny und Ignacio Serricchio die eines Mitglieds des Sinaloa-Kartells. In weiteren Rollen sind Dianne Wiest und Michael Peña zu sehen.

Die deutsche Synchronisation entstand nach der Dialogregie von Marianne Groß im Auftrag der FFS Film- & Fernseh-Synchron GmbH, Berlin. Jochen Striebeck spricht in der deutschen Fassung Earl Stone, Tobias Kluckert den Ermittler Colin Bates.

Die Produktion wurde im Juni 2018 begonnen. In Augusta wurde Anfang Juni 2018 vor der First Community Bank gedreht. In Augusta drehte man auch in den Shaw's Sunshine Gardens, der Saint Paul's Church und der Bethlehem Advent Christian Church, im Augusta Museum of History, in der Gegend um die Flatiron Bar, Clarke Pizza und Bambinelli's Italian Restaurant. Weitere Dreharbeiten erfolgten in der North Dekalb Mall in Decatur und in Las Cruces in New Mexico im Juli 2018. Ende Juli 2018 wurden die Dreharbeiten in Augusta beendet. Als Kameramann fungierte Yves Bélanger.

Die Filmmusik komponierte der aus Kuba ausgewanderte Jazz-Trompeter Arturo Sandoval.

Seine Weltpremiere feierte der Film am 10. Dezember 2018 im Regency Village Theatre in Los Angeles. Der Film kam am 14. Dezember 2018 in die US-amerikanischen Kinos und am 31. Januar 2019 in die deutschen Kinos. Am 6. März 2022 wurde The Mule in das Programm von Amazon Prime Video aufgenommen.

Rezeption

Altersfreigabe
In den USA erhielt der Film von der MPAA ein R-Rating, was einer Freigabe ab 17 Jahren entspricht. In Deutschland wurde er von der FSK ab 12 Jahren freigegeben. In der Freigabebegründung heißt es: "Drogenhandel oder Drogenkonsum werden nicht verherrlicht. Am Ende zeigt sich die Hauptfigur schuldbewusst und geht ins Gefängnis. Vereinzelt gibt es Gewaltszenen (z. B.: wenn ein Drogenboss erschossen wird), aber diese sind kurz gehalten und zurückhaltend inszeniert. Im Vordergrund steht das Charakterporträt der Hauptfigur, die Spannungen zwischen der alten und neuen Generation und eine positive Botschaft über den Wert von Familie."

Kritiken und Einspielergebnis
Der Film wurde von Kritikern bislang recht positiv aufgenommen und konnte bislang 70 Prozent der 193 Kritiker bei Rotten Tomatoes überzeugen.

Das Lexikon des Internationalen Films bewertete den Film mit vier von fünf möglichen Sternen und beurteilte ihn als Sehenswert. Der Film erzähle "schnörkellos und durchweg erheiternd die Geschichte eines Außenseiters, der im hohen Alter mit anderen Augen auf die verpassten Gelegenheiten seines Lebens zurückblickt."

Die weltweiten Einnahmen aus Kinovorführungen belaufen sich bislang auf knapp 175 Millionen US-Dollar.

Weblinks

Einzelnachweise

Filmtitel 2018
US-amerikanischer Film
Filmdrama
Gangsterfilm
Filmbiografie
Alter im Film
Historienfilm
Clint Eastwood

redpajama_set_name: RedPajamaWikipedia


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Q: Make Default Buttons Look Like Normal Buttons I have a JavaFX button that has been set as Default Button so the user can select it with the Enter key. Currently, it has a blue background:

But I'd like to make it look like a normal button:

I took a look at the JavaFX CSS Guide and it looks like there's only one feature to override (-fx-base).

But changing this feature has unpredictable effects—sometimes it eliminates the button's gradient; sometimes it makes the button transparent.
Is there a simple way to just get rid of the Default Button styling?

A: My guess is that you are looking in the wrong style sheet. The old default style sheet caspian.css was replaced with modena.css. So setting default value for -fx-base from modena.css should fix the issue:
.button:default {
    -fx-base: #ececec;
}

redpajama_set_name: RedPajamaStackExchange


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(English) Perform Work in Confined Space Operation is a Program
(English) Perform Work in Confined Space Operation
To identify the duties and responsibilities of all personnel involved in confined space work under the WSH Legislations and Code of Practice.
To identify confined space hazards.
Perform Work in Confined Space Operation is one of the core units in all process sectors of the Process Industry.
Learners who are:
Confined Space Entrant
Confined Space Attendant
Identify the duties and responsibilities of all personnel involved in confined space work under the WSH Legislations and Code of Practice.
Identify confined space hazards.
Use Gas Detection Instruments for atmospheric monitoring.
Comply with the Permit-to-Work system and safe work procedures when working in confined space.
Participate in an Emergency for confined space.
Practical Performance/ Case study
Upon completion of the course and passing the examination, a Statement of Attainment (SOA) from SkillsFuture Singapore (SSG) and a Safety Pass with 3 years validity from NTUC LearningHub will be awarded to the trainee.
Skills Development Fund (SDF) and SkillsFuture Funding:
Participants must attend at least 75% of the course, complete the exam with a pass or competent result.
Online applications are not applicable for companies applying for funding with Absentee Payroll.
Workforce Training Support (WTS) funding only applies to trainee who is 35 years old and above with a monthly income of $2,000 and below.
For Company Registration:
Customers who are applying funding for trainee(s), please submit Training Grant applications in SkillsConnect website before registration.
Training Grant number is to be submitted together with the registrations.
Payment for the course must be using company cheque or via GIRO.
For more information on SDF Training Grant application, please click here
Course reference code in SkillsConnect:
English: CRS-Q-0024214-PI
* UTAP supports 50% of the course fees paid cap at $250 per year. You must be a union member throughout the course duration and at the time of claim. You must achieve a minimum of 75% attendance for each application and have sat for all prescribed examinations. Other terms and conditions apply.
Assumed Skills and Knowledge
Learners will be able to listen, read, speak and write English at a proficiency level equivalent to the Employability Skills System (ESS) Level 2.
They will be able to manipulate numbers at a proficiency level equivalent to ESS Level 2.
Original Course Fee S$163.55 S$175.00
SkillsFuture Funding, >=21 yrs old S$32.71 S$44.16
WTS Funding (95%) S$8.18 S$19.63
After SDF Funding for non-SMEs Companies (80%)* S$32.71 S$44.16
After Enhanced Training Support for SMEs Companies (90%)** S$16.36 S$27.80
*Absentee Payroll of 80% of basic hourly salary, capped at $4.50 per hour.
** Absentee Payroll of 80% of basic hourly salary, capped at $7.50 per hour.
Please note that prices are subject to changes

redpajama_set_name: RedPajamaCommonCrawl


Following the official visit of HSH Prince Albert II to Russia in October 2013 it was decided that Monaco would host a year of Russia in Monaco to celebrate the links between the two nations.
The countries have enjoyed strong relations stretching back over 150 years and the planned events will reflect the close ties. There will be a focus on the cultural connections in education, science, and sport, including chess, food and fashion. The events have been brought to fruition through the close cooperation and enthusiasm of many Russian and Monaco individuals, associations and companies, as well as the authorities.
In a recent presentation by Mr Michel Roger, the head of the Principality's government highlighted that there is more to Monaco than the common perception of Monaco being the Royal family, the casino and the Grand Prix. While it is the smallest member of the UN it is home to 129 nationalities, 37,000 residents including 8,600 Monegasque nationals, and 450 Russians. Monaco is a real state with a diverse economy of 5,000 companies, an annual GDP of almost €5 billion and growth of 9.3% in 2013. Every day 38,000 individuals commuted to Monaco for their employment.
Mr Roger's emphasised the prudent financial policies followed by the government, which has resulted in a balanced budget and a public finances without debt. The country levies no income tax on residents, but is not tax free with 75% of state revenue generated from taxation and in recent years has signed 30 bilateral agreements on the exchange of tax information.
The speech concluded with Mr Roger illustrating the political ties between Monaco and Russia and the occasions in the Council of Europe when their respective positions coincide in the international arena.
At Rosemont we all look forward to this Year of Russia in Monaco, the closer links that will be fostered between the two countries now and for the future.


You can get to Comox in a number of ways … but we can assure you that once you have arrived … you are going to want to stay!
Our charter base is located in Comox, BC on the east coast of Vancouver Island. The Comox Valley Airport (YQQ) is centrally located, providing easy access to all points on central and northern Vancouver Island with daily flights from major cities including Vancouver (YVR), Calgary (YYC) and Edmonton (YEG) with connections beyond.
Pacific Coastal Airlines and Central Mountain Air offer convenient service to and from Vancouver, BC. Contact Pacific Coastal www.pacific-coastal.com (1-800-663-2872 or (604) 273-8666) and Central Mountain Air www.flycma.com (1-888-865-8585) for details on schedules, prices and reservations. The flight time from Vancouver to Comox is approximately 25 minutes.
WestJet operates direct flights daily between Calgary and Edmonton and Comox, with connections to many points east. For details on schedules, prices and reservations contact WestJet www.westjet.com (1-800-538-5696).
West Coast Air / Harbour Air offers daily harbour to harbour flights (weather permitting) between the downtown Vancouver terminal and the Comox Bay Marina. For details on pricing, schedules and reservations, contact them at www.westcoastair.com, www.harbourair.com or call 1-800-665-0212.
Kenmore Air Express offers daily non-stop flights to and from Seattle Boeing Field (BFI) to the Campbell River Airport (YBL), which is 45 minutes north of the Comox Valley. These flights are scheduled to run between June and September. For details on pricing, schedules and reservations, contact Kenmore Air www.kenmoreair.com (1-866-435-9524).
Private planes can fly into Courtenay Airpark (250) 334-8545, only minutes away from Comox.
There is convenient and frequent service between the Vancouver International Airport and Downtown Vancouver. For details check out the website www.translink.ca.
In Washington, the Quick Shuttle Service runs from the SeaTac Aiport, Downtown Seattle and Bellingham Airport to Vancouver, BC. In Vancouver, the service runs from Downtown Vancouver, the Vancouver International Airport and South Surrey to Washington. Check out their website at www.quickcoach.com or call 1-800-665-2122 for details.
Comox Taxi operates regular cars and larger vans so can accommodate small or larger groups, plus luggage. They have also added an 'Airport Shuttle Bus' to their list of services. You can book your taxi in advance of your arrival with their online service.
An alternative transportation to / from the Comox Airport is the Ambassador Shuttle. They can handle up to 7 people with luggage.
Another alternative transportation to / from the Comox Airport, as well as the Campbell River Airport and the Comox Valley, is the Sky High Shuttle Service. They can handle up to 7 people with luggage.
Corilair offers regularly scheduled floatplane service to and from Vancouver, BC and Campbell River from June through September ~ daily from June 15th to just after Labour Day. This includes drop off and pick up locations at Cortes Island, Refuge Cove, Prideau Haven and Desolation Sound, as required. They also offer charter services. For details check out the website or call.
You can fly via floatplane from Lake Union in Seattle to Comox, or directly into Desolation Sound, with Kenmore Air , if you have a minimum of 2 passengers. Call Kenmore Air for rates and to arrange these flights.
There are several ferry services available to Vancouver Island. The Tsawwassen to Duke Point (Nanaimo) ferry leaves south of Vancouver every 2.5 hours starting at 5:15 am until 10:45 pm. The crossing takes two hours and it is a 1 1/2 hour drive from Nanaimo to Comox. The Horseshoe Bay (West Vancouver) to Departure Bay (Nanaimo) ferry leaves every 2 hours starting at 6:30am to 12:30pm and 3pm to 9:00 pm. Crossing time is 1 hour 35 minutes and upon arrival at Departure Bay it is a 1 1/4 hour drive north up to Comox. For more information on ferry crossings and reservations please check out the BC Ferries website at www.bcferries.com or call 1-888-223-3779 (Canada & US). The August and September long weekends (typically the first Monday in the month) are the busiest weekends on the BC Ferries and we strongly recommend that you make a reservation if travelling around this time.
The Port Angeles to downtown Victoria ferry, MV Coho, is available on a daily basis offering car and walk-on passenger service. The crossing is approximately 90 minutes. Upon arrival in Victoria, it is a 3 1/2 hour drive north to Comox on Highway 19. For more up to date schedule and reservation information, call Black Ball Transport; in Port Angeles, WA at (360) 457-4491; in Seattle, WA at (206) 283-4400; in Victoria, BC at (250) 386-2202 or check their website at www.ferrytovictoria.com. Vehicle reservations are recommended.
The Anacortes to Sidney (Victoria) ferry sails once a day in the spring and fall and twice daily in the summer months. Then there is a 4 hour drive north up to Comox. For reservations and further schedule information please call Washington State Ferries at (206) 464-6400 in Seattle, or 1-888-808-7977 toll-free in State.
There is no vehicle ferry service directly between Seattle and Victoria. However, it is a 2.5 hour drive from Seattle to the ferry in Port Angeles. Discover more about the beautiful City of Victoria.
This might be an option for those flying into Seattle, WA. It is a bit of a trek but can work for some. There is a passenger only ferry from Seattle to/from Victoria called the Victoria Clipper. Check their website at www.victoriaclipper.com or call: toll-free 1-800-888-2535; Seattle (206) 448-5000; Victoria (250) 382-8100 for more details. The crossing takes 4 1/2 hours. Plan to overnight in downtown Victoria. Then the next day rent a car from Budget Car & Truck Rental. The drive up Island to the Comox Valley takes approximately 3 1/2 hours without stops. On return to Victoria, plan to catch the Clipper on the 5pm sailing back to Seattle.
The bus depot in Vancouver is downtown. Take a bus to the Horseshoe Bay ferry. On the ferry you can arrange to take a bus to downtown Nanaimo then connect on another bus to Courtenay. Check with your local Bus Depot or call Greyhound Courier Express at (250) 334-2475. Comox Taxi (250) 339-7955 will pick you up at the Courtenay bus terminal for the 15-minute ride to Comox. The trip from Vancouver to Comox takes approximately 5 hours.
IslandLink operates an Express Bus service several times daily between the Departure Bay Ferry Terminal in Nanaimo and a couple of locations in Courtenay. For more information and schedule details, check out their web site at www.islandlinkbus.com or call them on their toll-free number 1-877-954-3556.
We are working on our railroad!
Sorry, rail service between Victoria and Courtenay (E&N Rail) is currently not available due to railroad maintenance and repairs. For updates and information, you can check the website www.viarail.ca.
Check in at our main office first. If travelling by car, please proceed first to our MAIN OFFICE at #101-1797 Comox Ave, where we will finalize your paperwork and give you a time for both your yacht orientation and chart briefing.
If you are travelling by plane or bus, call Comox Taxi or one of the other services and they will pick you up for the 15-20 minute ride to our MAIN OFFICE.
All chartering skippers are required to attend our one hour Chart Briefing. During the briefing we will give you a thorough orientation to acquaint you with cruising the area and the services available. You will be advised of the highlights, points of interest, and emergency information, as well as the dangers of the areas.
A briefing of your Boat Systems is usually arranged on your Early Boarding day. However, if you are a 'late arrival' or do not wish to take advantage of Early Boarding, these briefings will be scheduled for the morning of your first charter day.


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Researchers reveal how microbes cope in phosphorus-deficient tropical soil
An Oak Ridge National Laboratory-led research team found genes for production of phytase enzymes that would be released by tropical soil microbes. Phytase enzymes will attack phytate molecules, releasing much needed phosphate molecules for the microbes' survival. The soil samples were collected in phosphorus-rich and -poor experimental sites at the Smithsonian Tropical Research Institute in the Republic of Panama. Credit: Melanie Mayes and Andy Sproles/Oak Ridge National Laboratory, U.S. Dept. of Energy
Topics: Clean Energy Supercomputing
OAK RIDGE, Tenn., Jan. 22, 2018 – A team led by the Department of Energy's Oak Ridge National Laboratory has uncovered how certain soil microbes cope in a phosphorus-poor environment to survive in a tropical ecosystem. Their novel approach could be applied in other ecosystems to study various nutrient limitations and inform agriculture and terrestrial biosphere modeling.
Phosphorus is a critical nutrient for global biological processes, such as collecting the sun's energy during photosynthesis and degrading plant debris and soil organic matter. Most tropical ecosystems endure long-term weathering that leaches phosphorus from soil.
The ORNL-led team set out to discover how soil microbial communities respond to the lack of phosphorus and other nutrient deficiencies at the molecular level. They collected soil samples at the Smithsonian Tropical Research Institute in the Republic of Panama, an experimental field site with phosphorus-rich plots and unfertilized control plots.
"This was the perfect place to test the optimal foraging theory, which is a model that helps predict an organism's behavior when searching for resources," said Chongle Pan, ORNL senior staff scientist and joint associate professor at the University of Tennessee. "We learned how this theory plays out when applied to microbial communities as they compete for nutrients."
The team analyzed the behaviors of many genes and proteins, and in the phosphorus-deficient, untreated soil, they found an increased number of genes responsible for producing phosphorus-acquiring enzymes. They also discovered more than 100 genes that work to pull phosphorus from phytate, which is a complex organic compound found in plant tissue.
"Finding so many genes to break apart and transport such a complex molecule tells us that microbes are hungry for phosphorus in untreated soil," said Melanie Mayes, an ORNL senior staff scientist who studies multi-scale environmental processes.
Conversely, she noted that when phosphorus was plentiful, more genes needed to acquire complex carbon compounds were present. "The microbial community prioritizes the breakdown of the most needed nutrients, focusing efforts on the most limiting element to balance their overall nutritional needs," she said.
The team ran each soil sample through a series of rigorous and comprehensive analyses. The DOE Joint Genome Institute conducted deep sequencing of the soils' metagenomes, or genetic material recovered directly from the soil. ORNL then used mass spectrometry and metaproteomics to identify more than 7,000 proteins in each sample.
ORNL's Titan supercomputer quickly analyzed the large amounts of metagenomics and metaproteomics data, comparing microbial activities in phosphorus-rich and -poor soils. Environmental Molecular Sciences Laboratory scientists further characterized the soils' organic matter at Pacific Northwest National Laboratory.
These unique tools working together enabled one of the deepest proteogenomics studies done on soil microbial communities, according to Pan.
The ORNL-led team plans to continue their research to characterize the ecology and evolution of soil microbial communities in nutrient-poor environments, which has applications in agriculture and terrestrial biosphere modeling worldwide. Additionally, Mayes and her team are incorporating metagenomics information into nutrient cycling models under a DOE Early Career Research Program Award.
Results from their three-year study titled, "Community Proteogenomics Reveals the Systemic Impact of Phosphorus Availability on Microbial Functions in Tropical Soil," were published in Nature Ecology & Evolution.
The paper's coauthors included Qiuming Yao, Zhou Li, Yang Song, Melanie A. Mayes and Chongle Pan of ORNL; S. Joseph Wright and Benjamin L. Turner of the Smithsonian Tropical Research Institute; Terry C. Hazen, University of Tennessee-ORNL Governor's Chair for Environmental Biotechnology; Xuan Guo of UT; Susannah G. Tringe of the DOE Joint Genome Institute; and Malak M. Tfaily and Ljiljana Paša-Tolic of Pacific Northwest National Laboratory.
The research was supported by the Laboratory Directed Research and Development program at ORNL. Metagenomic sequencing was conducted by the DOE Joint Genome Institute and soil organic matter analyses were performed using Fourier-transform ion cyclotron resonance mass spectrometry by PNNL's Environmental Molecular Sciences Laboratory, both DOE Office of Science User Facilities. This work also leveraged the Oak Ridge Leadership Computing Facility, a DOE Office of Science User Facility.
ORNL is managed by UT-Battelle for DOE's Office of Science. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States, and is working to address some of the most pressing challenges of our time. For more information, please visit http://energy.gov/science/.
Sara Shoemaker shoemakerms@ornl.gov, 865.576.9219
Melanie A Mayes
Terry C Hazen
Community proteogenomics reveals the systemic impact of phosphorus availability on microbial functions in tropical soil
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This article was written for propsocial.my and was published 2 months ago. When is the best time to buy a property? I am sure everyone has his/her personal answers based on their experience. Look for Opportunities For people who have not bought a property, the best time may yet to come—hopefully, it will be one day soon. … Read moreBest Time, Worst Time and Some Time.


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Home»Cricket»CLOSE-IN: Women's Cricket – A Rose By Any Other Name Would Smell As Sweet (IANS Column) On Cricketnmore
CLOSE-IN: Women's Cricket – A Rose By Any Other Name Would Smell As Sweet (IANS Column) On Cricketnmore
Image Source: IANS
The recent success, as regards the selling of the Rights of Women's IPL cricket tournament, truly reflects the progress that has been made by both the BCCI and cricket as a sport, in India. The game of cricket is the true benefactor, as it smells as sweet when played by either men or women.
The reason why India's marketing gurus find the property enticing is that Indian Women's cricketers bring in a feel of amateurism in the way that they play the game. They instil a breath of fresh air, a different look to the sport. It enables one watching it to enjoy cricket at a pace that is easier to follow.
Men's cricket, on the other hand, has become a contest, wherein, it has become professional with a serious outlook. The game of cricket and cricketers are thoroughly scrutinized. Whereas, in women's cricket one accepts errors and blunders and enjoys the naivety that it brings about. There is joy in watching women play the game in the way one enjoyed men playing it many years ago.
Love for cricket was the only factor that kept men's cricketers engrossed in the sport in the past. Although the reason to play is no different now, the game has taken a turn into becoming a serious one to pursue. The fun element and laughter that once prevailed in playing the game of cricket by boys and men at all levels of the sport, seems to have lost its charm. Cricket now seems to be a business in which winning has become the most important factor.
Women's cricket, on the other hand, has still the aura of being in the embryo stage. Although it has gone through many years of difficulty and hardships in the past, the IPL in April this year should catapult it into a huge leap for the better in the future.
I can still recall my conversation a decade ago, when I met the present Indian captain, Harmanpreet Kaur, at the MCA indoor nets. She was a girl from Haryana who had left the comfort of her home. She was nestled into accommodation in Mumbai, struggling to make two ends meet. She desired to continue playing cricket for India and to bring laurels to the country. The lack of facilities is what brought her to Mumbai, the Mecca of Indian cricket, along with several others from around the country. Harmanpreet along with the likes of Mithali Raj, Jhulan Goswami and Smriti Mandhana are household names now. Their success should catapult women's cricket in India to another level.
The platform is set for women's cricket to flourish; however, the challenge would be for the BCCI to structure facilities for them to excel. Girls aspiring to play the sport should be taken care of in every manner possible by providing them with the security and needs that are necessary in all respects.
At the other end of the spectrum is India's domestic cricket. With the season in full flow, one is astounded by the runs scored by batters in the Ranji Trophy tournament. There have been one triple and 18 scores of double centuries, over 40 scores of 150 plus runs and close to a century of centuries. These are phenomenal numbers and truly reflect the focus, fitness and mindset of the new breed of Indian batters.
One name that shines out like the North star, having had 3 years full of buckets of runs, is Sarfaraz Khan from Mumbai. He unfortunately has had, as one lightly conjectures, a piece of bad luck. This has been the case for many consistent performers playing in the domestic circuit. Jaydev Unadkat, the fiery left-arm fast bowler from Saurashtra, was another case in time. Fortunately, after 10 years of being in oblivion, he managed to get selected and has performed well enough to retain his place in the immediate future.
The irony of the domestic Indian cricket circuit is that established and BCCI-contracted players rarely play in any of the tournaments. The annual Indian International cricket calendar makes it difficult for them to do so. This makes the contracted players exclusi've and comfortably secured. The problem that surfaces is that the domestic performers do not get a window in which to stake their claim for an India cap.
Furthermore, without the top 35 Indian cricketers in the fray, there always is an element of doubt about the quality of domestic performances. The Indian A team tour was a good initiative as an incentive for an aspiring player. However, most other countries do not have the quality or quantity of players in their fold. In India in the earlier times, the Duleep and Irani Trophy matches were the selection trials for an Indian side playing in India or touring abroad. Both these tournaments have lost their lustre and therefore the domestic performers are now hoping to get recognized via the IPL route.
Also Read: Cricket Tales
This story has not been edited by Cricketnmore staff and is auto-generated from a syndicated feed
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Мирко «Миклавж» Златнар (; 2 февраля 1920, Любляна — 27 марта 1991, Лесце) — югославский военный и политический деятель, участник Народно-освободительной войны Югославии.

Биография
Изучал строительство на техническом факультете Люблянского университета с 1939 года, был активным общественным деятелем, состоял в общественно-культурном движении «Взаимность» (), член Коммунистической партии Словении с 1939 года. До декабря 1942 года был организатором технического отдела при ЦК КПС, в 1943 году брошен итальянскими фашистами в концлагерь Гонарс, откуда бежал после капитуляции Италии. Был помощник политрука при батальоне Оперативного штаба Посушья, Базовицкой бригады, политруком 30-й словенской дивизии и командиром отдела внутренней безопасности при 9-м словенском армейском корпусе. До 1950 года служил в УДБА, получил звание полковника. За проявленные качества в войне награждён медалью Партизанской памяти.

После войны Златнар занимал ряд должностей в СР Словении, до 1961 года работал в местном отделении Социалистического союза трудового народа (организационный секретарь исполкома), с 1961 по 1962 годы директор авиакомпании Adria Aviopromet.

Литература
 Enciklopedija Slovenije. (2001). Knjiga 15. Ljubljana: Mladinska knjiga.
 Gombač Metka: Zlatnar Mirko. Slovenski biografski leksikon 1925–1991. Elektronska izdaja. Ljubljana: SAZU, 2009.

Югославские партизаны
Разведчики Югославии
Члены Союза коммунистов Югославии
Коммунисты Словении
Политики Югославии
Политики Словении


text:
\section*{Introduction}
\addcontentsline{toc}{section}{Introduction}

The idea of application of biological evolution \cite{Darwin1859} and genetic \cite{Mendel1866} principles to the optimization problems was first sketched by Alan Turing in his 1948 essay titled \emph{Intelligent Machinery} \cite{Turing1948} and later extended by himself \cite{Turing1950} to a technique which is now called \emph{genetic programming} \cite{Koza1990}. These works were the very beginning of the \emph{evolutionary computations} (EC)---field of computer science devoted to the population-based, trial-and-error methods of problem solving. One of the first EC performed on a computer were done by Nils A. Barricelli in 1953 at the Institute for Advanced Study at Princeton, NJ \cite{Barricelli1962} on a machine built by John von Neumann's group \cite{Galloway2011}. Nowadays, EC field consists of many subfields---one of them is \emph{genetic algorithm} (GA) approach \cite{Holland1975}, subject of this work.

\section{Genetic algorithm}

\subsection{Genotype and its representation}

\emph{Genotype} $g$ is a finite polymorphic list of Boolean, real or integer values called \emph{genes} \cite{Fraser1957}. More precisely, $g \in X_0 \times \dots \times X_{c-1} = \prod_{i=0}^{c-1} X_i$, where $X_i$ is equal to $\mathbb{B} = \{{\rm false}, {\rm true}\}$ or is bounded subset of set of real numbers $\mathbb{R}$ or integer numbers $\mathbb{Z}$. This work considers subsets of kind of intervals of type $[a, b]$ or $[a, b]_{\mathbb{Z}} \equiv \left\{k \in \mathbb{Z} \mid a \leq k \leq b \right\}$. Despite the fact that \emph{a priori} every gene in genotype can be of different type, it is common practice to employ genotypes with pure \emph{representation}: \emph{binary} ($g\in\mathbb{B}^c$), \emph{floating-point} ($g\in\mathbb{R}^c$) or \emph{integer} ($g\in\mathbb{Z}^c$) \cite{Zhang2017}. Otherwise, the representation is called \emph{mixed} and is out of scope of this work.

Proper genotype for given optimization problem can have some additional constraints, $g \in G \subseteq \prod_{i=0}^{c-1} X_i$. The $G$ set can be arbitrary subset of $\prod_{i=0}^{c-1} X_i$, i.e. constraints imposed on different genes can be different and constraints for given gene can depend on values of all other genes. However, if $G = X_0^c$, then genotype is called \emph{uniform}. Moreover, $G$ can be defined as an extension of predicate $Q\colon \prod_{i=0}^{c-1} X_i \rightarrow \mathbb{B}$, i.e. $G = \{(x_0, \dots , x_{c-1}) \in \prod_{i=0}^{c-1} X_i \mid Q(x_0, \dots , x_{c-1}) \}$. One can define \emph{permutation representation}, where $G = \{(x_0, \dots , x_{c-1}) \in \{ 0, \dots, c - 1\}^c \mid \forall i \neq j\colon x_i \neq x_j \}$, i.e. it is extension of permutation condition predicate.

Value $c$, i.e. domain dimension of $\prod_{i=0}^{c-1} X_i$, is called \emph{genotype length} (or \emph{size}), while position in genotype is called \emph{locus} (pl. \emph{loci}), so if genotype is of length $c$ then \emph{locus} belongs to the set $\{ 0, \dots , c - 1\} \equiv \iota_c$ (notation inspired by the APL language \cite{Iverson1962}).

\subsection{Population and sequence of populations}

Sequence of genotypes of length $\mu$:
\begin{eqnarray}
\left( g_i \right)_{i=0}^{\mu - 1} \in \left( \iota_\mu \rightarrow \prod_{i=0}^{c-1} X_i \right) \equiv P_{X_0 , \dots , X_{c-1}}^\mu \subset \bigcup_{\mu =0}^{+\infty} P_{X_0, \dots , X_{c-1}}^\mu \equiv P_{X_0 , \dots , X_{c-1}}^*
\end{eqnarray}
is called \emph{population} or, in context of evolutionary step, \emph{generation} while $P_{X_0 , \dots , X_{c-1}}^\mu$ and $P_{X_0 , \dots , X_{c-1}}^*$ are sets of all possible populations of genotypes formulated basing on domain $\prod_{i=0}^{c-1} X_i$ with length $\mu$ or arbitrary (including zero), respectively. Zero-length population is marked with the symbol $\epsilon$.

Notion of population is insufficient to describe the evolutionary process, though---it is necessary to make one step further and define \emph{sequence of populations}:
\begin{eqnarray}
\left(\left( g_{i, j} \right)_{i=0}^{\mu (j) - 1}\right)_{j=0}^{\nu - 1} \in \left( \iota_\nu \rightarrow P_{X_0, \dots , X_{c-1}}^* \right) \equiv P_{X_0, \dots , X_{c-1}}^{*\nu} \subset \bigcup_{\nu = 0}^\infty P_{X_0, \dots , X_{c-1}}^{*\nu} \equiv P_{X_0, \dots , X_{c-1}}^{**} \\
\left(\left( g_{i, j} \right)_{i=0}^{\mu - 1}\right)_{j=0}^{\nu - 1} \in \left( \iota_\nu \rightarrow P_{X_0, \dots , X_{c-1}}^\mu \right) \equiv P_{X_0, \dots , X_{c-1}}^{\mu\nu} \subset \bigcup_{\nu = 0}^\infty P_{X_0, \dots , X_{c-1}}^{\mu\nu} \equiv P_{X_0, \dots , X_{c-1}}^{\mu*} \\
P_{X_0, \dots , X_{c-1}}^{\mu\nu} \subset P_{X_0, \dots , X_{c-1}}^{*\nu} \\
P_{X_0, \dots , X_{c-1}}^{\mu*} \subset P_{X_0, \dots , X_{c-1}}^{**}
\end{eqnarray}
where $P_{X_0, \dots , X_{c-1}}^{\mu\nu}$ is set of all possible sequences of length $\nu$ of populations of length $\mu$. Replacement of $\mu$ or $\nu$ to the star symbol ($*$) means all possible values of given parameter, e.g. $P_{X_0, \dots , X_{c-1}}^{*\nu}$ is set of all sequences of length $\nu$ of populations of arbitrary length.

Notation $P_{X_0, \dots , X_{c-1}}^*$ and $P_{X_0, \dots , X_{c-1}}^{**}$ are inspired by Kleene closure, but it is not equivalent to it, because--- according to Kleene algebra \cite{Kleene1951}---double application of Kleene star is equivalent to single application and here $P_{X_0, \dots , X_{c-1}}^{*} \neq P_{X_0, \dots , X_{c-1}}^{**}$, i.e. population concatenation does not occur automatically. To concatenate populations one can use flatten (\emph{flat}, i.e. Italian \emph{bemolle}) $\flat \colon P_{X_0, \dots , X_{c-1}}^{**} \rightarrow P_{X_0, \dots , X_{c-1}}^*$ function:
\begin{equation}
\flat \left( \left( g_{i,j} \right)_{i=0}^{\mu (j) - 1} \right)_{j=0}^{\nu - 1}
=
\left(
g_{0, 0}, \dots , g_{\mu (0) - 1, 0}
, \dots , \dots , \dots ,
g_{0, \nu - 1}, \dots , g_{\mu (\nu - 1) - 1, \nu - 1}
\right)
\end{equation}

\subsection{Fitness function}

Set of genotypes is by itself not very useful if there is no objective function to optimize over it, or---to put it differently---if there is no optimization problem to solve. In GA field, the term \emph{fitness function} is used and common practice is to define the problem in such a way, that this function is maximized. Fitness function, that is $f\colon G \rightarrow \mathbb{R}$, represents given maximization problem, but it does not need necessarily be formulated explicitly and calculation of its values might be costly. Fitness function ensures gradual enhancement of population ``quality'' in evolutionary process. In \emph{multi-objective GA} the fitness function is extended to the so-called \emph{cost function} $G \rightarrow \mathbb{R}^d$, where $d \in \mathbb{N}_+$ and this function is able to maximize many, often competing, parameters simultaneously and solution of such problem has form of set called \emph{Pareto frontier} \cite{Fonseca1993}. This work, however, is devoted to $d = 1$ case.

\subsection{Variation operators}

The essence of metaheuristics is intelligent search of space of potential solutions with intention of finding the best one. In order to achieve that in GA approach the mechanism of exploitation of successful genotypes' genes is applied. This mechanism includes \emph{variation operator} dependent on representation, which is a function $v_{n,m}\colon V_{X_0, \dots , X_{c-1}}^{n, m}$, where $V_{X_0, \dots , X_{c-1}}^{n, m} \equiv P_{X_0, \dots , X_{c-1}}^n \rightarrow P_{X_0, \dots , X_{c-1}}^m$. Variation $v_{n,m}$ applied on \emph{parents} $\left( g_i \right)_{i=0}^{n-1}$ results in \emph{offspring} $\left( h_i \right)_{i=0}^{m-1}$, where every element is called \emph{child}. Application of variation on population will be denoted with $v_{n,m} \left( g_i \right)_{i=0}^{n-1}$ or similar.

There are three main cases of variation: \emph{mutation} (or \emph{unary variation}) $v_{1,1}$ and two \emph{recombinations} (or \emph{binary variations})---$v_{2,1}$ (one child) and $v_{2,2}$ (two children). Variations of other kinds are less often used and are out of the scope of this work. Variations can be composed and are often used that way. For case of recombination and mutation the canonical composition is to first apply recombination and then the mutation. Mutation is in that case, using term taken from functional programming,  \emph{mapped} on every child obtained from the recombination process, i.e. $\left( {\rm map}_n v_{1,1}\right) \circ v_{2,n}$, where in special case of operations on populations ${\rm map}_n \colon V_{X_0, \dots , X_{c-1}}^{1, 1} \rightarrow V_{X_0, \dots , X_{c-1}}^{n, n}$, i.e. ${\rm map}_\mu v_{1, 1} \left( g_i \right)_{i=0}^{\mu - 1} = \left( v_{1, 1} \left( g_i \right) \right)_{i=0}^{\mu - 1}$.

\subsection{Probability distributions}

Variations are often based on drawing procedure from some probability distribution. In this work normal $\mathcal{N}$, uniform $\mathcal{U}$ and special case of Bernoulli distributions ${\rm B}$ will be used---their definitions can be easily found in literature. Normal distribution with mean $\mu$ and standard deviation $\sigma$ is marked here $\mathcal{N}(\mu , \sigma )$ (contrary to conventional form $\mathcal{N}(\mu , \sigma^2 )$). Uniform distribution has continuous form $\mathcal{U}(a, b)$ for $a, b \in \mathbb{R}$, where values are drawn from closed interval $[a, b]$, and discrete form  $\mathcal{U}\left\{ a, b \right\}$ for $a, b \in \mathbb{Z}$ or $a, b \in \mathbb{B}$, where values are drawn from set $[a, b]_{\mathbb{Z}}$ or $\left\{a, b\right\} \subset \mathbb{B}$, respectively. Furthermore, the following notation for drawing from set $X$ is also assumed:
\begin{equation}
\mathcal{U} (X) = \left\{
\begin{array}{lcl}
  \mathcal{U}(a, b) & \Leftrightarrow & X = [a, b] \\
  \mathcal{U}\{ a, b\} & \Leftrightarrow & X = [a, b]_{\mathbb{Z}} \vee X = \left\{ a, b \right\} \subset \mathbb{B} \\
\end{array} \right.
\end{equation}
For Bernoulli distribution ${\rm B}(1, p)$ the probability of drawing value $1$ (equivalent to ${\rm true} \in \mathbb{B}$) equals to $p$. Value $0$ (equivalent to ${\rm false} \in \mathbb{B}$) can be drawn with probability $1 - p$.

\subsection{Examples of mutation operators}

\begin{itemize}
\item \emph{Gaussian mutation} is a floating-point variation having two parameters: $\sigma \in \mathbb{R}_+$ and $p \in [0, 1]$. Variation of each gene in a given genotype occurs with probability $p$ and consists of addition of a value $\sigma \cdot \mathcal{N}(0, 1)$. In case where such mutation was to move \emph{locus} $i$ gene value out of constraints imposed by $X_i$ set, the $\inf X_i$ or $\sup X_i$ value is used instead.
\item \emph{Swap mutation} is an uniform genotype variation, where for genotype of size $c$ it consists of swapping values of two genes with \emph{loci} drawn from $\mathcal{U}(\iota_c)$.
\item \emph{Random-reset mutation} is a binary, floating-point and integer variation having one parameter $p \in [0, 1]$. Each gene of a given genotype is changed with probability $p \in [0, 1]$ and variation of gene \emph{locus} $i$ consists of assigning new value drawn from $\mathcal{U}(X_i)$.
\end{itemize}

\subsection{Examples of recombination operators}

\begin{itemize}
\item \emph{Arithmetic recombination} is a floating-point variation of type $V_{X_0, \dots , X_{c-1}}^{2,1}$ and when applied to $( x_i )_{i=0}^{c-1}$ and $( x_i' )_{i=0}^{c-1}$ then result consists of one child equal to $( (x_i + x_i') / 2 )_{i=0}^{c-1}$.
\item \emph{Single arithmetic recombination} is a floating-point variation of type $V_{X_0, \dots , X_{c-1}}^{2,2}$ and when applied to $( x_i )_{i=0}^{c-1}$ and $( x_i' )_{i=0}^{c-1}$ then result consists of two children equal to $( x_0 , \dots , ( x_k + x_k' ) / 2, \dots , x_{c-1} )$ and $( x_0' , \dots , \frac{1}{2} ( x_k + x_k' ) , \dots , x_{c-1}' )$, where \emph{locus} $k$ is drawn from $\mathcal{U}(\iota_c)$.
\item \emph{One-point crossover} is a binary, floating-point and integer variation of type $V_{X_0, \dots , X_{c-1}}^{2,2}$, where \emph{locus} $k$ is drawn from $\mathcal{U}(\iota_c)$ and genotypes $(x_0, \dots , x_{k-1} , x_k' , \dots , x_{c-1}' )$ and $(x_0', \dots , x_{k-1}' , x_k , \dots , x_{c-1} )$ are obtained, i.e. ``tails'' of parent genotypes $( x_i )_{i=0}^{c-1}$ and $( x_i' )_{i=0}^{c-1}$ are exchanged. This variation can be easily extended to $n$-point crossover.
\item \emph{Cut-and-crossfill recombination} is a permutation variation of type $V_{X_0, \dots , X_{c-1}}^{2,2}$, where \emph{locus} $k$ is drawn from $\mathcal{U}\left( \iota_c \setminus \left\{ 0 \right\}\right)$, first $k$ genes are copied from first parent to first child and, analogously, from second parent to second child, then genotype of first child is filled with not yet used genes of second parent in order of increasing \emph{loci} and, analogously, second child is filled with genes from first parent.
\end{itemize}

\subsection{Self-adaptive mutation}

Self-adaptive mutation \cite{Back2000} is an extension of Gaussian mutation, where standard deviation $\sigma$ also evolves and is \emph{de facto} part of the genotype. There are several types of self-adaptive mutation, but only the most popular version will be shown. It employs $c$ additional genes containing values of $\sigma_i$ on each direction of optimization problem, i.e. instead of $g = (x_0, \dots , x_{c-1}) \in \prod_{i=0}^{c-1} X_i$ and $G$, genotype $g_{\sigma} = (x_0, \dots , x_{c-1}, \sigma_0, \dots , \sigma_{c-1}) \in \prod_{i=0}^{c-1} X_i \times \prod_{i=0}^{c-1} \Sigma_i$ and $G_{\Sigma}$, where $\Sigma_i \subset \mathbb{R}_+$, are used. Genotype size is here equal to $c_{\sigma} = 2c$, domain $G_{\Sigma}$ can be defined as predicate extension as well, while the self-adaptive mutation is operator of class $V_{X_0, \dots , X_{c-1}, \Sigma_0 , \dots , \Sigma_{c-1}}^{1,1}$. Extension of the fitness function from $f\colon G \rightarrow \mathbb{R}$ to $f\colon G_{\Sigma} \rightarrow \mathbb{R}$ is trivial, because $\sigma_i$ does not influence $f$ values.

Contrary to Gaussian mutation each gene is mutated unconditionally (with probability equal to $1$) for self-adaptive mutation and the process itself has two stages. First, every $\sigma_i$ gene is mutated: $\sigma_i' = \sigma_i \cdot \exp \left( \tau_0 \cdot \mathcal{N}(0, 1) + \tau_1 \cdot \mathcal{N}_i (0, 1) \right)$, where $\mathcal{N}(0, 1)$ is drawn once while $\mathcal{N}_i (0, 1)$ is drawn for every gene $\sigma_i$. Next, every $x_i$ is mutated with use of new values of $\sigma_i'$ according to the formula $x_i' = x_i + \sigma_i' \cdot \mathcal{N}_i (0, 1)$. If mutation of gene $\sigma_i$ or $x_i$ was to move gene value out of constraints then, likewise in Gaussian mutation, infimum or supremum value is used instead. Self-adaptive mutation has two parameters, $\tau_0$ and $\tau_1$, which values depend on genotype length:
\begin{equation}
\tau_0 \propto 1 / \sqrt{2c}, \quad \tau_1 \propto 1 / \sqrt{2\sqrt{c}}
\end{equation}

\subsection{Predicate $Q$ violations}

Result of variation $v_{n,m} \left( g_i \right)_{i=0}^{n-1} = \left( h_i \right)_{i=0}^{m-1}$ for some combination of $v_{n,m}$, $\left( g_i \right)_{i=0}^{n-1}$ and $Q$ chosen by GA practitioner might violate predicate $Q$, i.e. $\exists i \in \iota_m \colon \neg Q h_i$, which is equivalent to $h_i \notin G$ for some $i$. From point of view of logic it might be considered as an imperfection of problem formulation. On the other hand, at some occasions, the cost of creation of new variation operator proper for the given predicate might outweigh time overhead resulting from slower algorithm. Proposed solution is to modify the fitness function so it would be able to treat problematic $h_i$. Previously defined fitness function $f\colon G \rightarrow \mathbb{R}$ can be extended to the whole domain, $f_Q \colon \prod_{i=0}^{c-1} X_i \rightarrow \mathbb{R}$:
\begin{equation}
  f_Q (g) = \left\{
  \begin{array}{ll}
    f(g) & g \in G \\
    -\Delta_f & g \in \prod_{i=0}^{c-1} X_i \setminus G
  \end{array}
  \right.
\end{equation}
where $-\Delta_f$ is chosen such, that $\forall g \in G \colon -\Delta_f \ll f(g)$, i.e. improper genotype has small chance of selection to the next generation and to the multiset of parents. This extension can be done provided that $\min_{g \in G} f(g) > -\infty$, which is reasonable assumption in numerical calculations. Unfortunately, $\min_{g \in G} f(g)$ might not be known \emph{a priori}, so for the sake of simplicity the fitness function can be modified even further taking $-\Delta_f = -\infty$, i.e. $f_Q \colon \prod_{i=0}^{c-1} X_i \rightarrow \mathbb{R} \cup \{ -\infty \}$.

\subsection{Stochastic variation operator}

Beside that variation operators are often stochastic \emph{per se}, for purpose of GA, \emph{stochastic variation operator} $S\colon V_{X_0, \dots , X_{c-1}}^{n, m} \times [0, 1] \rightarrow V_{X_0, \dots , X_{c-1}}^{n, m}$ is defined in such a way, that it randomly decides whether variation provided as its argument is applied or not:
\begin{equation}
S \left( v_{n,m}, p \right) \left( g_i \right)_{i=0}^{n-1}
=
\left\{
\begin{array}{ll}
  v_{n,m}\left( g_i \right)_{i=0}^{n-1} & {\rm if}\ s \\
  i_{n,m}\left( g_i \right)_{i=0}^{n-1} & {\rm if}\ \neg s \\
\end{array}
\right.
{\rm for}\ s = {\rm B}(1, p)
\end{equation}
where $i_{n,m}\colon V_{X_0, \dots , X_{c-1}}^{n, m}$ is defined for $n, m \geq 0$:
\begin{eqnarray}
  i_{n,n} \left( g_i \right)_{i=0}^{n-1} = \left( g_0, \dots , g_{n-1} \right) \phantom{,} & \\
  i_{n,n+1} \left( g_i \right)_{i=0}^{n-1} = \left( g_0, \dots , g_{k-1} , g_k , g_k, g_{k+1} , \dots , g_{n-1} \right) , &
  k = \mathcal{U}(\iota_n ) \\
  i_{n,n-1} \left( g_i \right)_{i=0}^{n-1} = \left( g_0, \dots , g_{k-1} , g_{k+1} , \dots , g_{n-1} \right) , &
  k = \mathcal{U}(\iota_n )
\end{eqnarray}
i.e. sequence is expanded (shortened) through copy (deletion) of randomly selected elements according to uniform probability distribution.

\subsection{Selection}

The second part of intelligent search of space of all possible solutions is genotype \emph{selection}. Selection is a function $p_{\mu\nu}^{\pi}\colon P_{X_0, \dots , X_{c-1}}^{*\nu} \rightarrow P_{X_0, \dots , X_{c-1}}^\mu$ and there are two important cases: \emph{parent selection} ($\nu = 1$) and \emph{survivor selection} ($\nu = 2$), which---for the purpose for this work---is called \emph{selection to the next generation}. Every algorithm of class $\nu = 1$ can be easily generalized into arbitrary $\nu > 0$ with composition $p_{\mu\nu}^{\pi} = p_{\mu 1}^{\pi} \circ \flat$. This composition will be useful, especially in case of stochastic universal sampling mechanism described further.

Selection algorithm $p_{\mu\nu}^{\pi}$ is parameterized with \emph{selection probability function} \cite{Holland1975} $\pi\colon P_{X_0, \dots , X_{c-1}}^{\mu '} \rightarrow [0, 1]^{\mu '}$, which determines selection probabilities of each genotype in a given population and which satisfies condition:
\begin{equation}
\sum_{i=0}^{\mu ' - 1} \left. \pi \left( g_0, \dots , g_{\mu ' - 1} \right) \right|_i = 1
\end{equation}

As an example of selection probability function \emph{fitness proportional selection} (a.k.a. fitness \emph{proportionate} selection) with \emph{windowing} procedure (FPS) was chosen:
\begin{equation}
  \left. \pi_{\rm FPS} \left( g_i \right)_{i=0}^{\mu ' - 1} \right|_{i_0} = \left\{
  \begin{array}{ll}
    \displaystyle \frac{f(g_{i_0}) - \min_{j \in \iota_{\mu '} \wedge g_j \in G} f(g_j) + 1 / \mu '}{1 - \mu ' \cdot \min_{j \in \iota_{\mu '} \wedge g_j \in G} f(g_j) + \sum_{j \in \iota_{\mu '} \wedge g_j \in G} f(g_j)} & g_{i_0} \in G \\
    0 & g_{i_0} \in \prod_{i=0}^{c-1} X_i \setminus G
  \end{array}
  \right.
\end{equation}
This function is well defined if $\exists i \in \iota_{\mu '} \colon g_i \in G$, otherwise optimization problem must be reformulated as there are too many violations of $Q$. In an extreme case of population size $\mu '$ of equally fit genotypes, e.g. $(g_0, \dots , g_0)$, this function returns $\left(1 / \mu ', \dots , 1 / \mu ' \right)$, which is the expected result.

The aforementioned FPS mechanism has insufficient selection pressure in some applications, though. If for two genotypes $g_0$, $g_1$ one of them is slightly more fit, $f(g_0) = f(g_1) + \varepsilon_f$, then also $\left. \pi_{\rm FPS} \left( g_i \right)_i \right|_0 \approx \left. \pi_{\rm FPS} \left( g_i \right)_i \right|_1$, i.e. there is practically no preference of $g_0$ over $g_1$ during selection. Therefore, \emph{ranking selection} \cite{Baker1987} will be introduced.

Let us, however, define several helper functions first. The $F_P\colon V_{X_0, \dots , X_{c-1}}^{*,*}$ function filters the population according to a given predicate $P\colon \prod_{i=0}^{c-1} X_i \rightarrow \mathbb{B}$:
\begin{equation}
F_P \left( g_i \right)_{i=0}^{\mu' - 1} = \left( g_{i_k} \right)_{i_k \in \left\{ j \in \iota_{\mu'} \mid P(g_j) \right\} },\quad i_0 < \dots < i_{\mu'' - 1},\quad \mu'' = \# \left\{ j \in \iota_{\mu'} \mid P(g_j) \right\}
\end{equation}
where $\#$ stands here for cardinality of set and will shortly be reused with new meaning. The $\#\colon P_{X_0, \dots , X_{c-1}}^* \rightarrow \mathbb{N}$ function returns size of the population, i.e. $\# \left( g_i \right)_{i=0}^{\mu' - 1} = \mu'$. Obviously, $\# \circ F_P \left( g_i \right)_{i=0}^{\mu' - 1} = \# \{ j \in \iota_{\mu'} \mid P(g_j) \}$. The last helper function, $\sigma_{f_Q}\colon V_{X_0, \dots , X_{c-1}}^{\mu' , \mu'}$, performs stable sort of the population according to the ascending fitness function values $f_Q$:
\begin{equation}
\sigma_{f_Q} \left( g_i \right)_{i=0}^{\mu' - 1} = \left( g_{i_k} \right)_{i_k \in \iota_{\mu'}},\quad f_Q (g_{i_0}) \leq \dots \leq f_Q (g_{i_{\mu' - 1}}),\quad f_Q (g_{i_j}) = f_Q (g_{i_{j+1}}) \Rightarrow i_j < i_{j+1}
\end{equation}

Finally, ranking selection (RS) can be defined as:
\begin{equation}
\pi_{\rm RS} \left( h_i \right)_{i=0}^{\mu ' - 1} = \flat \left( \left( 0 \right)_{j = 0}^{\mu_{\neg Q}' - 1} , \left( r_{\mu_Q' , j} \right)_{j = 0}^{\mu_Q' - 1} \right) , \quad \left( h_i \right)_{i=0}^{\mu ' - 1} = \sigma_{f_Q} \left( g_i \right)_{i=0}^{\mu ' - 1}
\end{equation}
where $\mu_{\neg Q}' = \# F_{\neg Q} \left( g_i \right)_{i=0}^{\mu' - 1}$, $\mu_Q' = \# F_{Q} \left( g_i \right)_{i=0}^{\mu' - 1}$ and $\mu' = \mu_{\neg Q}' + \mu_Q'$, while $r_{\mu_Q' , j}$ is selection probability with linear or exponential pressure:
\[
r_{\mu_Q' , j}^{\rm lin} = \left\{
\begin{array}{l}
  1 \\
  \frac{2 - s}{\mu_Q'} + \frac{2j (s - 1)}{\mu_Q' (\mu_Q' - 1)}, \, 1 < s \leq 2
\end{array}
\right.
, \quad
r_{\mu_Q' , j}^{\rm exp} = \left\{
\begin{array}{ll}
  1 & {\rm if}\ \mu_Q' = 1 \\
  \frac{1 - e}{\mu_Q' (1 - e) + e - e^{1 - \mu_Q'}} \cdot \left( 1 - e^{-j} \right) & {\rm if}\ \mu_Q' > 1
\end{array}
\right.
\]
Similarly to the FPS, ranking selection is well defined if at least one genotype in the population being its argument satisfies predicate $Q$. Contrary to the FPS, equally fit genotypes are given different selection probabilities with RS.

\subsection{Examples of selection $p_{\mu\nu}^{\pi}$}
\begin{itemize}
\item \emph{Roulette wheel algorithm} (RWA) is of class $p_{1, 1}^{\pi}$. This mechanism is traditionally explained with use of wheel with one arm and with fields of angular width proportional to selection probability function $\pi$ value for given genotype. Drawing genotype from this algorithm can be compared to spinning the wheel and drawn genotype is pointed out by the arm. In order to draw $\mu$ genotypes one has to perform $\mu$ algorithm runs.
\item \emph{Stochastic universal sampling} (SUS) \cite{Baker1987} is of class $p_{\mu 1}^{\pi}$ and is extension of RWA with $\mu$ equidistant arms where draw of $\mu$ genotypes occurs in one run.
\item \emph{Generational selection} (GS) is trivial algorithm of class $p_{\mu 2}$ where from two populations of equal sizes (current generation and offspring) returns second (offspring).
\end{itemize}

\subsection{Genetic algorithm}

GA starts with some initial population $\left( h_i \right)_{i=0}^{\mu - 1} \in P_{X_0, \dots , X_{c-1}}^\mu$. This population can be selected \emph{ad hoc} or randomly with some probability distribution---the only requirement is that the use of procedure $v_{0, \mu}\colon V_{X_0, \dots , X_{c-1}}^{0, \mu}$, which creates first generation $v_{0, \mu} \epsilon = \left( h_i \right)_{i = 0}^{\mu - 1}$, should guarantee that $\forall i\colon h_i \in G$. If random procedure was used, e.g. $h = \left( \mathcal{U}(X_i) \right)_{i=0}^{c-1}$, then afterwards $h$ should be rejected if $\neg Q(h)$ and procedure should be repeated. Selection of bounded sets in definition of gene stated previously is not accidental, because otherwise drawing from uniform distribution would violate Kolmogorov probability axioms \cite{Kolmogorov1950}.

After initial population selection, the algorithm performs loop, where next generation is created based on previous one. Next generation creation process starts with parent selection $p_{k \cdot n, 1}^{\pi}$. Parents population is divided into tuples of size $n$ and for every tuple variation $v_{n,m}$ is applied, resulting with offspring size $m$. Total offspring can be marked as $\left( h_i \right)_{i=0}^{\lambda - 1} \in P_{X_0, \dots , X_{c-1}}^\lambda$, where $\lambda = k \cdot m$. Then, selection to the next generation $p_{\mu 2}^{\pi}$ is applied, i.e. selection of $\mu$ genotypes from previous generation of size $\mu$ and offspring of size $\lambda$. Sequence of populations generated during evolutionary process consisting of initial population and populations generated through selection to the next generation is called \emph{evolution}. In GA it is common approach to use constant size of generation over whole evolutionary process, so if generation size equals to $\mu$ then evolution of size $\nu$ is an element of $P_{X_0, \dots , X_{c-1}}^{\mu\nu}$ while evolution of unknown size belongs to $P_{X_0, \dots , X_{c-1}}^{\mu *}$. It is easy to note, that evolution of type $P_{X_0, \dots , X_{c-1}}^{\mu *}$ is Markov chain with discrete time \cite{Aarts1989}.

Evolutionary loop stops when \emph{termination condition} in form of predicate $\mathbb{Z} \times P_{X_0, \dots , X_{c-1}}^{\mu *} \rightarrow \mathbb{B}$, taking loop counter and evolution produced so far, is fulfilled. Termination conditions can be joined with conjunction or disjunction.

\subsection{Examples of termination condition}

\begin{itemize}
\item Reaching of maximum number of permitted iterations.
\item Reaching of \emph{plateau} of fitness function.
\item Reaching previously specified value of fitness function by any genotype.
\end{itemize}

\subsection{GA extensions}

An \emph{abstract} GA was introduced here alongside with concrete example realizations of its constituents. However, there are some extensions to the basic algorithm, e.g. introducing spatial structure, i.e. \emph{cellular} GA \cite{Alba2008} (being special case of cellular automaton \cite{vonNeumann1966, Cerruti2020}), where genotypes are vertices of some connected graph and can recombine only with their neighbors. These extensions are out of scope of this work.

\subsection{GA implementation}

For the purpose of this work custom C++ implementation named Quilë available at \url{https://github.com/ttarkowski/quile/} was used.

\section{Optimization algorithm benchmark---test functions}

\subsection{Test functions. Algorithm tuning}

Optimization algorithms for problems of $\mathbb{R}^c \rightarrow \mathbb{R}^d$ type, including floating-point GA, can be benchmarked with use of so-called \emph{test functions} (TFs). The aim is to evaluate the performance of optimum finding capabilities of given algorithm or its parameterization---Pareto frontier in multi-objective optimization or point in $\mathbb{R}^c$ space in ordinary single-objective algorithm. Different parameterizations of one algorithm (e.g. genetic) can be compared with each other with use of TFs---this procedure can be used for algorithm \emph{tuning} in order to increase its performance. Here, floating-point single-objective GA effectivity and efficiency analysis with use of TFs will be presented.

It is common practice that TF $f^* \colon \prod_{i=0}^{c-1} X_i \rightarrow \mathbb{R}$ is minimized, i.e. one searches for point $\vec{x}_{\min} \in \prod_{i=0}^{c-1} X_i \subset \mathbb{R}^c$ such, that $\forall \vec{x}\in \prod_{i=0}^{c-1} X_i \colon f^* (\vec{x}_{\min}) \leq f^* (\vec{x})$. Point $\vec{x}_{\min}$ is also denoted as $\arg \min_{\vec{x}} f^* (\vec{x})$. From the numerical point of view function minimization relies on finding such approximation of minimum $\vec{x}_{{\rm approx} \min}$, which satisfies two conditions. Firstly, obviously, this approximation should be close to real minimum (``proximity in domain''), i.e. $| \vec{x}_{{\rm approx} \min} - \vec{x}_{\min} | \leq \varepsilon_{\vec{x}}$ for some small $\varepsilon_{\vec{x}}$. Secondly, function value at approximation point should approximate function value at real minimum (``proximity in codomain''), i.e. $| f^* ( \vec{x}_{{\rm approx} \min} ) - f^* ( \vec{x}_{\min} ) | \leq \varepsilon_{f^*}$ for some small $\varepsilon_{f^*}$. Both conditions are not equivalent---one can consider multimodal function with nearly deep minima to show that second condition does not imply the first one and unimodal function with discontinuity points around real minimum to show that first condition does not imply the second one.

History of research on optimization problems, not only floating-point, delivers substantial set of TFs (problems). These are scattered around different scientific reports and compiled into repositories and review articles of different size and quality (\emph{caveat emptor}). One of the positively standing out resource in regard to size, quality, documentation and ease of use is still developed MINLPLib repository (\url{http://www.minlplib.org/}), which contains problems of binary, integer, floating-point and mixed types with different complexity of objective function and predicate defining its domain formulated algebraically (complexity of type linear, quadratic, polynomial and signomial \cite{Peterson1966}).

For the purpose of this work 16 single-objective TFs were selected (Ackley, \emph{Alpine}, Aluffi-Pentini, Booth, Colville, Easom, \emph{exponential}, Goldstein-Price, Hosaki, Leon, Matyas, \emph{Mexican hat}, Miele-Cantrell, Rosenbrock, Schwefel, \emph{sphere}) from literature \cite{Ackley1987, AluffiPentini1985a, AluffiPentini1985b, Easom1990, Goldstein1971, Rosenbrock1960, Schwefel1981, Jamil2013, Jamil2013a}. These TFs are defined in Tab.~\ref{tab1}, visualized for selected cases in Fig.~\ref{fig1}, implemented in Quilë library and are not necessarily contained in aforementioned MINLPLib repository.

TFs can be classified with respect to continuity, convexity, codomain dimensionality (single- and multi-objective), domain dimensionality ($c$ value), number of local minima (uni- and multimodal), separability or using descriptive terms (e.g. ``valleys'', ``basins''). Separability occurs when:
\begin{equation}
\arg \min_{x_0, \dots , x_{c-1}} f^* (x_0, \dots , x_{c-1}) = \left( \arg \min_{x_0} f^* (x_0, \dots ) , \dots , \arg \min_{x_{c-1}} f^* (\dots , x_{c-1}) \right)
\end{equation}

Optimization algorithm tuning process is by itself optimization task. This raises natural question, whether GA parameterization can be found using some algorithm, even genetic. The answer is positive and such genetic mechanism is called \emph{metagenetic algorithm} \cite{Grefenstette1986} while from group of other procedures one can mention e.g. \emph{F-Race algorithm} \cite{Birattari2010}. Unfortunately, none of these techniques is commonly used by EC practitioners and it will not be employed here either. The tuning process will be performed using method of testing intuitively or conventionally chosen parameters. The key point of the whole process is statistical analysis.

\begin{table}[!hb]
    \caption{Test functions implemented in Quilë library: 1.~Ackley, 2.~\emph{Alpine}, 3.~Aluffi-Pentini, 4.~Booth, 5.~Colville, 6.~Easom, 7.~\emph{exponential}, 8.~Goldstein-Price, 9.~Hosaki, 10.~Leon, 11.~Matyas, 12.~\emph{Mexican hat}, 13.~Miele-Cantrell, 14.~Rosenbrock, 15.~Schwefel, 16.~\emph{sphere}. The $x_{0, {\rm AP}}$ value was calculated to 15 decimal places: $x_{0, {\rm AP}} = \left. \frac{2 \sqrt{3}}{3} \cos \left( \frac{1}{3} \arccos \left( -\frac{3 \sqrt{3}}{2} q \right) - \frac{2 \pi}{3} k \right) \right|_{q = \frac{1}{10},\, k = 2} \approx -1{.}046680531804602$.}
    \label{tab1}
    \centering
    \begin{tabular}{|r|l|l|l|l|}

    \hline
    \# &
    $c$ &
    $f^* \left( \vec{x} \right)$ &
    $\prod_{i=0}^{c-1} X_i$ &
    $\vec{x}_{\min}$ \\

    \hline\hline

    1. &
    $n$ &
    $\displaystyle -20 \exp\left( \frac{-0{.}02}{\sqrt{n}} \sqrt{\sum_{i = 0}^{n - 1} x_i^2} \right) - \exp\left( \frac{1}{n} \sum_{i = 0}^{n - 1} \cos \left( 2 \pi x_i \right) \right) + 20 + e$ &
    $[-35, 35]^n$ &
    $(0 , \dots , 0)$ \\

    2. &
    $n$ &
    $\displaystyle \sum_{i = 0}^{n - 1} \left| x_i \sin x_i  + 0{.}1 x_i \right|$ &
    $[-10, 10]^n$ &
    $(0 , \dots , 0)$ \\

    3. &
    $2$ &
    $\displaystyle \frac{1}{4} x_0^4 - \frac{1}{2} x_0^2 + \frac{1}{10} x_0 + \frac{1}{2} x_1^2$ &
    $[-10, 10]^2$ &
    $(x_{0, {\rm AP}}, 0)$ \\

    4. &
    $2$ &
    $\displaystyle (x_0 + 2x_1 - 7)^2 + (2x_0 + x_1 - 5)^2$ &
    $[-10, 10]^2$ &
    $(1, 3)$ \\

    5. &
    $4$ &
    $\displaystyle 100 \left( x_0 - x_1^2 \right)^2 + \left( 1 - x_0 \right)^2 + 90 \left( x_3 - x_2^2 \right)^2 + \left( 1 - x_2 \right)^2$ &
    $[-10, 10]^4$ &
    $(1, 1, 1, 1)$ \\
    %
    &
    &
    $\displaystyle +\ 10{.}1 \left( x_1 - 1 \right)^2 + \left( x_3 - 1 \right)^2 + 19{.}8 \left( x_1 - 1 \right) \left( x_3 - 1 \right)$ &
    &
    \\

    6. &
    $2$ &
    $\displaystyle -\cos x_0 \cdot \cos x_1 \cdot \exp \left( -(x_0 - \pi )^2 - (x_1 - \pi )^2 \right)$ &
    $[-100, 100]^2$ &
    $( \pi , \pi )$ \\

    7. &
    $n$ &
    $\displaystyle -\exp\left( -\frac{1}{2} \sum_{i = 0}^{n - 1} x_i^2 \right)$ &
    $[-1, 1]^n$ &
    $(0 , \dots , 0)$ \\

    8. &
    $2$ &
    $\displaystyle \left( 1 + \left( x_0 + x_1 + 1 \right)^2 \left( 19 - 14 x_0 + 3 x_0^2 - 14 x_1 + 6 x_0 x_1 + 3 x_1^2 \right) \right)$ &
    $[-2, 2]^2$ &
    $(0, -1)$ \\
    %
    &
    &
    $\displaystyle \cdot \left( 30 + \left( 2 x_0 - 3 x_1 \right)^2 \left( 18 - 32 x_0 + 12 x_0^2 + 48 x_1 - 36 x_0 x_1 + 27 x_1^2 \right) \right)$ &
    &
    \\

    9. &
    $2$ &
    $\displaystyle \left( 1 - 8 x_0 + 7 x_0^2 - \frac{7}{3} x_0^3 + \frac{1}{4} x_0^4 \right) x_1^2 \exp (-x_1)$ &
    $[-10, 10]^2$ &
    $(4, 2)$ \\

    10. &
    $2$ &
    $\displaystyle 100 \left( x_1 - x_0^2 \right)^2 + \left( 1 - x_0 \right)^2$ &
    $[-1{.}2, 1{.}2]^2$ &
    $(1, 1)$ \\

    11. &
    $2$ &
    $\displaystyle 0{.}26 \left( x_0^2 + x_1^2 \right) - 0{.}48 x_0 x_1$ &
    $[-10, 10]^2$ &
    $(0, 0)$ \\

    12. &
    $2$ &
    $\displaystyle -20 \frac{\sin g(x_0, x_1)}{g(x_0, x_1)}, \, g(x_0, x_1) = 0{.}1 + \sqrt{(x_0 - 4)^2 + (x_1 - 4)^2}$ &
    $[-10, 10]^2$ &
    $(4, 4)$ \\

    13. &
    $4$ &
    $\displaystyle \left( \exp (-x_0) - x_1 \right)^4 + 100 \left( x_1 - x_2 \right)^6 + \tan^4 (x_2 - x_3) + x_0^8$ &
    $[-1, 1]^4$ &
    $(0, 1, 1, 1)$ \\

    14. &
    $n$ &
    $\displaystyle \sum_{i = 0}^{n - 2} \left( 100 \left( x_{i + 1} - x_i^2 \right)^2 + \left( x_i - 1 \right)^2 \right)$ &
    $[-30, 30]^n$ &
    $(1, \dots , 1)$ \\

    15. &
    $n$ &
    $\displaystyle \sum_{i = 0}^{n - 1} \left( \sum_{j = 0}^i x_i \right)^2$ &
    $[-100, 100]^n$ &
    $(0, \dots , 0)$ \\

    16. &
    $n$ &
    $\displaystyle \sum_{i = 0}^{n - 1} x_i^2$ &
    $[0, 10]^n$ &
    $(0 , \dots , 0)$ \\

    \hline

    \end{tabular}
\end{table}

\begin{figure}
\centering
\includegraphics{figure1.pdf}
\caption{Selected test functions for 2-dimensional domain.}
\label{fig1}
\end{figure}

\subsection{Statistical parameters}

Statistical analysis of optimization algorithms performance is done for fixed parameterization---for each TF the series of minimization attempts is performed in order to obtain statistical sample. For purpose of performance description one can use several statistical parameters connected to the number of successfully finished optimization attempts, average number of fitness function or $Q$ predicate evaluations, average total number of generated unique genotypes or average ``best'' genotype's fitness function value at given moments of the algorithm \cite{Craenen}. The following parameters were here used:
\begin{itemize}
\item For description of algorithm's \emph{effectivity} standard SR (success rate) parameter was used. It is defined as fraction of successfully finished (i.e. optimum was found) search processes to the total number of processes.
\item \emph{Efficiency} is described by AUS and $\sigma_{\rm AUS}$ parameters equal to \underline{a}verage number of \underline{u}nique individuals to get a \underline{s}olution (i.e. in successfully finished search processes) and standard deviation (root of the unbiased estimator of variance) corresponding to the aforementioned average, respectively. The AUS parameter was designed specifically for purpose of this work.
\item Description of quality of minimum approximation found by the algorithm was done with average distance between function value at real minimum and its approximation $\overline{|\Delta f^*|}$ and with average distance between real minimum and its approximation $\overline{|\Delta \vec{x}|}$. Furthermore, corresponding standard deviations $\sigma_{\overline{|\Delta f^*|}}$ and $\sigma_{\overline{|\Delta \vec{x}|}}$ were also employed.
\end{itemize}

Given the fact, that Quilë library uses database of calculated fitness function values and that these values are computed once for each unique genotype, parameters AUS and $\sigma_{\rm AUS}$ should be good metric of stochastic algorithm complexity in case of objective function, which is costly to calculate, i.e. its computation time is of the order of magnitude of seconds or more.

\begin{table}
\caption{Maximum optimization effectivity (SR) realized by some GA parameterization ($2k$, $p_{\rm r}$, $p_{\rm m}$ and---in Gaussian mutation case---$r$) for $\varepsilon_{f^*} = 10^{-1}$, $\varepsilon_{\vec{x}} = 10^{-2}$ precision. Please see \emph{examples/benchmark/results\_detailed.txt} file in Quilë repository for more details.}
\label{tab2}
\centering
\medskip
\begin{tabular}{|c|c|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|}
\hline
 & $\pi$ & c & \rotatebox{90}{Ackley\phantom{o}} & \rotatebox{90}{\emph{Alpine}\phantom{o}} & \rotatebox{90}{Aluffi-Pentini\phantom{o}} & \rotatebox{90}{Booth\phantom{o}} & \rotatebox{90}{Colville\phantom{o}} & \rotatebox{90}{Easom\phantom{o}} & \rotatebox{90}{\emph{exponential}\phantom{o}} & \rotatebox{90}{Goldstein-Price\phantom{o}} & \rotatebox{90}{Hosaki\phantom{o}} & \rotatebox{90}{Leon\phantom{o}} & \rotatebox{90}{Matyas\phantom{o}} & \rotatebox{90}{\emph{Mexican hat}\phantom{o}} & \rotatebox{90}{Miele-Cantrell\phantom{o}} & \rotatebox{90}{Rosenbrock\phantom{o}} & \rotatebox{90}{Schwefel\phantom{o}} & \rotatebox{90}{\emph{sphere}\phantom{o}} \\ \hline
\hline
\multirow{9}{*}{\rotatebox{90}{Gaussian m., arithm. r.}} & \multirow{3}{*}{\rotatebox{90}{FPS}} & 2 & $100$ & $56$ & $99$ & $90$ & -- & $15$ & $100$ & $99$ & $0$ & $45$ & $100$ & $100$ & -- & $46$ & $100$ & $100$ \\
 & & 4 & $7$ & $4$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $27$ & $0$ & $72$ & $100$ \\
 & & 8 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & \multirow{3}{*}{\rotatebox{90}{lin-RS}} & 2 & $100$ & $56$ & $100$ & $100$ & -- & $100$ & $100$ & $100$ & $0$ & $100$ & $100$ & $100$ & -- & $82$ & $98$ & $100$ \\
 & & 4 & $0$ & $2$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $100$ & $0$ & $0$ & $100$ \\
 & & 8 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & \multirow{3}{*}{\rotatebox{90}{exp-RS}} & 2 & $100$ & $100$ & $99$ & $91$ & -- & $97$ & $100$ & $100$ & $0$ & $88$ & $100$ & $100$ & -- & $67$ & $100$ & $100$ \\
 & & 4 & $4$ & $5$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $35$ & $0$ & $10$ & $100$ \\
 & & 8 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 \hline
\hline
\multirow{12}{*}{\rotatebox{90}{Gaussian m., single arithm. r.}} & \multirow{4}{*}{\rotatebox{90}{FPS}} & 2 & $100$ & $52$ & $100$ & $91$ & -- & $32$ & $100$ & $100$ & $1$ & $31$ & $100$ & $100$ & -- & $26$ & $100$ & $100$ \\
 & & 4 & $22$ & $4$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $46$ & $0$ & $4$ & $100$ \\
 & & 8 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & & 16 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & \multirow{4}{*}{\rotatebox{90}{lin-RS}} & 2 & $100$ & $53$ & $100$ & $99$ & -- & $100$ & $100$ & $100$ & $0$ & $90$ & $99$ & $100$ & -- & $79$ & $99$ & $100$ \\
 & & 4 & $100$ & $14$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $100$ & $0$ & $1$ & $100$ \\
 & & 8 & $40$ & $0$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & & 16 & $0$ & $0$ & -- & -- & -- & -- & $98$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & \multirow{4}{*}{\rotatebox{90}{exp-RS}} & 2 & $100$ & $100$ & $100$ & $87$ & -- & $84$ & $100$ & $100$ & $1$ & $33$ & $100$ & $100$ & -- & $29$ & $100$ & $100$ \\
 & & 4 & $5$ & $3$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $29$ & $0$ & $3$ & $100$ \\
 & & 8 & $0$ & $0$ & -- & -- & -- & -- & $2$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & & 16 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 \hline
\hline
\multirow{15}{*}{\rotatebox{90}{random-reset m., single arithm. r.}} & \multirow{5}{*}{\rotatebox{90}{FPS}} & 2 & $100$ & $47$ & $100$ & $88$ & -- & $100$ & $100$ & $100$ & $0$ & $33$ & $78$ & $100$ & -- & $33$ & $87$ & $100$ \\
 & & 4 & $100$ & $13$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $1$ & $1$ & $0$ & $86$ \\
 & & 8 & $45$ & $2$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $4$ \\
 & & 16 & $0$ & $0$ & -- & -- & -- & -- & $57$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $0$ \\
 & & 32 & $0$ & $0$ & -- & -- & -- & -- & $0$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $0$ \\
 & \multirow{5}{*}{\rotatebox{90}{lin-RS}} & 2 & $100$ & $74$ & $100$ & $98$ & -- & $100$ & $100$ & $100$ & $0$ & $47$ & $54$ & $100$ & -- & $10$ & $87$ & $100$ \\
 & & 4 & $100$ & $33$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $0$ & $1$ & $1$ & $100$ \\
 & & 8 & $100$ & $6$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $1$ & $0$ & $100$ \\
 & & 16 & $100$ & $0$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & & 32 & $100$ & $0$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $100$ \\
 & \multirow{5}{*}{\rotatebox{90}{exp-RS}} & 2 & $100$ & $49$ & $100$ & $90$ & -- & $99$ & $100$ & $99$ & $0$ & $38$ & $83$ & $100$ & -- & $29$ & $78$ & $100$ \\
 & & 4 & $96$ & $13$ & -- & -- & $0$ & -- & $100$ & -- & -- & -- & -- & -- & $0$ & $0$ & $1$ & $100$ \\
 & & 8 & $17$ & $1$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $33$ \\
 & & 16 & $0$ & $0$ & -- & -- & -- & -- & $100$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $0$ \\
 & & 32 & $0$ & $0$ & -- & -- & -- & -- & $80$ & -- & -- & -- & -- & -- & -- & $0$ & $0$ & $0$ \\
 \hline
\end{tabular}
\end{table}

\subsection{Benchmark method. Results}

The Quilë library GA performance benchmark was done for TFs from Tab.~\ref{tab1} for $c \in \{2^{i} \mid i \in \iota_{\eta} \setminus \{ 0 \} \}$, where $\eta$ value was chosen individually for different variation operators. The recombination and mutation operators were applied stochastically with recombination probability $p_{\rm r}$ and mutation probability $p_{\rm m}$ equal to $1$ or $0{.}5$. Exploitation was done mostly through the recombination, while exploration---through mutation. Calculations were divided into three groups differentiated by variation operator:
\begin{itemize}
\item arithmetic recombination with Gaussian mutation with $p = 1 / c$, while $\sigma$ was adapted to each TF individually with formula $\sigma = r \cdot \min_{i \in \iota_c} ( b_i - a_i )$, where $[a_i, b_i] \equiv X_i$ and $r \in \{ 50\% , 5\% , 0{.}5\% \}$,
\item single arithmetic recombination with Gaussian mutation with parameters identical with the point above,
\item single arithmetic recombination with random-reset mutation with $p = 1 / c$.
\end{itemize}

Generation size $\mu$ was equal to $100$, which is relatively small number and implies low probing of space of possible solutions during creation of first random generation. Simulations were done for parent multiset of size $2k \in \{ 2, 4, 8, 16, 32, 64 \}$. Each genetic process used SUS mechanism in order to enhance quality of parent selection and selection to the next generation---FPS and RS with linear (lin-RS, $s = 2$) and exponential (exp-RS) pressure procedures were used. Absolute precision of minimum finding in codomain $\varepsilon_{f^*}$ was set to $10^{-1}$, while in domain $\varepsilon_{\vec{x}}$ to $10^{-2}$. GA was terminated when some genotype approached the real minimum to the distance of at most $\varepsilon_{f^*}$ in codomain and to the distance of at most $\varepsilon_{\vec{x}}$ in domain \emph{or} after reaching limit of $10^5$ iterations in order to stop ineffective processes. The numerical simulations were done for every possible parameter combination and for each parameterization they were performed $100$ times in order to collect appropriate statistics. The result for each parameterization and for each TF consists of SR, AUS, $\sigma_{\rm AUS}$, $\overline{|\Delta f^*|}$, $\sigma_{\overline{|\Delta f^*|}}$, $\overline{|\Delta \vec{x}|}$ and $\sigma_{\overline{|\Delta \vec{x}|}}$. The best SR values are shown in Tab.~\ref{tab2}. The detailed results can be assessed by analyzing the \emph{examples/benchmark/} directory of the Quilë library repository. For the sake of brevity only the most important conclusions will be shown further.

\subsection{Conclusions}

By analyzing the numerical simulations results one can observe several properties of described GA. Firstly, choosing each parameter value of GA process in isolation might lead to poor performance, even when every parameter might be individually proper. This parameterization applied to concrete TF might be unable to find function minimum, while other might have for this concrete TF the SR equal to $100$.

Secondly, optimization performance is obviously decreasing with problem dimensionality. It happens, because potential solution space volume grows exponentially with dimension. With the increase of $c$ value the AUS parameter increases and SR decreases. Fortunately, the AUS parameter grows slower than size of space of possible solutions, which can be assessed analyzing the best calculation series for Ackley, \emph{exponential} and \emph{sphere} TFs in case of random-reset mutation with single arithmetic recombination with lin-RS, where SR parameter was equal to $100$ for $c \in \{2, 4, 8, 16, 32\}$. Moreover, for Ackley function the best efficiency was achieved by the same parameterization ($p_{\rm m} = 0{.}5$, $p_{\rm r} = 1$, $2k = 64$) and relation ${\rm AUS} \sim c^{1{.}85 \pm 0{.}08}$ has occurred.

Thirdly, some TFs (Colville, Hosaki) were not optimized at all with chosen strategy and some were optimized with moderate efficiency. This observation is emanation of NFL theorem \cite{Wolpert1997}: GA is comparatively versatile tool, but, on the other hand, its efficiency is not high. This rule is confirmed even with apparent exception of \emph{sphere} TF for optimization with Gaussian mutation. This function has its minimum on the edge of domain, which causes that Gaussian mutation, being unable to cross the boundary, can very quickly select the point on edge, which drastically helps finding the minimum.

\section*{Summary}
\addcontentsline{toc}{section}{Summary}

Theory of genetic algorithm was discussed. Algorithm tuning with use of test functions was done and the best parameterization was found. Evolutionary computations has found wide applications in many disciplines which is proven by review literature \cite{Katoch2021, Ghaheri2015, Goudos2016, Kudjo2017, Lee2018, Drachal2021}. Genetic algorithm is the tool worth knowing.

\section*{Acknowledgments}
\addcontentsline{toc}{section}{Acknowledgments}

This work is a result of the projects funded by the National Science Centre of Poland (Twardowskiego 16, PL-30312 Kraków, Poland, \url{http://www.ncn.gov.pl/}) under the grant number \mbox{UMO-2016}\allowbreak{}\mbox{/23}\allowbreak{}\mbox{/B}\allowbreak{}\mbox{/ST3}\allowbreak{}\mbox{/03575}.

\begin{multicols}{2}

  \bibliographystyle{elsarticle-num}
  \addcontentsline{toc}{section}{References}

redpajama_set_name: RedPajamaArXiv


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