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About the Lansing Central AA Office
What is the Lansing Central AA Office?
I am responsible...
When anyone, anywhere, reaches out for help, I want the hand of AA always to be there. And for that I am responsible.
The Lansing Central AA Office is a service office established to aid AA meetings and other groups in their common purpose of carrying the Alcoholics Anonymous message to the alcoholic who still suffers.
Where do the contributions come from to operate?
The Central Office depends upon contributions from local members and meeting groups for the necessary support to carry out its responsibilities. This support comes in the form of volunteer help and financial contributions. Our efficiency and the continuation of services are related to the level of support we receive from the recovery community.
And what do we do with them?
Answer inquiries from those seeking help including suffering alcoholics, sober alcoholics, family members, professionals and the general public.
Carry AA's message into treatment facilities, hospitals and rehabilitation centers by arranging for volunteer groups to attend weekly meetings at these facilities.
Organize and host sober events in the community for members and their families. Our newsletter "Reaching Out" provides a forum for the local community to share their experience, strength and hope in print.
Work with the professional community to create an awareness of AA, especially those professionals that are likely to encounter active alcoholics. "The focus is on cooperation, not affiliation".
Inform the public about the AA program and present informational talks to universities, businesses, and civic groups.
Coordinate the work of those who carry the message to alcoholics 'behind the walls', working in contact with the Tri-County area correctional facilities.
Provide an information exchange for local groups and communities.
Publish tri-county meeting directory and monthly newsletter "Reaching Out".
Order, sell and distribute conference-approved literature.
Volunteer at the Central Office - Help by answering our hotline phones.
12 Step Volunteer - Sign-up to be available to meet with suffering alcoholics who wish to become sober.
Communicate with the Central Office to maintain current information about meetings, locations, times, and special events throughout the Lansing-area, Michigan, the US, and many international destinations.
Be a Group Representative - Represent your group at the monthly business meetings.
Participate on a Board Committee listed below:
Activities Committee
CPC (Cooperation with the Professional Community)
If you would like to help out then please contact us:
Email: aalansing@att.net
Location: 1915 E Michigan Ave. Lansing, MI 48912
Or get in touch with us directly by using the following form:
What are you intrested in *
We are here to help, reach out and get in touch with us
Reaching out for help can be scary - especially when you do not know where to start. The first thing to do is recognize that you are ready for a change. Are you tired of the grip alcohol has on your life? Have you tried to control your drinking and failed? Do you think your life is hopeless? Are you sick and tired of being sick and tired? If you answered yes to any of these questions or think you may have a problem with alcohol - you are ready to take the first step toward recovery to reclaim your life and learn a new way of living. Your first step could be to attend a meeting. You can also call the Lansing Central Office at: 517-377-1444. When you make that call you will talk to an AA member who understands precisely where you are and how you are feeling because they have been there too.
Call 517-377-1444 or Click here to contact us
Lansing Central AA - 2016 ©
Home - Meetings - Community Events - FAQ - Resources - New to AA - Contact


ANGELBLACKWOLF has no current links.
Merry Meet. May the Goddess bless us all.
Official Intro I honestly wanted to join this site because I do believe being different from the mainstream is extremely important.


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The Sunday Subject – December 26, 2021
Published on December 26, 2021 December 24, 2021 by subjectmedia
Welcome to Subject's weekly news roundup. We present you the essential headlines, local and beyond.
Last Sunday West Virginia Senator Joe Manchin reversed his stance on the Build Back Better Act, announcing that he will not vote for the legislation in its current state.
The Build Back Better Act, the centerpiece of the Biden administration's economic agenda, included an array of progressive initiatives, such as an expanded child tax credit, paid family leave, universal pre-K, affordable housing, and an expansion of Medicare, Medicaid, and the Affordable Care Act. After weeks of negotiations, Democrats will likely have to water down some of the bill's core policies. Jen Psaki, the press secretary, stated, "Just as Senator Manchin reversed his position on Build Back Better this morning, we will continue to press him to see if he will reverse his position yet again, to honor his prior commitments and be true to his word."
After the Starbucks on Elmwood Ave. became the first company-owned Starbucks store in the country to unionize, a Starbucks executive pledged the company will bargain in good faith during contract negotiations.
Rossann Williams, Starbucks' North American president, said the company respects the legal process and wants to "get to the table as soon as possible, sit across from management and bargain a fair contract that benefits customers and partners alike."
On Tuesday about 1,400 Kellogg workers on strike ratified a new contract, ending the strike that began in early October.
The strike affected four of Kellogg's US cereal plants. Anthony Shelton, the president of the workers' union, the Bakery, Confectionery, Tobacco Workers and Grain Millers International Union, said in a statement: "This agreement makes gains and does not include any concessions."
Mayor Byron Brown has announced plans for increasing development in Buffalo.
His intent is to focus on partnering with both the state and county, in addition to developers and other private companies, to drive further commercial and residential investment throughout the city. According to city statistics, Buffalo has received more than $8.3 billion in development activity since Brown took office in 2006, with most of that being since 2012. "Our goal is to continue that renaissance, as quickly as possible," Brown stated. "Things are being built in the City of Buffalo, and we are very proud of that."
Children aged five and older must now show proof of vaccination to enter KeyBank Center or Highmark Stadium.
Children must now be vaccinated to attend concerts and events at these arenas, including Bills and Sabres games. The new policy, announced Wednesday, is in accordance with the latest New York State mandate.
The United States has eased the pressure of sanctions on the Taliban in Afghanistan.
As the combination of the pandemic, a severe drought, the loss of foreign aid and frozen currency reserves have left the country's economy on the brink of collapse, the Biden administration issued new "general licenses" to help aid flow and mitigate the humanitarian crisis. The United States still does not recognize the Taliban as the legitimate government of Afghanistan.
Articles, FeaturedNews
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Brunson leaves a mark on Turkey-US history
Hakki Ocal
Hakki Ocal @hakkiocal
erhaps in 10 years' time people will say, "Once upon a time, strange things had come to pass between two good allies, Turkey and the U.S., because of a man." They will tell the story of Andrew Brunson, who had worked in İzmir, Turkey for almost 20 years as a pastor in a small Protestant church with 25 congregants and was arrested in October following the July 15, 2016 coup attempt. They will go on saying that two years after his arrest a U.S. vice president called on President Recep Tayyip Erdoğan to release him or face significant sanctions.
A month later, the U.S. Department of Treasury imposed sanctions on two Turkish government officials who were involved in the pastor's detention. That man was released last week by a Turkish court that sentenced him to three years in prison but ruled he won't serve time behind bars because of time already served.
In 10 years the Turkish and American people will not even remember what happened to that pastor – if he really was only that. Some libertarian U.S. scholars would have written accounts of the events and shown the links between U.S. Vice President Mike Pence and the evangelical Christian churches and the roles played by their votes in the 2018 midterm elections.
Should the democrats gain both houses in U.S. Congress and impeach President Donald Trump as some expect, the relationship between the man who would fill the occupancy in the Oval Office and the Christian cults would be known better. The chroniclers would have said that all that jazz between Turkey and the U.S. had not worked. If "rescuing a Christian man of God from the hands of infidels in the land where the first Evangelists had walked on" works and the good old Republican Party crusaders keep their majority on Capitol Hill, then all that trouble would have been paid off for Pence and Trump.
Again, I assure you, Turkish people won't forget one thing: Trump's national security adviser's confession that the Washington Administration had conspired against Turkey, which is – at least on paper – an ally of the Americans. Pence has threatened Turkey several times with economic sanctions over Andrew Brunson. He said Turkey should have taken "immediate action," as if Turkey were a country where the courts of law take orders from the political authority.
Of course, the executive branch could do nothing to get him released, and Turkey had to endure several sanctions including punitive, that is to say, illegal, taxes on Turkish exports to the U.S. All the government could do was to bravely retaliate against the sanctions.
Yet, in those days something else happened too: Turkey faced a lira crisis; the value of Turkish currency hit an all-time low. Almost all economists, financial experts, even the Wall Street Journal said that this downfall had nothing to do with sanctions per se. John Perkins, who has books on the "operations of economic hit men," said Turkey was undoubtedly being targeted by the U.S. and some other governments.
During those dark days, when Erdoğan and his cabinet feverishly fought to calm the markets and halt the sliding of currency, Qatar had encouraged Turkey by infusing more than $15 billion into Turkey's economy. This ugly American shamelessly told Reuters in an interview during a visit to Israel that "the Turkish government made a big mistake in not releasing pastor Brunson," adding that a Qatar's "cash pumping" would not help Ankara.
This was the U.S. national security adviser's Freudian slip:
"Every day that goes by that mistake continues, this crisis could be over instantly if they did the right thing… and release pastor Brunson without condition."
Some in the U.S. media tried too hard to correct it, but this "blurb" is now the major trademark of what Turkish people endured since last August. The country has suffered (and continues to suffer) an American-made economic fratricide, which did not – could not – kill the Turkish people, but it definitely killed the fraternity of the two nations.
Once upon a time, Turkey had an ally that now exists only on paper.
Source: Daily Sabah
TagsTurkey Turkish türkiye US usa
Malaysians protest against Hindu extremism, criticize Indian high commissioner
Turkey's Spyke Games raises $55M for casual mobile games
Turkey is preparing a new batch of "Bayraktar" (TB2) UCAVs for Ukraine
Hakkı Öcal is a columnist at both Daily Sabah and Milliyet newspapers, which are based in Istanbul. He is also an advisor to the President of Ibn Haldun University.
Why it's hard to believe the Saudi narrative on Jamal Khashoggi
Bavarian State Elections; First Look


A quick update: We just announced the second call for late-breaking work and position papers at #Microposts2016 (Making Sense of Microposts) at the World Wide Web conference on 11 April 2016, Toronto, Canada. Beside the Main track and SocSci track, this workshop is a lot about promoting inter-field/domain discussion. We'd love to see Semantic Web and Computational Social researchers out with late-breaking work or work-in-progress. Submission deadline is 18 March 2016. More details here.
Also, we are thrilled to announce that Mihajlo Grbovic, Senior Research Scientist at Yahoo Labs, is the invited talk speaker at Microposts2016 in Toronto. Follow Microposts2016 for updates.


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'Body Bags' creator Jason Pearson passed away in December
The artist's family announced this week that Pearson died from natural causes at the age of 52 last month.
Jason Pearson, the creator of Body Bags and a founding member of Gaijin Studios, passed away on Dec. 19 at the age of 52. His family revealed that he died on his Facebook page.
"Jason leaves behind a legacy of work that will be cherished by readers for decades to come," their statement reads, which says he passed away from natural causes. "His hyper-kinetic style and breathless pace will be studied by both aspiring artists and seasoned professionals as long as the comic book medium exists. While sometimes a controversial figure, no one could ever question his commitment to the craft or the quality of work he produced as both a writer and artist."
Obit posted by Pearson's family to his Facebook page
Over the years Pearson's art appeared in comics for Marvel, DC, Dark Horse, Image Comics and Penthouse Comix, among others. His career began in earnest in the early 1990s, working for the now-defunct publisher Innovation as well as for DC on an issue of Starman with Peter David and Keith Giffen, as well as back-up stories in Legion of Super-Heroes with Giffen and co-writers Tom and Mary Bierbaum, during the "Five Years Later" storyline.
Gaijin Studios, an Atlanta-based collective of artists, formed in 1991. Pearson was one of the original members of a group that would include Cully Hamner, Adam Hughes, Tony Harris, Dave Johnson and many other prominent comic artists of the 1990s and 2000s.
"He was great *at everything*. He could draw like nobody's business in a style that was unique to him," Hamner wrote on Twitter. "He was an excellent storyteller, draftsman, inker, colorist… you name it. Whatever angle you could come at comic art, he was formidable."
The studio would propose an anthology series to Image that the publisher ultimately passed on, but Pearson's contribution would have been Body Bags, which he continued to develop.
Pearson's art would appear in Maze Agency, Justice League Quarterly, Uncanny X-Men and other titles in the early 1990s. In 1995, he wrote and drew Dragon: Blood & Guts, a miniseries starring Erik Larsen's Savage Dragon:
And in 1996, Body Bags ultimately saw publication, as a launch title for Dark Horse Comics' Blanc Noir line of books that were produced by Gaijin Studios. The first series would run for four issue, with the final issue being delayed due to Pearson falling ill. A six-issue follow-up never materialized, as Pearson again fell ill during its production and he moved on to other projects once he was well.
In 2005, 12-Gauge Comics would re-release the original miniseries, which was followed by a one-shot that collected some shorter stories that appeared in Dark Horse Presents. Eventually a one-shot featuring new material was released in 2008.
Over the years, Pearson drew many comics for various publishers, including issues and stories of Hellboy, Astonishing X-Men, Global Frequency and Punisher, while also drawing covers for Amazing Spider-Man, Deadpool, Robin and more. In 2010, he worked with writer Duane Swierczynski on the Deadpool miniseries "Wade Wilson's War."
But as the death announcement from his family noted, he wasn't without controversy. In 2015 he launched a Kickstarter for a new Body Bags project that was successfully funded but was never completed. Last year he accused artist Afua Richardson of not paying her dues, starting a heated social media exchange. Over the years Pearson would talk online about his struggles with his mental health, which many creators acknowledged in their tributes to him on social media. And many others paid tribute to the impact he had on them and the industry.
Jason was a brilliant, funny guy, who really lost his way some time ago, and struggled with himself and everyone around him. I'd always hoped he could find his way back.
We own one cover of his.
Jason Pearson, you were far too young, and had so many tales left untold. pic.twitter.com/I4NPekzeDm
— Joyce Chin (@TJoyceChin) January 17, 2023
Our relationship… was complicated. I don't want to go into it too much, but I also don't want to gloss over it. It's no secret that he and I were estranged for a while. I never really understood it, just as I couldn't quite wrap my head around our thaw the last few years. /3
— Cully Hamner (@CullyHamner) January 17, 2023
RIP Jason Pearson.
A flawed person like the rest of us.
He lifted me up once, when I was down on the ground. pic.twitter.com/nDcxxCck69
— Joseph P. Illidge (@JosephPIllidge) January 17, 2023
My friend and brother Jason Pearson has passed. We are and always will be GAIJIN STUDIO. He's The first of our clan to fall. Go easy brother….. pic.twitter.com/KTlTyGft4Q
— TONYEFFINGHARRIS' wont tolerate yer bullshit (@TONYFINGHARRIS) January 17, 2023
We are saddened to hear of the passing of comic artist Jason Pearson. Jason was a brilliant artist with an unmistakable dynamic style in comics, including Deadpool, X-Men, and many other acclaimed titles across the industry. Our condolences go out to his family and friends. pic.twitter.com/5J0ErZ7Per
— Marvel Entertainment (@Marvel) January 17, 2023
Something I always appreciated about Jason Pearson was that he never seemed to compromise. Nothing was 'just a gig'. This project he did for a Wildstorm special in 2003 is a prime example. When given a 12 page short, he went above and beyond with character redesigns. pic.twitter.com/wGEq9XphjV
— Eric Zawadzki (@ericxyz) January 17, 2023
Terrible news hearing about the passing of Jason Pearson. One of my favorite comic artists when I was in high school. Unique, clean style w/ excellent action. Tremendously talented draftsman and designer. Rest in peace. My condolences to his family and friends.
— Kazu Kibuishi (@boltcity) January 17, 2023
R.I.P., Jason Pearson…a fantastic artist and I always loved the Michael Golden influence that showed through in his art. pic.twitter.com/SaAVbNgMGf
— Pat Brosseau (@droog811) January 17, 2023
Jason Pearson's BODY BAGS was one of my faves, and the influence on Hack/Slash is probably obvious. A massive talent. Panda and Clownface will always grace my shelves. pic.twitter.com/yxnoSrhvZZ
— Tim Seeley (@HackinTimSeeley) January 17, 2023
Damn. This one hits hard. Jason Pearson has passed away, age 52. He was an early champion of mine back in the days of CAPE in Dallas, Texas. Showing my work around, giving me pointers, just being a nice guy. Rest in peace. pic.twitter.com/P2lAKfNEtd
— Kody Chamberlain (@KodyChamberlain) January 17, 2023
Author JK ParkinPosted on January 17, 2023 January 17, 2023 Categories CreatorsTags comic creators, Jason Pearson, passings
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Cebu City Mayor Edgar Labella just announced and decided to extend the Enhanced Community Quarantine (ECQ) in Cebu City until May 15, 2020. This is due to the city's still increasing number of individuals found positive of the novel coronavirus disease 2019 (COVID-19) despite the said quarantine.
This is also based on the recommendations of the health experts in the city as the COVID-19 cases continue to rise due to the city's continued efforts in targeted mass testing of residents in the barangays where there are confirmed cases.
As per Mayor Labella, he will issue the executive order of the ECQ extension anytime next week. He added that his team will continue to closely monitor the city's situation and should there be a significant decrease on the cases, he can and will immediately lift the ECQ.
The mayor appealed to the public to strictly observe quarantine protocols.
"I understand that the increasing numbers being reported is a cause of concern and worry for all of us. However, what the city government needs right now is the full cooperation of everyone as we continue to fight this invisible enemy."
As of April 22, 2020, there are one hundred forty-three (143) additional cases from Cebu City of which one hundred twenty-seven (127) are from BJMP Cebu City Jail while the sixteen (16) are residents of Cebu City. The total cases in the city are now at three hundred eleven (311). Lapu-Lapu City also has five (5) new cases bringing the total to eighteen (18) while Mandaue City cases remain at nine (9).
According to Health spokesperson Ma. Rosario Vergeire, the Department of Health has recorded 6,710 cases of COVID-19 nationwide, with 693 recoveries and 446 deaths and this does not include yet the new recorded cases in Cebu City.
Enhance Community Quarantine ECQ Exension Cebu City Cebu City ECQ COVID-19


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The NAS program is designed to help students develop a knowledge base of and appreciation for Lakota/Dakota culture, society, and history, including the traditional and contemporary land base and natural resources, traditional and contemporary forms of government, traditional philosophy and worldview, ceremonies, values, belief system, kinship and social systems. This program also includes courses of a comparative nature, which places Lakota/Dakota culture and society in the context of other Native North American people. This program is useful for individuals interested in becoming teachers or working in various tribal programs on Standing Rock.
The LDL program is useful for individuals interested in studying the Lakota/Dakota language, becoming teachers or working in various tribal programs on Standing Rock and Lakota/Dakota speaking communities.


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The font - possibly Norman.
St. Egryn gave his name to the Church of St Mary and St Egryn and it, in turn, gave its name to the village of Llanegryn.
Little is known about St Egryn. He probably lived as a monk in the seventh century A.D. and he was the patron saint of Llanegryn Church from the earliest times until the Cistercian monks of Cymer Abbey near Dolgellau renamed the church after St Mary the Virgin. The church was attached to Cymer Abbey for a considerable time but after the departure of the Cistercians the church readopted St Egryn into its name.
The age of the church is not really known. There was undoubtedly an early church on the site, possibly going back to the time of St Egryn or even earlier but the first record we have of the church is in 1253 and the architectural style of the present church suggests that it was built in the thirteenth century.
The Screen and Rood Loft are the best known features of the church. This ancient masterpiece by unknown craftsmen is reputed to have been brought from Cymer Abbey at the time of the dissolution of the monasteries by Henry VIII in 1536. This is likely to be romantic legend with the screen actually having been produced by local craftsmen sometime in the period between 1475 and 1530.
The font is also ancient, possibly Norman and even predating the present church though it is impossible to date it with any accuracy.


Author(s): O. Benek, L. Aitken, L. Hroch, K. Kuca, F. Gunn-Moore, K. Musilek. University of Hradec Kralove, Faculty of Science, Department of Chemistry, Rokitanskeho 62, 500 03 Hradec Kralove, Czech Republic.
The amyloid-β peptide (Aβ) has been associated with Alzheimer's disease (AD) for decades. The original amyloid cascade hypothesis declared that the insoluble extracellular plaques were responsible for Aβ toxicity. Later, this hypothesis has been updated and soluble intracellular Aβ forms and their effects within the cell have come into focus. Mitochondrial dysfunction plays an important role in the pathophysiology of AD. Aβ was detected inside mitochondria and several mitochondrial proteins were found to interact directly with Aβ. Such interactions can affect a protein's function and cause damage to the mitochondria and finally to the whole cell. This review summarizes the current knowledge of mitochondrial proteins directly interacting with Aβ and discusses their significance for the development of therapeutics in the treatment of AD.
Keywords: Alzheimer's disease (AD), amyloid-β peptide (Aβ), drug target, enzyme inhibiton, mitochondria, pharmacotherapy.
Affiliation:University of Hradec Kralove, Faculty of Science, Department of Chemistry, Rokitanskeho 62, 500 03 Hradec Kralove, Czech Republic.
Keywords:Alzheimer's disease (AD), amyloid-β peptide (Aβ), drug target, enzyme inhibiton, mitochondria, pharmacotherapy.
Abstract:The amyloid-β peptide (Aβ) has been associated with Alzheimer's disease (AD) for decades. The original amyloid cascade hypothesis declared that the insoluble extracellular plaques were responsible for Aβ toxicity. Later, this hypothesis has been updated and soluble intracellular Aβ forms and their effects within the cell have come into focus. Mitochondrial dysfunction plays an important role in the pathophysiology of AD. Aβ was detected inside mitochondria and several mitochondrial proteins were found to interact directly with Aβ. Such interactions can affect a protein's function and cause damage to the mitochondria and finally to the whole cell. This review summarizes the current knowledge of mitochondrial proteins directly interacting with Aβ and discusses their significance for the development of therapeutics in the treatment of AD.


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\section{Introduction}

The combinatorial optimization (CO) problems and their solution techniques are widely applied in a number of real-world industries such as manufacturing, supply chain, retailing, etc. Combinatorial optimization is targeting at finding the value of the decision variable $x^\ast$ from a finite set $\mathcal{X}$ that is \textit{feasible}  and that optimizes the objective function, where the objective function is usually a cost function or a loss function to be minimized, or a value function to be maximized. Here a \textit{feasible} solution $x\in\mathcal{X}$ is the value of decision variable that satisfies the problem's constraints. In practical problems, the decision variable $x$ is generally with high dimensionality, making the scale of $\mathcal{X}$ exponentially large.  Consequentially the  algorithms on solving combinatorial optimization problems, especially the ones with large scale, is of  great interest of research for decades. To solve the large-scale problems within a limited computing time period, heuristic and meta-heuristic methods are developed to achieve a good  balance between computational time and solution quality, among which the Large Neighborhood Search (LNS) is a popular one due to its close-to-optimal solution quality and fast converging speed. LNS can be applied together with other meta-heuristic methods such as Tabu search and Simulated Annealing for better performance.

LNS roots from Neighborhood Search heuristics. Neighborhood search algorithms try to improve the initial feasible solution  by repeatedly searching within a \textit{neighborhood} of current solution, where \textit{neighborhood} is defined as a set of feasible solutions that are similar to the current one. The neighborhood of solution $x$ is described mathematically as: $N(x):\{x^\prime=\mathcal{N}(x)\}$ where $\mathcal{N}$ is the exploration function to traverse the similar feasible solutions $x^\prime$ from current solution $x$.  The choice of neighborhood from where the new solution is chosen is apparently essential for better solution quality and for better exploration effectiveness. LNS was introduced in \cite{shaw1998using} to extend the  neighborhood, because a larger neighborhood yields a better result by preventing algorithms from getting trapped in local optima. However it is time-consuming to search a larger neighborhood thoroughly. This fact poses a challenge on the design of LNS heuristics which is capable to converge to a solution of good quality within a reasonable amount of computing time. LNS tackles this challenge by expanding the neighborhood into $N(x):\{x^\prime=\mathcal{N}(x^{\prime\prime}), x^{\prime\prime}\in x\bigcup N(x)\}$, meaning that an updated solution $x^\prime$ is accepted (i.e., updating to $x^\prime$ from $x^{\prime\prime}$) at each iteration even if it does not improve the solution quality. In this way the search in a relatively larger neighborhood is implemented in an iterative manner. Meanwhile the exploration function $\mathcal{N}$ has been replaced into the combination of two consecutive operators: a destroy operator and a repair operator, following the idea that part of the current solution is destroyed and then is repaired afterwards. Using Vehicle Routing Problem (VRP) as an example, the destroy operator eliminates a portion of customer nodes from current routes, then the repair operator inserts the removed nodes back into the alternative or the same routes. This process is shown as in Fig \ref{Fig:lns}.

\begin{figure}
    \centering
    \includegraphics[width=.95\linewidth]{LNS_.png}
    \caption{An example of large neighborhood search. From left to right: the original solution; a destroyed one; a repaired one.}\label{Fig:lns}
\end{figure}

The key aspect of LNS is the design of operators, with consideration of both the computational time and the search efficiency. The most commonly used destroy operators include random customer removal, random route removal, related route removal or workday level operators. Typical repair operators include least cost heuristic and regret based heuristic. Besides the design of operators, the degree of destruction is one of the most important parameters to be determined. There are different strategies of setting the degree of destruction, for example, a constant degree, or a random degree, or an adaptive degree depending on the current solution. In recent years, multi-level approaches such as Adaptive Large Neighborhood Search (ALNS) \cite{ropke2006adaptive} and Slack Induction by String Removals (SISR) \cite{christiaens2020slack} are introduced to improve the searching efficiency and effectiveness. The main takeaway of ALNS is that the combination of multiple heuristics is generally better than a single heuristic, and the weights of the multiple heuristics shall be adaptive. The main takeaway of SISR is that clustering of removed nodes rather than scattering is always preferable. These design considerations are the major inspirations of our  research work proposed in this paper.

Another family of approaches to solve the combinatorial optimization problems is based on the deep learning and the reinforcement learning models. Researchers have been proposing various deep learning algorithms recently. Among them, the pointer network \cite{vinyals2015pointer}, which is inspired by the Seq2seq \cite{sutskever2014sequence} model and the attention mechanism\cite{graves2014neural}\cite{bahdanau2014neural}, is one of the earliest attempts. Later, more approaches have been proposed, which can be grouped into two categories in general. One category is to train a neural network model end-to-end to produce  a solution directly, by adopting the Encoder-Decoder framework or attention structures \cite{nazari2018reinforcement}\cite{kool2018attention}. Another paradigm focuses on solving the problems with iterative improvements like many heuristic search algorithms \cite{chen2019learning}\cite{gao2020learn}.

We focus on the second paradigm, say, by applying a neural network heuristic to improve the solution repeatedly, because of its guarantee to the solution quality and the explainability of the network model. Several insights of the optimization problems and their heuristic techniques are to be examined for a reasonable design of the network. The first insight is that an excessive amount of combinatorial optimization problems can be expressed by a Graph $\mathcal{G}=(\mathcal{N}, \mathcal{A})$, where $\mathcal{N}$ represents the nodes  and $\mathcal{A}$ represents the arcs. For example, Network Flow problem, Vehicle Routing problems, Generalized Assignment problems, etc, can be depicted in this way. The recent developing on Graph Neural Network \cite{scarselli2008graph} can be leveraged to the network design for this purpose due to its power on  the information embedding and belief propagation of the graph topology \cite{khalil2017learning}. Other insights on the heuristic techniques include the considerations on the operators' design such as the degree of destruction, the adaptive operators, and the clustering of removed nodes in the graph.

Following the insights and considerations, we propose a novel network design for LNS heuristics on combinatorial optimization problems that can be depicted by a graph $\mathcal{G}$. The proposed adaptive destroy operator for LNS is called Dynamic Partial Removal (DPR) by introducing and applying the Hierarchical Recurrent Graph Convolutional Network (HRGCN). We use capacitatied VRP with time windows (CVRPTW) as an example to show how this approach works and its experimental results comparing to existing LNS algorithms. This approach can be easily applied to other variants of VRP, and to other combinatorial problems as well.
Our approach differs from other deep-learning-based algorithms in the following aspects: a) this model can solve VRP with tight constraints, e.g. CVRPTW, which is described as ``a challenging task" in some recent papers \cite{nazari2018reinforcement}; b) this approach is able to be generalized to mixed-scale problems; c) this approach has the bandwidth to solve large-scaled VRP and its variants efficiently with as many as 800 customer nodes or even more.

This paper is organized as below. Our method along with the problem definition, the new design of heuristic search (DPR) and the structure of the neural network (HRGCN) are explained in Section 2. The experiment settings, hyper-parameters, and results are presented in Section 3. The final conclusion and future works are discussed in Section 4.

\section{Proposed Model}

\subsection{Problem Definition}

VRP is an integer programming problem that defines a group of fleet routes to serve a set of customer nodes. The solution is represented by a directed graph $\mathcal{G}=(\mathcal{N},\mathcal{A})$, where the nodes of the graph $i\in\mathcal{N}=\{0,1,...,N\}$ represents the customers to be served if $i>0$ or the depot if $i=0$. Each customer $i>0$ is associated with a demand (a number of goods to be delivered) $q_i$. Each arc $a_{i,j}\in\mathcal{A}$ represents a segment of a route that connects node $i$ and $j$. In capacitated vehicle routing problems with time windows (CVRPTW), vehicles have limited carrying capacities, and each customer has a service time window $[s_i, e_i]$, as well as a service (or, handling) time period $t_i$. The duration for each route is limited by the depot's time window $[s_0, e_0]$, where $s_0$ is usually 0.

\subsection{Dynamic Partial Removal as a Destroy Heuristic}

The destroy operator proposed in our algorithm is called "dynamic partial removal" (DPR). There are three parameters for this operator: an anchor node, the route coefficient, and the number of nodes to be removed.
Given the current solution at step $t$ as $x^{(t)}=[x^{(t)}_{r, n_r}]$, which is a matrix where the row $r$ indicates the $r$-th route, and the element at row $r$ and column $n_r$ indicates the $n$-th node on $r$-th route. The destroy operator is to remove a subset of elements $\{x^{(t)}_{r^\prime, n_r^\prime}\}$. This subset is clustered around the anchor node $\{x^{(t)}_{r^0, n_r^0}\}$. The route coefficient defines the allocation of this subset across different rows (i.e., routes in VRP), and the size of this subset determines the number of nodes to be removed, or the degree of destruction equivalently.  Figure \ref{fig:coeff_step} shows a concrete example of DPR, where the successive elements (nodes) on the route $r^0$ are removed with a maximal number determined by the route coefficient, and the same removal logic is applied to next closest row (route) if the degree of destruction is not satisfied, and so on so forth. Note that the depot (the $0^{th}$ node) will never be removed.  The similar approach can be applied to other combinatorial optimization problems where the decision variable $x$ is expressed in the form of a matrix. Please refer to figure \ref{fig:coeff_step} for details.

When the route coefficient is close to 1, the operator prefers a string removal pattern as to delete multiple consecutive nodes on the same path. If the route coefficient is close to 0, the operator tends to delete nodes with closest Euclidean distance.

\begin{figure}[ht]
    \centering
    \begin{subfigure}{0.2\linewidth}
        \centering
        \includegraphics[width=\linewidth]{coeff_steps_0.png}
        \caption{ } \label{fig:coeff_step_a}
    \end{subfigure}
    \hspace*{\fill}
    \begin{subfigure}{0.2\linewidth}
        \centering
        \includegraphics[width=\linewidth]{coeff_steps_1.png}
        \caption{ } \label{fig:coeff_step_b}
    \end{subfigure}
    \hspace*{\fill}
    \begin{subfigure}{0.2\linewidth}
        \centering
        \includegraphics[width=\linewidth]{coeff_steps_2.png}
        \caption{ } \label{fig:coeff_step_c}
    \end{subfigure}
    \hspace*{\fill}
    \begin{subfigure}{0.2\linewidth}
        \centering
        \includegraphics[width=\linewidth]{coeff_steps_3.png}
        \caption{ } \label{fig:coeff_step_d}
    \end{subfigure}
    \caption{An illustration of DPR. Figure (a) is the original solution which includes three routes: R1, R2, and R3. The routes have 8 nodes, 12 nodes, and 12 nodes, respectively. The original anchor is node A, and the degree of destruction is 12. The four nearest neighbors of node A (including itself) are A, B, C, and D. Assume the route coefficients for these four nodes are 0.5, 0.25, 0.25, and 0.5, respectively. The destruction starts with the anchor node A: A belongs to R2 which has 12 nodes, and the coefficient is 0.5, therefore 6 out of 12 nodes are removed as shown in figure (b). The same logic is applied to node B since the degree of destruction (12) is larger than the accumulated number of removed nodes (figure (c)). Here node C is skipped since it is already purged. When the destruction comes to node D, the coefficient is 0.5 which means 4 out of 8 nodes should be removed along route R1, however the accumulated number of removed nodes is 9 up to this point, consequently only 3 nodes are to be removed from R1 and the DPR stops as degree of destruction is satisfied.} \label{fig:coeff_step}
\end{figure}

We use the least-cost heuristic as the repair operator to repair the connections, by picking up the removed nodes at random order and inserting them at the feasible locations with minimum detour \cite{azi2014adaptive}. The algorithm (\ref{alg:DPRR}) shows the process of DPR, where $f(\theta_a)$ is the policy to pick up the anchor and $f(\theta_c)$ is the policy to output the route coefficients.

\begin{algorithm}[!htb]
    \caption{Dynamic Partial Removal}
    \label{alg:DPRR}
    \begin{algorithmic}
        \STATE \textbf{Input:} $x^{(t)}$
        \STATE Set $L_{destroy}$ as an empty list
        \STATE anchor $\leftarrow$ select an anchor according to $f(\theta_a)$
        \FOR{node $i$ in Neighbor(anchor)}
        \STATE Find the route $r$ to which the node $i$ belongs
        \STATE $removals \leftarrow removeSelected(r, i, f(\theta_c), L_{destroy})$
        \STATE $L_{destroy} \leftarrow L_{destroy} \cup removals$
        \IF{$len(L_{destroy}) = n_{destroy}$}
        \STATE \textbf{Break}
        \ENDIF
        \ENDFOR
        \STATE Remove the nodes in $L_{destroy}$ from $x^{(t)}$
        \STATE Shuffle the $L_{destroy}$
        \STATE Reinsert the nodes in $L_{destroy}$ into $x^{(t)}$
        \STATE \textbf{Output:} $x^{(t)}$
    \end{algorithmic}
\end{algorithm}

\subsection{HRGCN}

The details of the neural network that generates the above-mentioned anchor node and the route coefficients as well are explained in the following subsections in terms of node embedding, hierarchical network architecture, and the training method.

\subsubsection{Embeddings}

We embed each node into an 10-dimensional vector $n_i$, with each dimension as: 1) the node's $x$ coordinate, 2) the node's $y$ coordinate, 3) the customer's demand $q_i$, 4) the starting time of the service time window $s_i$, 5) the ending time of the service time window $e_i$, 6) the service time period $t_i$, 7) sum up of demands $q_i$ of the corresponding route till this node, 8) accumulated traveling distance along this route till this node, 9) a total demand of all nodes on the corresponding route, and 10) a total traveling distance of the corresponding route. The $3^{rd}$, $7^{th}$, and $9^{th}$ embedding elements are normalized by the capacity of the vehicles, and the rest are normalized by the time span of the depot $t_{max}$.

\subsubsection{Hierarchical Graphs}
The anchor node and the route coefficients are generated by a neural network namely Hierarchical Recurrent Graph Convolutional Network (HRGCN). The key ideas underlying HRGCN are the spatial propagation and the temporal propagation, as explained below. The architecture of HRGCN is illustrated as Figure \ref{Fig:actor_net}. It starts from a graph convolutional network $GCN_0$ whose nodes are the depot and customer nodes, and the arcs are the k-nearest-neighbor (k-NN) connections for each node. The input to $GCN_0$ is the 10-dimensional node embedding for each node, and the output is the enhanced node embedding with a higher dimensionality $N_A$ by integrating the information on topological contiguous nodes.  The output of $GCN_0$ is fed to two identical graph convolutional networks $GCN_{route}$ in a row, whose nodes are with the $N_A$ dimensional embedding and arcs are the segments of the routes in the current solution. This type of hierarchy $GCN_0\rightarrow GCN_{route}\rightarrow GCN_{route}$ helps spatial exploration and increases the \textit{receptive field} that is extended to longer hops among the nodes, especially along the current routes. A residual connection from $GCN_0$ to the last $GCN_{route}$ is added to prevent from gradients vanishing or exploding. This type of hierarchy is replicated consecutively with $GCN_0$ being replaced by $GCN_{near}$ and $GCN_{route}$ being replaced by $GCN_{route, inv}$, where $GCN_{near}$ is identical to $GCN_0$ except for the dimensionality of the input  node embedding  being $N_A$ instead of 10, and $GCN_{route, inv}$ is identical to $GCN_{route}$ except for the arcs being the segments of the current routes in a reversed direction. For example, given a route in current solution as $A\rightarrow B \rightarrow C \rightarrow D$, the arcs in $G_{route, inv}$ are $D \rightarrow C$, $C \rightarrow B$, and $B \rightarrow A$.  The purpose to introduce $G_{route,inv}$ is to provide a scheme about propagating node information from future nodes who are to be visited later, as a backward view.

\begin{figure}
    \centering
    \includegraphics[width=.6\linewidth]{actor_network2.png}
    \caption{Illustration of the actor's network HRGCN.}\label{Fig:actor_net}
\end{figure}

The temporal propagation that integrates information from historical solutions is carried out by a Gated Recurrent Unit (GRU) as shown in Figure \ref{Fig:actor_net}. The input to this GRU cell is the embedding of the previous iteration's anchor node, coupled with the hidden state from the previous cell. At each iteration, the hidden state $h_i$ helps calculate the output (say, the anchor node and the route coefficients) as a multiplicative adaptive weight.

The last layer of HRGCN outputs the probability of each node being the anchor node, by a softmax function. Two additional scalars $\alpha_i$ and $\beta_i$ are calculated by the $elu$ function for each node $i$. The parameterized Beta distribution $Beta(\alpha_i, \beta_i)$ is the probability distribution from which the route coefficients are sampled. HRGCN outputs the parameterized distribution on route coefficients rather than the deterministic coefficients values, because randomness introduced by the distribution helps the exploration efficiency.

Instead of using one anchor at each step, we have discovered from experiments that DPR with multiple anchors at each iteration usually yields better performance. Sampling multiple anchor points from this softmax function can search several areas simultaneously, thus prevents the searching process from falling into a local optima for medium-to-large scaled problems.

\begin{figure}[!hbt]
    \centering
    \includegraphics[width=.6\linewidth]{hrgcn.png}
    \caption{The recurrent perspective of HRGCN carried out via the GRU cell.}\label{Fig:hrgcn}
\end{figure}

\subsubsection{PPO for Training}

This model is trained by the Proximal Policy Optimization (PPO) framework, where the HRGCN is the actor network, and the loss function is defined as:
\begin{eqnarray}
L_A(\theta) &=& \hat{\mathbb{E}}_t[\text{min}(r_t(\theta)\delta_{\text{TD}}^{(t)}\text{, clip}(r_t(\theta), 1-\epsilon, 1+\epsilon)\delta_{\text{TD}}^{(t)})]\notag\\
L_C(\theta) &=& MSE(v, R) \notag\\
L_E(\theta) &=& Entropy(d_c) + Entropy(d_b) \notag\\
Loss(\theta) &=& -L_A(\theta)+0.5*L_C(\theta)-0.01*L_E(\theta)
\end{eqnarray}

Here $v$ represents the output of the critic network; $R$ is the discounted cumulative reward; $d_c$ is a vector of probabilities for each node being selected as the anchor node, and this vector is the output of softmax function at the last layer of HRGCN; $d_b$ denotes the beta distribution from which the route coefficient is sampled. The reward function is as simple as the delta of the cost function $r(c_{t-1}, c_{t}) = c_{t-1} - c_{t}$, where $c_{t}$ is the cost at the $t$-th iteration.

The critic network is a multi-layer fully-connected neural network containing two hidden layers with a size of $N_C$ for both layers. The input of the critic network is the hidden state $h_i$ of the actor network, and the output is a scalar variable representing the value of the current state.

\section{Experiments}

\subsection{Problem Generation}

In this section we manifest the experiments' results of solving the CVRPTW by the proposed approach as an example. Many VRPs involve scheduling visits to customer nodes who are only available to be served during specific time windows, therefore it is a more meaningful scenario in practice. Meanwhile the tight constraints on time-windows also pose a challenge to the algorithms.

We train the model using synthetic data sets produced by a data generator, and test it on two data sets: the synthetic data sets, as well as the Solomon benchmarks and Gehring \& Homberger benchmarks which are the \textit{de facto} benchmark data sets for VRP. The synthetic data sets are generated in a way that the positions of the customer nodes are randomly located on a map or clustered into several groups, where the number of clusters is randomly chosen from $[5, max(6, N_{nodes}/5))$. The demands are sampled from the normal distribution $\mathcal{N}(20, 121)$. If the demand is lower than 1 or higher than 45, then it will be resampled from a uniform distribution $U[5, 36]$. The service time periods for customers are identical for each instance of problem, which is randomly chosen between 10 and 100. Each customer will have a probability $P_{start}$ that the time window is not limited. For the other customers with limited time windows, the starting time $T_{Start}$ is picked from a uniform distribution $U[0, t_{max}]$, where $t_{max}$ is chosen between 600 and 10000. The end time is then calculated by $T_{End} = T_{Start}+T_{Gap}$ where $T_{Gap}$ varies from 10 to 1000.

\subsection{Setup}

We have tested the model with different settings by 1) with or without the GRU cells in the actor network and 2) by using one anchor or multiple anchors. The results verify our proposal that recurrent GRU cells that propagate information in a temporal horizon, together with multiple anchors that search more spatial areas, can notably boost the efficiency of the heuristic. Furthermore, networks trained for large-scale problems are also tested regarding their solution qualities and computational speed.

For the aforesaid purpose, 4 DPR-based reinforcement learning models are trained as DPR$_{RL-nG}$, DPR$_{RL-nGL}$, DPR$_{RL-G}$, and DPR$_{RL-n}$, where $n$ represents using multiple anchors rather than one anchor, $G$ represents using the GRU cells, and $L$ represents the model is trained with large-scale problems. More specifically, DPR$_{RL-nG}$, DPR$_{RL-G}$, DPR$_{RL-n}$ are trained with mixed-scale problems containing 25 to 200 customers, and DPR$_{RL-nGL}$ is trained with problems containing 400 to 800 customers.

\subsection{Training Details}

The initial solution is generated by: 1) removing all the nodes from the solution; 2) then by inserting each node into the solution using the least cost heuristic. The models are trained with Adam optimizer. The learning rate equals $1e-5$. In our experiments, $N_A$ = 128, $N_C$ = 256, $\gamma$ = 0.99, $K_{epoch}$ = 2, and $\epsilon_{clip}$ = 0.2. The initial and the final temperatures for simulated annealing are 100.0 and 1.0, respectively.

The degree of destruction $n_{ruin}$ is set to $\sqrt{N_{nodes}}$ in case of one anchor, or 20\% larger than $\sqrt{N_{nodes}}$ in case of multiple anchors. The number of anchors is 1 in  DPR$_{RL-G}$, 2 in DPR$_{RL-nG}$ and DPR$_{RL-n}$, and 3 in DPR$_{RL-nGL}$.

It takes 8 hours on one single Nvidia Geforce 2080Ti GPU for training. To better representing each nodes in a large-scale problem, $N_A$ and $N_C$ in DPR$_{RL-nGL}$ are doubled, and the training process takes 16 hours.

\subsection{Experiments Results}
The inference time of our model is shown as table \ref{tab:experiment_time} running on one single  Nvidia Geforce 2080Ti. For problems with no more than 200 nodes, the solving time is less than 1 second. For large-scale problem with 400 - 800 nodes, the solving time is still within a reasonable range. The speed will be faster if running in parallel on multiple GPUs.
\begin{table}[!htb]
    \centering
    \begin{tabular}{llll}
    \toprule
               & DPR & DPR & DPR  \\
    Problem    & $_{RL-nG}$ & $_{RL-G}$ & $_{RL-n}$  \\
    \midrule
    CVRPTW25  & 0.1070 & 0.1041 & 0.1026 \\
    CVRPTW50  & 0.1724 & 0.1785 & 0.1829 \\
    CVRPTW100 & 0.3690 & 0.3657 & 0.3704 \\
    CVRPTW200 & 0.9398 & 0.9316 & 0.9286 \\
    \midrule
    & DPR$_{RL-nGL}$ & \\
    \midrule
    CVRPTW400 & 6.474 & & \\
    CVRPTW600 & 13.58 & & \\
    CVRPTW800 & 20.44 & & \\
    \bottomrule
    \end{tabular}
    \caption{Inference time (time to converge to the final solution by a well trained network) for CVRPTW with different scales, on one Nvidia Geforce 2080Ti and in seconds.}\label{tab:experiment_time}
\end{table}

\begin{table*}[!ht]
    \centering
    \bigskip
    \begin{tabular}{@{}*{9}{l}@{}}
        \multicolumn{9}{@{}l}{\em(a) Experimental results of CVRPTW problems from Solomon benchmarks and Gehring \& Homberger benchmarks.}\\
        \toprule
        \multicolumn{2}{c}{ } & \multicolumn{4}{c}{Heuristic Methods} & \multicolumn{3}{c}{DL Methods} \\
        \cmidrule(r){3-6}
        \cmidrule(r){7-9}
        Problem & GT & RAND & ALNS & SISR & DPR & DPR$_{RL-nG}$ & DPR$_{RL-G}$ & DPR$_{RL-n}$ \\
        \midrule
        CVRPTW25  & 331.27 & 365.60 & 364.00 & 355.03 & 349.72 & \textbf{342.07} & 352.59 & 349.68 \\
        CVRPTW50  & 581.02 & 678.53 & 673.16 & 644.59 & 622.52 & \textbf{608.84} & 618.48 & 618.73 \\
        CVRPTW100 & 995.89 & 1196.37 & 1202.54 & 1151.82 & 1107.52 & \textbf{1067.42} & 1097.72 & 1080.49 \\
        CVRPTW200 & 2780.80 & 3698.65 & 3776.98 & 3455.53 & 3268.78 & \textbf{3107.67} & 3265.72 & 3159.38 \\
        \midrule
        & & & & & & DPR$_{RL-nG}$ & DPR$_{RL-nGL}$ & \\
        \midrule
        CVRPTW400 & 6461.14 & 9462.62 & 10134.9 & 9091.25 & 8431.59 & 8161.93 & \textbf{8131.39} & \\
        CVRPTW600 & 13078.9 & 20938.3 & 21885.0 & 19875.2 & 18221.0 & 17696.4 & \textbf{17527.8} & \\
        CVRPTW800 & 22127.9 & 36936.1 & 38327.3 & 34750.5 & 32053.7 & 30597.3 & \textbf{30498.3} & \\
        \bottomrule
    \end{tabular}

    \bigskip\bigskip
    \begin{tabular}{@{}*{8}{l}@{}}
        \multicolumn{8}{@{}l}{\em(b) Experimental results of CVRPTW problems on synthetic data set.}\\
        \toprule
        & \multicolumn{4}{c}{Heuristic Methods} & \multicolumn{3}{c}{DL Methods} \\
        \cmidrule(r){2-5}
        \cmidrule(r){6-8}
        Problem & RAND & ALNS & SISR & DPR & DPR$_{RL-nG}$ & DPR$_{RL-G}$ & DPR$_{RL-n}$ \\
        \midrule
        CVRPTW25  & 114.54 & 116.64 & 114.09 & 109.98 & 110.12 & \textbf{109.94} & \textbf{109.94} \\
        CVRPTW50  & 348.96 & 360.48 & 348.67 & 331.04 & \textbf{325.01} & 327.24 & 325.38 \\
        CVRPTW100 & 1170.96 & 1217.02 & 1161.89 & 1058.32 & \textbf{1042.29} & 1063.69 & 1054.02 \\
        CVRPTW200 & 4554.98 & 4632.34 & 4454.54 & 4066.86 & \textbf{3938.87} & 3945.95 & 3962.68 \\
        \midrule
        & & & & & DPR$_{RL-nGL}$ & & \\
        \midrule
        CVRPTW400 & 12261.2 & 11901.2 & 11301.2 & 9699.34 & \textbf{9358.82} & & \\
        CVRPTW600 & 29109.9 & 26528.6 & 25788.6 & 21515.2 & \textbf{20328.7} & & \\
        CVRPTW800 & 53628.2 & 48277.8 & 45645.0 & 36992.8 & \textbf{34400.8} & & \\
        \bottomrule
    \end{tabular}

    \bigskip
    \caption{Experimental results on Solomon benchmarks and Gehring \& Homberger benchmarks and on synthetic data sets. 150 iterations with the same solution initialization method are applied to both the heuristic methods and our models are tested. In this experiment, 4 variants of our models are presented, which are 1) DPR$_{RL-nG}$ (25-200 nodes), 2) DPR$_{RL-nGL}$ (400-800 nodes), 3) DPR$_{RL-G}$ (25-200 nodes), and 4) DPR$_{RL-n}$ (25-200 nodes)}\label{tab:experiment_result}

\end{table*}

The results are compared with: 1) the ground truth result (GT); 2) LNS with random node removal operator and least cost heuristic (RAND); 3) adaptive large heuristic search (ALNS) \cite{azi2014adaptive}; and 4) Slack Induction by String Removals (SISR) \cite{christiaens2020slack}. The initial solutions for these heuristic methods are generated in the same way as explained above. For some benchmark cases where the ground truths are not available, the best-known heuristic results are applied instead. For some 50-nodes Solomon benchmarks where both the ground truth and the heuristic results are not available, we use the SISR method running 1 million iterations as the benchmark. Table \ref{tab:experiment_result} shows that for medium-size CVRPTW problems, DPR$_{RL-nG}$ outperforms traditional heuristic search results in most cases, implying that both the recurrent structure and multiple anchors at each iteration improve the average quality of the solutions. The results also show the great potential of our model in solving large scale problems.

Fig. \ref{fig:descents} illustrated the convergence of the averaged inference results on benchmark data sets. It shows that the proposed model has a faster converging speed than the traditional heuristic algorithms.
\begin{figure}
    \centering
    \begin{subfigure}[b]{0.475\linewidth}
        \centering
        \includegraphics[width=\linewidth]{descent25.png}
        \caption[]%
        {{\small Scale = 25 nodes}}
        \label{fig:descent25}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.475\linewidth}
        \centering
        \includegraphics[width=\linewidth]{descent50.png}
        \caption[]%
        {{\small Scale = 50 nodes}}
        \label{fig:descent50}
    \end{subfigure}
    \vskip\baselineskip
    \begin{subfigure}[b]{0.475\linewidth}
        \centering
        \includegraphics[width=\linewidth]{descent100.png}
        \caption[]%
        {{\small Scale = 100 nodes}}
        \label{fig:descent100}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.475\linewidth}
        \centering
        \includegraphics[width=\linewidth]{descent200.png}
        \caption[]%
        {{\small Scale = 200 nodes}}
        \label{fig:descent200}
    \end{subfigure}
    \caption[]
    {\small The average costs of solutions at each iteration step using different heuristics. The results are tested on the Solomon benchmark (25-100 nodes) and the Gehring \& Homberger benchmarks (200 nodes). }
    \label{fig:descents}
\end{figure}

Fig. \ref{Fig:coefficients} shows the average route coefficients per iteration step produced by HRGCN on Solomon benchmarks (with 25, 50, 100 nodes) and on  Gehring \& Homberger benchmarks (with 200 nodes). From the plot one can conclude that the route coefficients automatically decrease along the iteration process, hence the search areas effectively zoom in from a coarse granularity to a fine one. The trend of zooming-in is more salient (say, larger initial value, deeper descending trend) for problems with larger scale, showing that this model is also adaptive to different scales.

\begin{figure}[!hbt]
    \centering
    \includegraphics[width=.7\linewidth]{route_coefficients.png}
    \caption{The averaged route coefficients per iteration step.}\label{Fig:coefficients}
\end{figure}

\section{Conclusion}

In this paper, we proposed a novel approach for LNS heuristics on combinatorial optimization problems. Our model consists of an innovative neural network design namely Hierarchical Recurrent Graph Convolutional Network (HRGCN) which acts as the destroy operator of LNS heuristic in a way we introduce as Dynamic Partial Removal (DPR). DPR is inspired by Adaptive LNS (ALNS) \cite{ropke2006adaptive} about the adaptive removal selection, as well as by Slack Induction by String Removals \cite{christiaens2020slack} about the clustered-destruction insight. DPR extends the above insights in a way with more intelligence and context-awareness provided by the HRGCN, due to the fact that HRGCN is able to propagate and incorporate information from both the spatial context (the topological neighbors and adjacent nodes, as well as the contiguous nodes as a string along the routes), and the temporal context (the embedded information of the entire solutions on previous iterations). We test our model both on a set of well-known benchmarks and on synthetic data sets. The experimental results show that our model outperforms in terms of the solutions' quality and computational efficiency. Although we use CVRPTW as an example for illustration and demonstration,  the proposed model can be applied to other combinatorial optimization problems that can be structured as a graph, e.g., Network Flow problem, Generalized Assignment Problems, and other VRP variants including Multi-Depot VRP (MDVRP), VRP with Mixed Delivery \& Pickup (VRPMDP), Pick-up and delivery with time windows (PDPTW), and etc.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


Tags: Science – Section A: The Secret of the Machines Question Answers for class 7, Free PDF file of Question and Answer of The Secret of the Machines for 7th class, Solution of the exercise of The Secret of the Machines for 7th standard, Coursebook -7 Britannica Learning - The English Channel class 7 solutions pdf, the english channel coursebook 7 answers, the english channel literature reader 7 answers.
1. Rewrite this paragraph to show the correct process of the formation of machines.
Metals are extracted from their ores through heating. The shaped metals are used to make tools and machines. The extracted metals are purified. The ores are extracted through mining. The purified metals are shaped through moulding and hammering. The extracted ores are purified.
Ans. The ores are extracted through mining. The extracted ores are purified. Metals are extracted from their ores through heating. The extracted metals are purified. The purified metals are shaped through moulding and hammering. The shaped metals are used to make tools and machines.
2. What is the 'nine-decked city'? Why is it described as 'monstrous'?
Ans. The 'nine-decked city' is referred to Mauretania, a high-speed luxury passenger ship, launched in 1906. It is described as 'monstrous' because it was the world's biggest passenger ship at that time.
3. What do you understand by the line 'shall we pipe aloft and bring you water down'?
Ans. The line means that the machines can go up to a great height and bring water down where human beings live.
4. Which stanza shows us that the machines have mastered almost all the common human activities?
5. What actions are the machines incapable of doing?
Ans. Machine cannot detect lie. Besides, machines are not built to love or hate its owner or anyone. Thus, machines are emotionless and have no feelings and can be dangerous if not handled properly.
6. What is the warning issued by the machines?
Ans. We must accept the fact that our dependency on machines are increasing day by day. A time is about to come when people will depend on a machine to wake them from sleep and then to put them back to sleep, walk and eat. If this really happens, life will be different – without feelings, sympathy, pity, forgiveness and love.
7. Which lines tell us that for every little input, the machines are able to provide constant, daily service to humans?
We will serve you four and twenty hours a day!.
8. Which two opposing claims do the machines make in the poem?
Ans. We are everything on earth—except The Gods!
9. Which lines tell us that the all-powerful nature of the machines is only an illusion?
Written in the early decades of the twentieth century, this poem looks back at the scientific and technological advancements that had taken place over the past two centuries.
1. Look up the internet and make a chronological note of the major advancements that took place in science, medicine, and technology between 1700 and 1900. Share and discuss the collected information in class.
2. Write about any two inventions made during this period and their impact on the lives of the people at the time.
Ans. Telephone - The telephone has had a big impact on the world. When the telephone was first introduced it could only be afforded by the rich as the materials needed for connection were very expensive (Pool, 1977). The telephone was promoted on the grounds that it would increase wealth, employment and improved means of communication. The invention of the telephone lead to development of city centers, office buildings and the concept of an urban worker society. It has led to the creation and destruction of jobs. The need for positions such as messenger boys, telegraphers and, ironically, operators, became virtually unnecessary (Bauer, 1995). It has changed the pace of business and made the world smaller and more accessible to all. The telephone has provided security and helped in emergency situations.
Bicycles - Bicycles were introduced in the late 19th century in Europe. The bicycle's invention has had an enormous effect on society, both in terms of culture and of advancing modern industrial methods. Several components that eventually played a key role in the development of the automobile were initially invented for use in the bicycle, including ball bearings, pneumatic tires, chain-driven sprockets and tension-spoked wheels. From the beginning and still today, bicycles have been and are employed for many uses. In a utilitarian way, bicycles are used for transportation, bicycle commuting, and utility cycling. It can be used as a 'work horse', used by mail carriers, paramedics, police, messengers, and general delivery services. The bicycle is also used for recreational purposes, such as bicycle touring, mountain biking, physical fitness, and play.
A stanza, as you would know, is a division of a poem consisting of two or more lines arranged together as a unit. You can compare it to a paragraph in a piece of prose writing.
Some of the most common stanza forms are named according to the number of lines in them.
Here are the names of some common stanza forms.
What is the stanzaic pattern of the poem you just read?
The poem is divided into eight stanzas, of which four consist of eight lines (Octave) and the other four have four lines (quatrain) each.
Jump to... Main Course Page The English Channel (Class 7) – The Adventure of.. The English Channel (Class 7) – Windmill in Trou.. The English Channel (Class 7) – A Night with a W.. The English Channel (Class 7) – The Stolen Bacil.. The English Channel (Class 7) – Daffodils (Poem .. The English Channel (Class 7) – Tippitty, the Fl.. The English Channel (Class 7) – What Katy Did (A.. The English Channel (Class 7) – Crabbed Age and .. The English Channel (Class 7) – The Shadow and t.. The English Channel (Class 7) – Travelling Throu.. The English Channel (Class 7) – When the Fish La.. The English Channel (Class 7) – Instead of the W.. The English Channel (Class 7) – Indian Weavers (.. The English Channel (Class 7) – Leading the Way The English Channel (Class 7) – Edward Jenner The English Channel (Class 7) – The Last Stand a.. The English Channel (Class 7) – My Native Land (.. The English Channel (Class 7) – Ranikhet's Gift ..


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text:
BriefInternet
Netflix, Hotstar Join But Amazon Rejects: The Curious Case Of Self-Regulation in India
By Divya Nayak
BriefAbhishek - January 3, 2021 0
Happy B'Day Gordon Moore: One Of The Founding Fathers Of Silicon Valley
Gordon Earle Moore co-founded the paramount Intel Corporation (NASDAQ: INTC) with Robert Noyce in July 1968, which is worth $204.16...
BriefAbhradeep Ghosh - January 13, 2021 0
WhatsApp Might Lose 60 Million Indian Users Post Updated Policy Changes, New Survey Reveals!
The Facebook-owned instant messaging platform's decision to update their privacy and terms of service brought about a...
BriefKhushi Rebekah - January 12, 2021 0
Uber and Ola In Hot Water: India Authorities Launch Fresh Probe!
The Directorate General of Goods and Services Tax Intelligence (DGGI) sent a summons to Uber and Ola...
With more and more film-makers and producers joining the digital bandwagon, rolling down the web route, creative freedom has certainly gone way off the hook, for some! Maybe that's the reason there has been this snap call for attention towards the whole buzz around "self-regulation"!
The Internet and Mobile Association of India (IAMAI) released its OTT self-regulation document called Code of Best Practices for online curated content providers. The different signatories include eight over the top online video streaming platforms, namely Netflix (NASDAQ: NLFX), Hotstar, Voot, Zee5, Arre, SonyLIV, ALT Balaji and Eros Now. However, looks like Amazon Prime has not taken-up this code of self-regulatory best practice in a positive way. According to reports, Amazon Prime isn't a part of this self-regulation.
The code, which was in the making for about a year now, further concretes the regulations for OCCPs to air content that is transparent, and at the same time acceptable for the sensitive audience of the country. This code also highlights the need for protecting consumer interests to its best in order to raise the digital streaming spectrum.
The ABCs of the Proposed Code!
OTT content has not been under India's heavy-handed censorship umbrella. The rules and regulations thus mentioned are administered by the country's Central Board of Film Certification. Apparently, the strict watchdog is considering its chances to subject online streaming content to the same rules.
The signatories of the code have agreed not to entertain the following:
Content maliciously intended at disrespecting the national emblem or national flag.
Content representation of any child engaged in sexual activities, be it real or simulated.
Representation of sexual parts of children for obscene purposes.
Content deliberately and maliciously intending to harm religious sentiments and thus leading to any sort of disharmony or outrage.
Content deliberately and maliciously, promoting or encouraging terrorism or any such form of violence against India.
Content that is formerly banned for display or online distribution under applicable laws or any competent jurisdiction headed by any court.
Amazon's Polarity and The Big Why?
The Seattle-based technology company, offering online video streaming service called Amazon Prime, has opted not to sign up to the code. Apparently, it claims that the existing Indian laws and norm made for online streaming content is sufficient to deal with disapproved content.
It was anticipated much ahead of the whole spark of the aforementioned code that Amazon, Facebook and Google are quite unlikely to sign up for the code. Evident enough, since these tech leviathans may be sort of uncomfortable with the whole move that threatens the regulation of the internet and as a result, sure to interfere with creative freedom.
Amazon has straight-away distanced itself from signing the code, concluding that current laws are enough to fulfil the pursuit taken so draconianly by the IAMAI.
Netflix's Big-Wig Compromise:
After having riled many sections with explicit content, both Netflix and Hotstar agreed to adopt the "best practices internationally" and have settled down with the guideline to self-censor their content they shall further broadcast. This means that there is a high chance that the most awaited sequel of the original Indian series "Sacred Games" shall go underground with any sort of explicit content, be it sexual or violent.
It's common knowledge that both television and film content is regulated in India. However, over-the-top services such as Netflix and likewise have been free from such norms – The reason being that they are relatively new in the streaming hub!
Netflix which has been already under dark clouds with the lawsuit filed against it, over the portrayal of the former prime minister of India, late Rajiv Gandhi, in "Sacred Games" has, maybe, been intimidated and hence, bowed down to this code. Because, why not? What's better than having a concrete code cloaking one's already cold feet!
With the code being out in the open, fresh air of debate has been sparked. With actors, film-makers, critics and likewise pouring in their own opinions, this debate is only going to rage further, lest it goes unnoticed. Given the fact that content on the web is available to everyone, it is going to be quite an uphill climb to curate and control the content being broadcasted online. Again, one question that looms around is although one may try to check on streaming platforms to a certain extent, what about Youtube? Controlling the Indian streaming market may even come easy, but what are the odds against winning the global market?
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India's Biggest IT Firms Reported Sharp Jump in Employee Hiring In FY Q3 2021
Khushi Rebekah - January 14, 2021 0
India's IT sector has been on a steady rise after the turbulence the first half of 2020 caused. On Wednesday, major IT...
In-Depth: Dprime
Will 'TikTok By Microsoft' Be A Winner?
Jayesh Sharma - August 13, 2020 0
For the last two years, TikTok has been in the public eye for all sorts of reasons. First, it was the exploded...
Facebook Subscription Model: Looking Beyond Ad Dollars?
DI Prime Jayesh Sharma - July 30, 2020 0
Seldom do job listings create a stir this gripping. However, when the job listing in question is a stealth post from Twitter,...
Will The Online Food Delivery Market in India End Up Becoming A Two-Horse Race?
DI Prime Abhradeep Ghosh - June 9, 2020 2
It's pretty much evident that the food delivery space in India is all set to get riled up soon enough as one...
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Amazon Follows Netflix's Footsteps: Launches Mobile-Only Plan for Prime Video Users In India!
After Netflix, now Amazon Prime Video has rolled out their mobile-only plan to woo potential Indian smartphone users in the country.
The Facebook-owned instant messaging platform's decision to update their privacy and terms of service brought about a massive ripple effect which is...
Reliance Retail's New Stratagem: Exit JioMart's Direct Sale, Engage Kiranas
Brief Jayesh Sharma - January 13, 2021 0
For a conglomerate to increase its presence and function in the most optimal of ways, the think tank must always be on...
The Directorate General of Goods and Services Tax Intelligence (DGGI) sent a summons to Uber and Ola officials on Monday regarding tax...


We found 0 results for memory care in Oakland, Illinois. We have also included 20 results in surrounding areas. Dementia care costs in Illinois range from about $51 to $314 per day, with a median cost running about $184. The per month expense averages around $5,517 and ranges between $1,519 and $9,425. Annually, the average cost is about $66,198, which is higher than the US average of $60,900.
Oakland is a town in Coles County, Illinois. While the encompassing metro area includes 1,300,421 people, there are only 1,637 residing within the city limits. Residents who are over the age of 55 represent about 34% of the total community.
Oakland has a medium SeniorScore™ of 68. The city has an average per capita income of $22,000 and an average household income is $45,000 (the Illinois state average is $54,000). The current unemployment rate is roughly 12.59% and the mean home price is $99,000, which is less than the state average of $187,500.
Oakland has moderate mean temperatures, with comfortable winters and calm summers. The city gets average amounts of precipitation annually. Oakland has average air quality ratings when compared to other cities in the United States.
To see information on the SeniorScore™ for Oakland, IL, please visit senioradvice.com/seniorscore/senior-living-in-oakland-il.


There is a lot of pressure in the office: one of the employees is completely overburdened and frustrated because she has to do her own work as well as her colleague. What can you as Chef do?
Although she regularly surpasses her own goals with much diligence, commitment and dedication. However, this is not much felt by her colleague. Quite the contrary: It creates so little that a part of their jobs must be taken over by the efficient employee - only in this way can all operations in the department be kept going.
An office classic, as it is in the book. But what happens here? On the one hand, workload and pressure accumulate among an employee; she feels abandoned by her colleague.
In addition, the lack of understanding of the fact that the salary does not reflect their different use is also likely to grow. Finally, it is quite unjust if both are paid almost equally.
The hard-working employee does not want to drag the colleague along with her. However, until a team member addresses such a problem to the supervisor, the proverbial cask is about to overflow. Who likes to go to the boss to blacken a colleague?
The situation is also difficult for the executive. Perhaps the boss can do little to solve the problem. A good opportunity, however, is offered by the employee discussion, because the overworked team member is given priority.
Depending on the flexibility of the corporate structures, a complaint may actually be an impulse, for example to make the remuneration system more equitable. More relevant to the success and satisfaction of the team, however, is that the supervisor fulfills his role more consistently.
Understanding: Signal a colleague complaining, "I understand your point, I realize that the issue of justice is important to you, and I will try to make it happen."
Get away from expectations: To understand the employee, however, does not mean to give him the right. Leaders should dissociate themselves from this - as a rule, such a statement only fosters expectations that are not, or are difficult to fulfill.
Avoid spongy requirements: Say linguistically precise and as concrete as possible, what to do and how you want to see the instructions implemented. With a phrase like, "I expect more quality from you." no employee can do something. How should he know what quality is for the supervisor?
Specific instructions: Instead, targets are more likely to be met when the boss instructs, "By the end of the week, I'll need an overview of all of your channel partners with the following details: xyz, then we'll discuss the next steps."
Transparent reviews: Create transparent structures to assess employees' performance. It is important that all team members can understand them.
Often, unevenly loaded teams are in Company grown over years, because harmony and solidarity are important values in many companies. However, this makes it difficult to evaluate a work performance even critically - at least when appropriate.
Clear structures and performance assessments make the system more transparent, transparent and fair to all employees. On this basis, supervisors can lead more easily and more consistently.
Thanks for the hint. Since you should perhaps think about the change to another department or another company.


Yummy Star is a square game for mobile where you'll have to make 4 stars to form a square. In this fun square game for mobile you'll have to get a square oriented on any position and in any size. This is an online and free square game for mobile!


June 2015 - The Meador family celebrates 100 years of continual ownership and operation of the X Bar Ranch!
January 1, 2015 - X Bar Ranch Nature Retreat announces it is closing all trails to mountain biking effective immediately. This is a very tough decision we've had to make. We would like to thank all of the wonderful riders we had visit over the years. There are many good memories of the 12 X Bar Shoot Out mountain bike races and the hundreds of riders who came to pick their way through the "rock garden" over the past 15+ years- to all of you, many thanks and Happy Trails!
October 8-15, 2012 - Eldorado Star Party 10th Anniversary Event!
Please notice that X Bar Ranch Nature Retreat is in NO WAY related to X Bar Ranch Inc. We have received a number of reports of unfounded charges being made to credit cards by X Bar Ranch Inc. Those charges are NOT being made by or going to X Bar Ranch Nature Retreat.
March 2011 - Feature article, A Ranchland Retreat, appears in The Cattleman.
November 1-7, 2010 – Eldorado Star Party, held annually at X Bar Ranch Nature Retreat.
October 2010 - Feature article, Chasing Monarchs, Catching Stars, appears in Texas Highways magazine.
May 2010 – X Bar Ranch featured in Texas Wildlife, magazine of the Texas Wildlife Association.
April 2010 – Stan Meador featured in eReviw of Tourism Research, Volume 8, Issue 2.
September 2009 – X Bar Ranch Nature Retreat recognized by the Texas Nature Tourism Council and the Texas Travel Industry Association with the inaugural Texas Nature Tourism Achievement Award.


A new PSA for children's mental health organization the Hincks-Dellcrest Foundation shows how much hasn't changed since the '70s.
A lot has changed since the '70s. Car seats for babies and seat belts are now the law. We know it's not OK to smoke in the car with the kids.
But what about what hasn't changed?
Still, a young member of the family who looks like she may be struggling with depression is consistent with many faces we see today.
And that disparity is exactly the point. In 40 years, while we've made advancements in physical health and safety, little progress has been made when it comes to mental health.
"Research into kids' mental health hasn't advanced since the 1970s, which means there's a lack of up-to-date science that could really help children with mental health issues," Donna Duncan, CEO of Hincks-Dellcrest, said in a press release.
The PSA will be shared on the organization's digital and social channels.


San Sebastian, known as Donostia in Euskara, the language of the Basque Country….
Oh god another language to get our heads around !
As we discovered, food in the city of San Sebastian is far more than just something to survive on.
In this corner of Spain, food and all it encompasses is life! , so we've pretty much eaten our way around Spain and this place may just top them all.
This is reason enough to visit San Sebastian, as it's lovely to walk around a city that is this picturesque.
No matter what direction you look, there is either a beautiful building or great scenery to see!
So here are some of our highlights in case you are planning a visit !
El Peine de Los Vientos, translated as the comb of the winds in English, is a series of sculptures at the base of Mount Igeldo. They are kind of strange looking and even stranger close up, as I didn't realise how rusty they were!
The three sculptures attached to the rocks are an interesting sight, as they look like little creatures hanging onto the rocks for dear life!
La Concha Bay is one of the nicest beaches I've ever been to, never mind in Spain. The beach itself is great, even if I was visiting in February , it still looked great. What really makes La Concha special though, is the view across the Bay!
The views across La Concha are spectacular and are just one of the reasons that I feel San Sebastian is perhaps the most beautiful places in Spain! The rock outcrop in the middle of the bay and the hills either side frame the beach and make for an amazing setting!
Parte Vieja, which roughly translates as the Old Town in English, is one of the best places to visit in San Sebastian!
It's very similar to many other old towns in Spain, in that the streets are quite narrow and the buildings are all squashed together with little space around.
Parte Vieja is arguably the beating heart of San Sebastian.
When I was walking around at lunchtime, the area was abuzz with activity. People walking to and from work, going to cafes to get their lunch.
There's plenty of bars here if you fancy sampling the local cuisine as well as the beautiful architecture!
One of San Sebastian's most famous landmarks is the statue of Christ on top of Monte Urgull that looks over the city.
Looking up at San Sebastian's Christ statue from below you don't even realize there is a castle! The Mota Castle, or Castillo de la Mota, has historical significance, some parts date back to the 12th century and it was conquered by Napoleon's French Army.
So these are our favourite bits, but this place has so so much more that it's now on the 'must go back' list .
If you like the pictures in this "San Sebastián, what a great stop over to end our tour of Spain."article, Can i suggest that you follow our Instagram account where you can find a lot more!