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text:
\section{Introduction}
In the last several decades there has been an extensive research effort on developing different metaheuristics for finding near optimal solutions for hard optimization problems. Most metaheuristic approaches focus on how to balance the global search (exploration) and  local search (exploitation) in examining the solution space.  There have been several directions in this research. Early methods include simulated annealing \cite{Sim1} and tabu search \cite{Tabu1,Tabu2} where the search is focused near the best found solution and on mechanisms of escaping local optima. In later stages population based methods have proven to be very powerful. The general approach in such methods is generating a large number of solutions and including different types of learning mechanism. In case of genetic algorithms \cite{GA} and differential evolution \cite{DIF} the main idea is in combining different high quality solutions with the addition of a certain level of randomization. Particle swarm optimization \cite{PSO1,PSO2}   explores the solution space through generating new solutions based on the positions of the globally and locally best found solution. This basic idea has been incorporated in a wide range of similar methods like cuckoo search \cite{CS}, artificial bee colony algorithm \cite{ABC}, bat algorithm \cite{yang2013bat}, krill herd algorithm  \cite{GANDOMI20124831} and many others. (The reader should note that we are fully aware about the controversial discussion with respect to some of these or similar approaches; see \cite{SoerensenITOR}.) The ant colony optimization \cite{dorigo2005ant,Jovanovic20115360} uses a population based method to add a learning mechanism to greedy algorithms.

One of the most common methods for improving population based metaheuristics is  by combining them   with  local searches. The variable neighborhood search \cite{hansen2001variable} metaheuristic focuses on the efficient use of local searches. The performance of the original metaheuristics is often improved by different types of enhancements or by creating hybridized methods that combine one or more of such metaheuristic methods \cite{blum2011hybrid,TSAI200467,MARINAKIS20114684}. The main problems with such methods is the increased complexity of implementation. This problem is most evident if we observe publication in fields other than operational research and applied mathematics. In the vast majority of them only the original, simple to implement, method is used to solve the problem of interest.

The Greedy randomized adaptive search procedure (GRASP) \cite{feo1995greedy,hs87} is one example of how simplicity is important. Although it generally has a worse performance than combining one of the more complex methods with a local search it is extensively used. The advantage of more complex metaheuristics often occurs only for very large problem instances, some examples in case of ACO can be seen in \cite{jovanovic2016ant,jovanovic2018partitioning}. Because of this, it is reasonable to attempt to increase  the size of problems that GRASP can solve, but in a way that there is a  minimal increase in complexity of the original method.

In this paper we focus on developing this type of method through adding a simple learning mechanism to GRASP. Some examples of such methods are GRASP with path relinking \cite{Festa2013} and the dynamic convexized method    		\cite{7984713}. Both of these methods produce a significant level of improvement. Let us note that both of them  use the standard concept of intensifying  the search of the solution space based on the location of globally and locally best found solutions. The basic concept of the proposed  fixed set search method (FSS) is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This idea of exploiting elements that belong to high quality solutions is used in ACO, were the randomized greedy algorithm is directed to chose such elements.
The ideas for developing  this method may be based on earlier notions of chunking \cite{vg98,woo98}, vocabulary building and consistent chains \cite{sv99} as they have been used, e.g., in relation to tabu search. In those notions one relates given solutions of an optimization problem as
composed of parts (or chunks). Considering the traveling salesman problem (TSP), for instance, a part may be a set of nodes to be visited consecutively. Moreover, some parts may be closely related to some other parts so that a corresponding connection can be made between two parts. Similar ideas are even found in the POPMUSIC paradigm \cite{TaillardVoss99}.
 The general idea of the proposed approach is  to fix a set of elements that exist in high quality solutions and dedicate computational effort on ``filling in the gaps".

 This concept is illustrated on the symmetric TSP through adding a learning mechanism to GRASP.  We should note that exact codes for the TSP are available \cite{CONCORDE}. Nevertheless, due to its widespread investigation it seems appropriate to use it for illustration purposes. As it will be seen in the following, this type of approach can easily be added to existing GRASP algorithms and produces a high level of improvement in the quality of found solutions and computational cost.

The paper is organized as follows. In the first section we give a brief description of the GRASP method for the TSP. In the following section we present the FSS and show how it is applied to the TSP. In Section 4, we discuss the  performed computational experiments.

\section{GRASP}

In this section we give a short outline of the GRASP algorithm used for solving the TSP. The pseudocode for the general GRASP algorithm is given in Alg. \ref{Alg:GRASP}.

\begin{algorithm}
\begin{algorithmic}
\While{ Not Stop Criteria Satisfied}
\State{Generate Solutions $S$ using randomized greedy algorithm}
\State{Apply local search to $S$}
\State{Check if $S$ is the new best}
\EndWhile
\end{algorithmic}
\caption{\label{Alg:GRASP} Pseudocode for GRASP}
\end{algorithm}

In the case of the TSP it is common to use a randomization of the nearest neighbor greedy algorithm with a  restricted candidate list (RCL) based on the cardinality of nodes \cite{RCLDLB}. In case of the local search, the most commonly used ones are the 2-OPT \cite{2OPT} and 3-OPT \cite{3OPT} searches. In practice instead of the original versions of the two local searches it is common to use a RCL of edges that will be used for evaluating the proposed improvement.

\section{Fixed set search}

In this section we present the proposed fixed  set search metaheuristic and show how it can be used in combination with GRASP. Before giving the details of the method we give the basic concepts on which it is constructed.

One of the main disadvantages of GRASP is the fact that it does not incorporate any learning mechanism. On the other hand, such an improvement should be designed in a way that it is simple to implement. In this paper we propose one such method called the fixed set search (FSS). In the following  we will assume that a solution $S$ of the problem of interest can be represented in the form of a set. In case of the TSP, the solution $S$ can be viewed as a set of edges $\{ e_1, e_2, .., e_2\}$. The development of FSS is based on two simple premises:

\begin{itemize}
\item{A combinatorial optimization problem is generally substantially easier to solve if we fix some parts of the solution, and in this way lower the size of the solution space that is being explored.}
\item{There are some parts of high quality solutions that are ``easy to recognize". We say this in the sense that they appear in many good solutions. In general there is no need to dedicate a significant amount of computational effort to analyze them. }
\end{itemize}

The general idea of FSS is to fix such ``easy to recognize" parts of good solutions and dedicate computational effort in finding the optimal solution for the corresponding subset of the solution space.  Informally, we take the common sections of good solutions, which we will call the {\it fixed set}, and try to ``fill in the gaps".
In the following sections we will illustrate how this simple idea can be incorporated in the GRASP metaheuristic for the TSP.  The proposed algorithm has three basic steps. The first one is finding a fixed set. The second is adapting the randomized greedy algorithm to be able to use a preselected set of elements. Finally, specify and apply the method which gains experience from previously generated solutions.

\subsection{Fixed set}

As previously stated, to be able to implement the proposed method is is necessary that we can represent a solution of the problem in the form of a set $S$. In case of the TSP, a solution $S$ corresponds to the set of edges that represent a Hamiltonian cycle.  Let us use the notation $\mathcal{P}$ for the set of all the generated solutions (population). In relation, let us define $\mathcal{P}_n$ as the set of $n$ best generated solutions based on the objective function, the path length. Further, let us use the notation $F$ for a {\it fixed set} that will be used in the search. In the following we define a method for finding a {\it fixed set} $F$ for a population of solutions $\mathcal{P}$. The proposed method should satisfy the following requirements:
\begin{itemize}
\item{(R1) A generated fixed set $F$ should consist of elements of high quality  solutions.}
\item{(R2) The method should be able to generate  many different random fixed sets  that can be used to generate new high quality solutions.}
\item{(R3) A generated fixed set $F$ can be used to generate a feasible solution. More precisely, there exists a feasible solution $S$ such that $F \subset S$}
\item{(R4) Ability to control  the size of the generated fixed set $|F|$.}
\end{itemize}

The first two requirements can be achieved if we  only use some randomly selected high quality solutions for generating the fixed sets. This can be achieved by simply selecting $k$ random solutions from the set  $\mathcal{P}_n$.  Let us define $\mathcal{S}_{kn}$ as the set of selected solutions. The initial idea is to use the intersection of all the solutions in $\mathcal{S}_{kn}$ for the fixed set $F$. The problem is that we have no control over the size of the intersection. A simple idea to control the size of $F$ is instead of using the intersection of $\mathcal{S}_{kn}$, is to select the elements (edges) that are a part of the highest number of solutions. The problem with this approach is that such a selection can potentially contain edges that could not be used to generate a feasible solution.

Both of these issues can be avoided if a base solution $B \in \mathcal{P}_m$ is used in generating a fixed set $F$.  More precisely, we can select the elements of $B$ that occur most frequently in $\mathcal{S}_{kn}$. Let us define this procedure more formally. We will assume that we are finding a fixed set $|F| = Size$ for a set of solutions $\mathcal{S}_{kn} = \{S_1, .., S_k\}$ and base solution $B = \{ e_1, ... e_m\}$. Let use define the function $C(e_x, S)$ which is equal to $1$ if $e_x \in S$ and $0$ otherwise. Using $C(e_x, S)$ we can define the  function that counts the number of times an edge $e_x$ occurs in the $\mathcal{S}_{kn}$ as follows.

\begin{equation}
O(e_x, \mathcal{S}_{kn}) = \sum_{S \in \mathcal{S}_{kn}}C(e_x,S)
\end{equation}

Now,  we can define $F \subset B$ as the set of edges $e_x$ that have the largest value of $O(e_x, \mathcal{S}_{kn})$. In relation let us define function $F = Fix(B,\mathcal{S}_{kn}, Size)$ that corresponds to the fixed set generated for a base solution $B$, a set of solutions $\mathcal{S}_{kn}$ having $Size$ elements.  An illustration of the method for generating a fixed set for the TSP can be seen in Fig. \ref{fig:FixSet}.

\begin{figure}[thb]
\centering
\includegraphics[width=0.85\textwidth]{fixset}

\caption{\label{fig:FixSet} Illustration of generating a fixed set. The input is $\mathcal{S}_{kn}$ (top left), a set of four randomly selected solutions out of the six best ones, and a base solution $B$ (left bottom). The value on an edge of $B$ represent the number of occurrences of that edge in elements of $\mathcal{S}_{kn}$. The edges on the right hand side present the corresponding fixed set of size four.}
\end{figure}

\subsection{Randomized greedy algorithm with preselected elements}

To be able to use the fixed set within a GRASP setting we need to adapt the greedy randomized algorithm. Let us first note that in case of the TSP, the fixed set $F$ will consist of several paths (sequence of edges which connect a sequence of vertices) of graph $G$.  This effects the greedy algorithm in two ways.  First, the inside nodes of the path should be removed from the candidate list.  Secondly, if a node that is a start or end node of a path in the fixed set, is added to the current partial solutions the whole path must be added in the proper direction. Pseudocode for the adapted greedy algorithm can be seen in the Alg. \ref{Alg:RGF}.

\begin{algorithm}
\begin{algorithmic}
\State{Set $Paths$ to all paths in $F$}
\State{$Candidates = V$}
\State{$Candidates = Candidates \setminus F$}
\ForAll{$p \in Paths$}
\State $Candidates = Candidates \cup p[First] \cup p[Last]$
\EndFor
\State{Select Random start city from $Candidates$}
\While{Not Completed Tour}
\State{Select next city $c$ using $RCL$}
\ForAll{$p \in Paths$}
\If {$(c = p [First]) \wedge (c = p [Last])$}
\State{Add path $p$ to current solution in correct direction}
\State{{\textbf{break}}}
\EndIf
\EndFor
\EndWhile
\end{algorithmic}
\caption{\label{Alg:RGF} Pseudocode for Greedy algorithm with preselected elements}
\end{algorithm}

In relation, let us define the function $S = RGF(F)$, for a fixed set $F$, as the solution acquired using this algorithm.

\subsection{Learning mechanism}

In this section we present the FSS which is used as a learning mechanism for GRASP.  Before presenting details of the proposed methods, let us first make a few observations. In the general case the early iterations of GRASP frequently manage to improve the quality of the best found solution. At later stages such improvements become significantly less frequent and the method becomes dependent on ``lucky" hits. The idea is to use a fixed set $F$, for some promising region of the solution space, generate a solution $S = RGF(F)$ and apply a local search to $S$.  In this way we increase the probability that a higher quality solution will be found. An important aspect is how to select the size of the fixed set. In case it is small, it efficiently performs a global search but after a certain number of executions, as in the case of GRASP, it will to a large extend be dependent on ``lucky" hits. On the other hand if $F$ is large, it will only explore the parts of the solution space that are close to already generated solutions. As a consequence, there is a high risk of being trapped in locally optimal solutions.

This indicates that the size of the fixed set should be adapted during the execution of the algorithms.  For simplicity, we can a priori define an array $Sizes$  of fixed set sizes that will be tested, using the following formula:

\begin{equation}
\label{FixedSizes}
 Sizes[i] = |V| - \frac{V}{2^i}
\end{equation}

In \eqref{FixedSizes}, $V$ represents the set of nodes of the graph on which the TSP is being solved. The maximal value of an element in the array $Sizes$ is chosen based on the problem being solved. Using this array let us give an outline of the FSS. We will first generate an initial population of solutions $\mathcal{P}$ by executing GRASP for $N$ iterations. This initial population will be used to find the fixed sets. We start from a small fixed set and generate solutions until stagnation, in the sense of not finding new best solutions for a large number of iterations, has occurred. When stagnation occurs, we increase the size of the fixed set (selecting the next element of $Sizes$) and repeat the procedure. In this way  a more focused exploration of the search space is executed. This procedure is repeated until the largest element in $Sizes$ is tested.

At this stage it is expected that the set $\mathcal{P}_m$ of $m$ best solutions has significantly changed and contains higher quality solutions than in the initial population. Because of this,  there is a potential that even for smaller sized fixed sets, since they are now generated using better solutions,  there is a higher probability of finding new quality solutions. So, we can repeat the same procedure from the smallest fixed set size. Let us note that after a large number of solutions is generated the new solutions acquired using small fixed sets are rarely new best ones. The importance of their revisit  is in generating new types of high quality solutions. In case not even high quality solutions, not being one of the  $m$ best ones, can be found, small fixed sets can be excluded  from the search. The pseudocode for FSS can be seen in Alg. \ref{Alg:FSS}.

\begin{algorithm}
\begin{algorithmic}

\State{Initialize $Sizes$}
\State $Size = Sizes.Next$
\State Generate initial population  $\mathcal{P}$ using $GRASP(N)$
  \State
 \While{(Not termination condition)}
 \State
 \State{Set $\mathcal{S}_{kn}$ to random $k$ elements of $\mathcal{P}_n$}
 \State{Set $B$  to a random solution in $\mathcal{P}_m$}
 \State{$F = Fix(B, \mathcal{S}_{kn}, Size)$}
 \State
  \State{$S = RGF(F)$}
  \State{Apply local search to $S$}
  \State{$\mathcal{P} = \mathcal{P} \cup \{S\}$}
   \State
 \If{Stagnant Best Solution}
  \If{(Stagnant Candidates) $\wedge$ ($Size = Min(Sizes)$)}
		 \State	{Remove $Size$ from $Sizes$}
 \EndIf

 \State	{$Size = Sizes.Next$}
 \EndIf
  \State
 \EndWhile
\end{algorithmic}
\caption{\label{Alg:FSS} Pseudocode for the fixed set search}
\end{algorithm}

In the pseudocode for the FSS, the first step is initializing the sizes of fixed sets using  \eqref{FixedSizes}.  Next the initial population of solutions is generated performing $N$ iterations of the basic GRASP algorithm. The current size of the fixed set $Size$ is set to the smallest fixed set size. In the main loop, we first randomly generate a set of solutions $\mathcal{S}_{kn}$ by selecting $k$ elements from $\mathcal{P}_n$.  Next, we select a random solution $B$  out of the set $\mathcal{P}_m$. Using $\mathcal{S}_{kn}$, $B$ and $Size$ we generate the fixed set $F$ as described in the previous text. Using $F$ we generate a solution $S= RGF(F)$ using the randomized greedy algorithm with preselected elements. Next, we apply the local search to $S$ and check if we have found a new best solution and add it to the set of generated solutions $\mathcal{P}$. After a new solution is generated we check the two stagnation conditions. The first one checks if the search for the best solution has become stagnant. If so, we set the value of $Size$ to the next value in $Sizes$. Let us note, that the next size is the next larger element of array $Sizes$. In case $Size$ is already the largest size, we select the smallest element in $Sizes$. Before  updating $Size$, we also check if stagnation has occurred in the search of high quality solutions (we have not found a solution which is among the best $n$ or $m$ ones). In case this is true the current $Size$ is removed from $Sizes$. It is important to note, that this is only done if $Size$ is equal to the smallest member of $Sizes$. This is due to the fact that if we have managed to find an improvement for a smaller fixed set than $Size$, it is expected that we have just been ``unlucky" and there is no need to remove this value from the search. This procedure is repeated until the array $Sizes$ is empty or some other termination criterion is satisfied.

\section{Results}

In this section we present the results of our computational experiments used to evaluate the performance of the proposed method. This has been done in a comparison with the GRASP algorithm presented in \cite{Marinakis2005} and the dynamic convexized method (DCTSP) from \cite{7984713}. The focus of the comparison is on the quality of found solutions.

The FSS and GRASP have been evaluated for both 2-OPT and 3-OPT as local searches. In case of the DCTSP a combination of 2-OPT and 3-OPT has been used as a local search. GRASP has been included to be able to evaluate the effect of the learning mechanism included in the FSS. DCTSP has been used in the comparison since it is a good representative of a metaheuristic whose search is focused on regions near the best solution. In case of the FSS the randomized greedy algorithm used a RCL with 20 elements. In case of both local searches, 2-OPT and 3-OPT, the same size of RCL has been used. To increase the computational efficiency of the local searches we have used the standard approach of ``don't look bits" (DLBs) \cite{RCLDLB}. Let us note, that  when we apply the local search inside the main loop of FSS some of the DLBs could be preset based on the fixed set which significantly decreased the computational cost. The parameters for FSS are the following, the  $k=10$ random  solutions are selected from the best $n=500$ ones for the set of solutions $\mathcal{S}_{kn}$. The base solution is selected from the $m=100$ best solutions. The size of the initial population was $100$. The stagnation criterion was that no new best or high quality solution has been found in the last $Stag=100$ iterations for the current fixed set size. The FSS and GRASP with 2-OPT have been implemented in C\# using Microsoft Visual Studio 2017.  The calculations have been done on a machine with Intel(R) Core(TM) i7-2630 QM CPU \@ 2.00 Ghz, 4GB of DDR3-1333 RAM, running on Microsoft Windows 7 Home Premium 64-bit.

The comparison of the methods has been done on the standard benchmark library TSPLIB \cite{TSPLIB}. The test instances are the same as in \cite{7984713}. A  total of 48 test instances with Euclidean distances are used,  with the number of nodes ranging from 51 to 2392. Note, that in FSS the fact that distances are Euclidean is not exploited. The termination criterion was that a maximal number of solutions has been generated. The limit was the same as in \cite{7984713}, more precisely in case of problem instances having less than a 1000 nodes it was $100|V|$, with $V$ the set of nodes of the considered problem instance,  and in case of larger problem instances it was $10|V|$. For each of the problem instances a single run of each of the methods has been performed, as in \cite{7984713}. The results of the computational experiments can be seen in Table \ref{table:Res}. In it, the results for DCTSP are taken from \cite{7984713} and for GRASP with 3-OPT are taken from \cite{Marinakis2005}. Note, that the results for GRASP-3OPT are very similar to the ones from \cite{Marinakis2005} and to our implementation.

\begin{table*}[htb]
\footnotesize
\center
\scriptsize
\caption{\label{table:Res}Comparison of the proposed algorithms with GRASP and DCTSP for different TSPLIB instances.}

\begin{tabularx}{420pt}{X*{13}{c}}

\toprule
 &   \multicolumn{6}{c}{Tour Length}  &&\multicolumn{5}{c}{Relative Error [\%]}\\
  \cmidrule{2-7}   \cmidrule{9-13}
Instance  & \multicolumn{2}{c}{2OPT} &\multicolumn{3}{c}{3OPT} & Known Best &  &
\multicolumn{2}{c}{2OPT} &\multicolumn{3}{c}{3OPT}\\
  \cmidrule(l){2-3}   \cmidrule(l){4-6}   \cmidrule(l){9-10}   \cmidrule(l){11-13}
   & GRASP & FSS &   GRASP & DCTSP & FSS& &  &  GRASP & FSS &   GRASP & DCTSP & FSS\\

\midrule
eil51 & 426 & 426 & 426 & 426 & 426 & 426 &  & 0.00 & 0.00 & 0.00 & 0.00 & 0.00\\
berlin52 & 7542 & 7542 & 7542 & 7542 & 7542 & 7542 &  & 0.00 & 0.00 & 0.00 & 0.00 & 0.00\\
pr76 & 108351 & 108159 & 108159 & 108159 & 108159 & 108159 &  & 0.18 & 0.00 & 0.00 & 0.00 & 0.00\\
rat99 & 1223 & 1211 & 1211 & 1211 & 1211 & 1211 &  & 0.99 & 0.00 & 0.00 & 0.00 & 0.00\\
kroA100 & 21282 & 21282 & 21282 & 21282 & 21282 & 21282 &  & 0.00 & 0.00 & 0.00 & 0.00 & 0.00\\
kroB100 & 22157 & 22141 & 22141 & 22141 & 22141 & 22141 &  & 0.07 & 0.00 & 0.00 & 0.00 & 0.00\\
kroC100 & 20802 & 20749 & 20749 & 20749 & 20749 & 20749 &  & 0.26 & 0.00 & 0.00 & 0.00 & 0.00\\
kroD100 & 21468 & 21309 & 21294 & 21294 & 21294 & 21294 &  & 0.82 & 0.07 & 0.00 & 0.00 & 0.00\\
kroE100 & 22106 & 22100 & 22068 & 22068 & 22068 & 22068 &  & 0.17 & 0.15 & 0.00 & 0.00 & 0.00\\
rd100 & 7960 & 7910 & 7910 & 7910 & 7910 & 7910 &  & 0.63 & 0.00 & 0.00 & 0.00 & 0.00\\
eil101 & 638 & 629 & 629 & 629 & 629 & 629 &  & 1.43 & 0.00 & 0.00 & 0.00 & 0.00\\
lin105 & 14379 & 14379 & 14379 & 14379 & 14379 & 14379 &  & 0.00 & 0.00 & 0.00 & 0.00 & 0.00\\
pr107 & 44394 & 44303 & 44303 & 44303 & 44303 & 44303 &  & 0.21 & 0.00 & 0.00 & 0.00 & 0.00\\
pr124 & 59159 & 59030 & 59030 & 59030 & 59030 & 59030 &  & 0.22 & 0.00 & 0.00 & 0.00 & 0.00\\
ch130 & 6135 & 6110 & 6110 & 6110 & 6110 & 6110 &  & 0.41 & 0.00 & 0.00 & 0.00 & 0.00\\
pr136 & 98614 & 96920 & 96772 & 96772 & 96772 & 96772 &  & 1.90 & 0.15 & 0.00 & 0.00 & 0.00\\
pr144 & 58554 & 58537 & 58537 & 58537 & 58537 & 58537 &  & 0.03 & 0.00 & 0.00 & 0.00 & 0.00\\
ch150 & 6586 & 6549 & 6528 & 6528 & 6528 & 6528 &  & 0.89 & 0.32 & 0.00 & 0.00 & 0.00\\
kroA150 & 26768 & 26524 & 26524 & 26525 & 26524 & 26524 &  & 0.92 & 0.00 & 0.00 & 0.00 & 0.00\\
pr152 & 74315 & 73682 & 73682 & 73682 & 73682 & 73682 &  & 0.86 & 0.00 & 0.00 & 0.00 & 0.00\\
rat195 & 2391 & 2330 & 2331 & 2323 & 2323 & 2323 &  & 2.93 & 0.30 & 0.34 & 0.00 & 0.00\\
kroA200 & 29803 & 29368 & 29380 & 29382 & 29368 & 29368 &  & 1.48 & 0.00 & 0.04 & 0.00 & 0.00\\
kroB200 & 29909 & 29447 & 29482 & 29437 & 29437 & 29437 &  & 1.60 & 0.03 & 0.15 & 0.00 & 0.00\\
ts225 & 127485 & 127301 & 126643 & 126643 & 126643 & 126643 &  & 0.66 & 0.52 & 0.00 & 0.00 & 0.00\\
pr226 & 80714 & 80369 & 80414 & 80369 & 80369 & 80369 &  & 0.43 & 0.00 & 0.06 & 0.00 & 0.00\\
gil262 & 2456 & 2378 & 2385 & 2379 & 2378 & 2378 &  & 3.28 & 0.00 & 0.29 & 0.04 & 0.00\\
pr264 & 50744 & 49135 & 49135 & 49135 & 49135 & 49135 &  & 3.27 & 0.00 & 0.00 & 0.00 & 0.00\\
a280 & 2658 & 2584 & 2589 & 2579 & 2579 & 2579 &  & 3.06 & 0.19 & 0.39 & 0.00 & 0.00\\
pr299 & 49522 & 48256 & 48235 & 48207 & 48191 & 48191 &  & 2.76 & 0.13 & 0.09 & 0.03 & 0.00\\
rd400 & 15986 & 15322 & 15385 & 15299 & 15284 & 15281 &  & 4.61 & 0.27 & 0.68 & 0.12 & 0.02\\
fl417 & 12066 & 11883 & 11895 & 11883 & 11871 & 11861 &  & 1.73 & 0.19 & 0.29 & 0.19 & 0.08\\
pr439 & 110564 & 107259 & 107401 & 107303 & 107217 & 107217 &  & 3.12 & 0.04 & 0.17 & 0.08 & 0.00\\
pcb442 & 52790 & 50945 & 50946 & 50860 & 50846 & 50778 &  & 3.96 & 0.33 & 0.33 & 0.16 & 0.13\\
d493 & 36192 & 35055 & 35253 & 35136 & 35018 & 35002 &  & 3.40 & 0.15 & 0.72 & 0.38 & 0.05\\
rat575 & 7143 & 6795 & 6863 & 6814 & 6776 & 6773 &  & 5.46 & 0.32 & 1.33 & 0.61 & 0.04\\
p654 & 35113 & 34812 & 34707 & 34658 & 34645 & 34643 &  & 1.36 & 0.49 & 0.18 & 0.04 & 0.01\\
d657 & 51226 & 49258 & 49531 & 49110 & 49014 & 48912 &  & 4.73 & 0.71 & 1.27 & 0.40 & 0.21\\
rat783 & 9352 & 8869 & 8897 & 8848 & 8815 & 8806 &  & 6.20 & 0.72 & 1.03 & 0.48 & 0.10\\
pr1002 & 276251 & 264737 & 262060 & 260218 & 259512 & 259045 &  & 6.64 & 2.20 & 1.16 & 0.45 & 0.18\\
pcb1173 & 61210 & 57788 & 57676 & 57061 & 56965 & 56892 &  & 7.59 & 1.57 & 1.38 & 0.30 & 0.13\\
d1291 & 54537 & 51026 & 51616 & 51099 & 50862 & 50801 &  & 7.35 & 0.44 & 1.60 & 0.59 & 0.12\\
rl1304 & 270441 & 255867 & 255185 & 253842 & 253361 & 252948 &  & 6.92 & 1.15 & 0.88 & 0.35 & 0.16\\
rl1323 & 288538 & 271837 & 273115 & 271914 & 270678 & 270199 &  & 6.79 & 0.61 & 1.08 & 0.63 & 0.18\\
fl1400 & 21044 & 20398 & 20310 & 20167 & 20149 & 20127 &  & 4.56 & 1.35 & 0.91 & 0.20 & 0.11\\
fl1577 & 23274 & 22512 & 22427 & 22352 & 22300 & 22249 &  & 4.61 & 1.18 & 0.80 & 0.46 & 0.23\\
rl1889 & 339151 & 322883 & 319250 & 317825 & 317801 & 316536 &  & 7.14 & 2.01 & 0.86 & 0.41 & 0.40\\
d2103 & 86179 & 81197 & 81312 & 81078 & 80551 & 80450 &  & 7.12 & 0.93 & 1.07 & 0.78 & 0.13\\
pr2392 & 409970 & 387169 & 386017 & 380030 & 379307 & 378032 &  & 8.45 & 2.42 & 2.11 & 0.53 & 0.34\\
\midrule
\multicolumn{7}{l}{Number of found best known solutions}  &  & 2 & 20 & 22 & 27 &30\\
\multicolumn{7}{l}{Average relative error}  &  & 2.73 & 0.40 &0.39  & 0.15 &0.05\\
\bottomrule

\end{tabularx}
\end{table*}

From the results in Table \ref{table:Res}, we can first observe that the GRASP-2OPT has a significantly worse performance than all the other methods finding best known solution for only 4 test instances and having an average relative error of 2.73\%. In case of FSS-2OPT, the improvement is very significant: 20 known best solutions are found and the average relative error was 0.40 \%.  What is very interesting is that FSS-2OPT performs only slightly worse than GRASP-3OPT which finds 22 known best solutions and has an average relative error of 0.39\%. This indicates that the use of the proposed method can be very beneficial in case of less powerful local searches. Although FSS-2OPT had an overall worse performance than DCTSP, it managed to find better solutions for 5 problem instances.  From the results in Table \ref{table:Res}, it is evident that FSS-3OPT has the best performance. It manages to find better solutions than all the other methods for all instances or equal in case methods have found best known solutions. It managed to find 3 more known optimal solutions than DCTSP and has a notable improvement in relative average error. It is important to note that FSS-3OPT never had an error greater than 0.40\%.

The parameters selected for specifying FSS have been chosen empirically through extensive testing.  Overall the FSS is not highly sensitive to these parameters. The parameter $k$ used to specify the number of solutions selected for  generating the set $S_{kn}$ had the following effect. In case of small values, the selection would result in highly randomized fixed sets. The reason for this is that there are no clear ``good elements", especially in case of larger problem instances where there are not  many common elements in all the solutions. In case of large values of $k$, the method would select very similar fixed sets. The parameter $m$ used to specify the population from which the base solution would be selected has the following effect. In case of small values of $m$ the convergence speed would initially be very fast but would quickly get trapped in locally optimal solutions. This is due to the fact that it becomes very hard to find new high quality solutions. Such values of $m$ are useful in case we can only generate a small number of solutions. In case of high values of $m$, the convergence speed is much slower. The problem  is that when the fixed set is generated for a lower quality solution $B$, although the method manages to find solutions of higher quality than $B$, it is unlikely that very high quality ones will be found. The effect of parameter $n$ for specifying the size of the population used for generating $S_{kn}$ had a similar effect but to a much lower extent. We found that the best choice of parameters for stagnation, both for finding best and high quality solutions, was the same as the number of iterations from which GRASP would rarely find new best solutions. In general, it is important to avoid very small values for this parameter because it results in prematurely stopping the evaluation of small fixed sets.

\begin{figure}[ht]
\centering
\includegraphics[width=0.75\textwidth]{rd400}
\caption{Average solution quality of 10 independent  runs of FSS and GRASP for the TSPLIB problem instance {\it rd400}.}
\label{fig:pr264}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width=0.75\textwidth]{pr1002}
\caption{Average solution quality of 10 independent  runs of FSS and GRASP for the TSPLIB problem instance {\it pr1002}.}
\label{fig:pr1002}
\end{figure}

In Table \ref{table:Res} we did not include computational times, since they are highly dependent on structures used for implementing the local searches. We would like to note that in case of our implementation of FSS and GRASP there was a significant decrease in computational time. This is due to the fact of a smaller candidate set for the greedy algorithm. The second reason is that  the number of iterations needed to generate the solution was significantly lower. As it is well known, the computational cost of 2-OPT and 3-OPT local searches is significantly higher than for generating the initial solution. An extensive analysis of the computational cost of 2-OPT can be found in \cite{Englert2014}. In case of FSS, we exploit the fact that the fixed set is a subset of a locally optimal base solution $B$ through ``don't look bits". More precisely, the DLBs of all the inner points of paths in the fixed set can be preset. Note that, the number of preset DLBs is close to the size of the fixed set. In practice this means instead of having the computational cost of the first iteration of 2-OPT being proportional to $|V|C$, were $C$ is the size of  the RCL, it is close to  $(|V| -|F|) C$. Similar analysis can be done for the 3-OPT local search. In case of very large fixed sets, the time FSS generated a new solution and applied the local search was a fraction of the time need to accomplishing the same task in GRASP.  It is expected that a similar behavior would be present in applying FSS to other combinatorial problems.

This decrease in computational cost of the FSS compared to GRASP directly effects the convergence speed.  This is illustrated in Fig. \ref{fig:pr264}, \ref{fig:pr1002} for representative problem instances. In each of the figures the convergence speed of the average solution length for ten independent runs of GRASP and FSS, with 2-OPT and 3-OPT used as local searches, are shown. It can be observed that there is a drastic increase in the convergence speed after the initial population is generated for the FSS.

\section{Conclusion}

In this paper we have presented a new metaheuristic called fixed set search that exploits the common elements of high quality solutions. The proposed metaheuristic represents a method of adding a learning mechanism to the GRASP metaheuristic. It is expected that FSS can be applied to a wide range of problems since the only requirement is that the solution can be represented in a set form. A very important aspect of FSS is the simplicity in which a GRASP algorithm can be adapted to it. This is done with two basic steps. Firstly, the  randomized greedy algorithm, used in the GRASP, is adapted to a setting were some elements are preselected. We have shown that this can be trivially achieved in case of the TSP, and it is expected that this is the case for many other combinatorial problems. Secondly, the method for generating a fixed set needs to be implemented which consists in selecting several solutions and tracking the number of times their elements occur in a selected base solution.

  We have illustrated the effectiveness of the proposed approach on the TSP. Our computational experiments have shown that the proposed method has a significantly better performance than the basic GRASP approach when both solution quality and convergence speed are considered. Further, we have shown that the approach has a considerably better performance than the  dynamic convexized method applied to the TSP in case 3-OPT is used as a local search. The proposed method has proven very efficient in improving the performance of GRASP in case of a less powerful local search.

  It is important to note that there is a wide range of potential improvements to the proposed method. Some examples are having a more intelligent method of selecting the solutions used in generating the fixed set; or adapting the computational effort used to solve the subproblem related to a specific fixed set. Our objective was to show that even in the most basic form the proposed method can produce a significant improvement. We would like to note that the concept of using a fixed set can potentially be used to hybridize other metaheuristics like ACO,  genetic algorithms and similar, for solving large scale problems through focusing the search in some promising areas of the solution space. On the other hand the idea of fixing elements of a solution can easily be included in mixed integer programs so there is a potential of adapting FSS to a matheuristic setting.

redpajama_set_name: RedPajamaArXiv


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Adeseye "Seye" Akinola Ogunlewe (* 30. August 1991 in Lagos) ist ein nigerianischer Leichtathlet, der sich auf den Sprint spezialisiert hat.

Sportliche Laufbahn
Erste Erfahrungen bei internationalen Meisterschaften sammelte Seye Ogunlewe bei den Commonwealth Games 2014 im schottischen Glasgow, bei denen er über 200 Meter mit 21,11 s in der ersten Runde ausschied. Kurz darauf schied er bei den Afrikameisterschaften in Marrakesch ebenfalls über 200 Meter in der ersten Runde aus, gewann aber als Vorläufer der nigerianischen 4-mal-100-Meter-Staffel die Goldmedaille. 2015 nahm Ogunlewe an den Afrikaspielen in Brazzaville teil und belegte dort im Finale mit 10,45 s den fünften Platz. 2016 qualifizierte er sich erstmals für die Olympischen Spiele in Rio de Janeiro, bei denen er über 100 Meter mit 10,26 s im Vorlauf ausschied. Zwei Jahre später belegte er bei den Commonwealth Games im australischen Gold Coast im 100-Meter-Lauf in 10,19 s den vierten Platz und wurde mit der nigerianischen 4-mal-100-Meter-Staffel im Finale disqualifiziert. Im August gewann er bei den Afrikameisterschaften im heimischen Asaba in 38,74 s die Silbermedaille mit der Staffel hinter Südafrika. Zudem belegte er über 100 Meter in 10,45 s den fünften Platz. 2019 nahm er erneut an den Afrikaspielen in Rabat teil und erreichte dort über 100 Meter das Halbfinale, in dem er mit 10,45 s ausschied. Zudem kam er in der Staffel im Vorlauf zum Einsatz und trug somit zum Gewinn der Silbermedaille bei. Dadurch erhielt er auch einen Startplatz in der Staffel für die Weltmeisterschaften in Doha im Oktober, wurde dort aber in der Vorrunde disqualifiziert. 2022 erreichte er bei den Afrikameisterschaften in Port Louis das Halbfinale über 100 Meter und schied dort mit 10,29 s aus und belegte mit der Staffel in 39,98 s den vierten Platz.

Zwischen 2015 und 2017 wurde Ogunlewe nigerianischer Meister im 100-Meter-Lauf. Er ist der Sohn des nigerianischen Politikers Adeseye Ogunlewe und lebte ab 2008 in Irland und studierte anschließend an der University of Essex und schloss dort ein Studium für Law and Politics ab.

Persönliche Bestzeiten
 100 Meter: 10,11 s (+1,7 m/s), 9. Juni 2019 in Rehlingen
 60 Meter (Halle): 6,68 s, 27. Januar 2013 in Lee Valley
 200 Meter: 20,99 s (0,0 m/s), 23. April 2016 in Waco

Weblinks

100-Meter-Läufer (Nigeria)
200-Meter-Läufer (Nigeria)
4-mal-100-Meter-Staffel-Läufer (Nigeria)
Olympiateilnehmer (Nigeria)
Teilnehmer der Olympischen Sommerspiele 2016
Teilnehmer an den Commonwealth Games (Nigeria)
Teilnehmer an den Afrikaspielen (Nigeria)
Afrikameister (4-mal-100-Meter-Staffel, Leichtathletik)
Nigerianischer Meister (Leichtathletik)
Absolvent der University of Essex
Nigerianer
Sportler (Lagos)
Geboren 1991
Mann

redpajama_set_name: RedPajamaWikipedia


Schofield Interiors' kitchens offer a factory built, fully assembled, cam and doweled cabinet. All cabinets are constructed with 18mm MFC colour co-ordinated board and are made with 18mm Solid tops and backs. Each cabinet is complimented with Blum soft close hinges and drawer packs are fitted with Blum soft close tandem drawer boxes. The cabinets are edged using a 2mm ABS edging to the front as standard. All base units have a standard 50mm services void and are 560mm overall depth. All wall units have a standard 20mm void and are 300mm overall depth. All cabinets can be made to bespoke sizes. Here are some samples of the many different kitchen door ranges we do here at Schofield Interiors. We have samples of all the doors in our showroom for you to view.


The Overcooked Gourmet Edition stirs together the smash hit co-op cooking game and the Lost Morsel content pack into one delicious package that will test your culinary skills to the limit! The Overcooked Lost Morsel content pack continues the chefs' crazy culinary adventure through six new campaign levels, featuring challenging new kitchens set in an exotic jungle world, a new vehicle to navigate the world map in and six new chef characters to unlock!
Cram the turkey into the oven, pour yourself a Christmas tipple and settle down for the gourmet treat of the year! The Overcooked Holiday Bundle brings together the smash hit co-op cooking game, the Lost Morsel DLC pack and the all-new Christmas DLC - it's a feast of culinary delights!


$5 OFF Battery Service or ReplacementReceive $5 off Battery Service or Replacement. One special per visit. Not valid with other offer or special. Coupon must be presented in advance. Some limitations may apply.


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Johnny Depp, Jeff Beck Accused of Stealing Lyrics on Their New LP
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Erica Banas // Rock Music Reporter August 5th, 2022
Johnny Depp and Jeff Beck released an album together in July titled 18. That album features a song titled "Sad Motherf—in' Parade," and it's billed as a "Johnny Depp original." However, it might not be as original as it claims.
Per Rolling Stone, the track's lyrics are a near word-for-word rip-off from a poem titled "Hobo Ben." (The outlet published and compared the very NSFW lyrics for comparison which can be read here.
The poem is featured in the 1974 book Get Your Ass in the Water and Swim Like Me by Bruce Jackson. Jackson's book is a collection of "toasts," which Rolling Stone described as "a wildly outlandish, funny, ribald form of narrative Black folk poetry." (An album featuring recordings of these toasts was released in 1976.) "Hobo Ben," in particular, was the original work of a man referred to as Slim Wilson. Jackson met Wilson while in the Missouri State Penitentiary in 1964.
Jackson told Rolling Stone, "The only two lines I could find in the whole piece that [Depp and Beck] contributed are 'Big time motherf—er' and 'Bust it down to my level.' Everything else is from Slim's performance in my book. I've never encountered anything like this. I've been publishing stuff for 50 years, and this is the first time anybody has just ripped something off and put his own name on it."
Rolling Stone also shared a statement from a spokesperson for Depp and Beck's album saying, "We are reviewing the enquiry relating to the song 'Sad Motherf—in' Parade' on the '18' album by Jeff Beck and Johnny Depp. If appropriate, additional copyright credits will be added to all forms of the album."
In the lead-up to the album's release, Beck said in a statement about Depp, "I haven't had another creative partner like him for ages. He was a major force on this record. I just hope people will take him seriously as a musician because it's a hard thing for some people to accept that Johnny Depp can sing rock and roll."
As of publishing, neither Depp nor Beck have responded to the report about the lyrics featured on Sad Motherf—in' Parade."
Johnny Depp: Rockstar
Hollywood Vampires Perform At Hessentag In Herborn
HERBORN, GERMANY - MAY 29: Actor/Musician Johnny Depp of Hollywood Vampires performs onstage at Hessentags-Arena during the 56th Hessentag on May 29, 2016 in Herborn, Germany. (Photo by Andreas Rentz/Getty Images)
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HERBORN, GERMANY - MAY 29: Actor/Musician Johnny Depp and Musician Joe Perry of Hollywood Vampires perform onstage at Hessentags-Arena during the 56th Hessentag on May 29, 2016 in Herborn, Germany. (Photo by Andreas Rentz/Getty Images)
The 58th GRAMMY Awards – Red Carpet
LOS ANGELES, CA - FEBRUARY 15: (L-R) Singer Alice Cooper, musician Joe Perry and actor/musician Johnny Depp of Hollywood Vampires attend The 58th GRAMMY Awards at Staples Center on February 15, 2016 in Los Angeles, California. (Photo by Larry Busacca/Getty Images for NARAS)
The 58th GRAMMY Awards – Show
LOS ANGELES, CA - FEBRUARY 15: (L-R) Actor/musician Johnny Depp, singer Alice Cooper and musician Joe Perry of Hollywood Vampires perform onstage during The 58th GRAMMY Awards at Staples Center on February 15, 2016 in Los Angeles, California. (Photo by Kevork Djansezian/Getty Images)
HERBORN, GERMANY - MAY 29: Musician Alice Cooper (R) and Actor/Musician Johnny Depp of Hollywood Vampires perform onstage at Hessentags-Arena during the 56th Hessentag on May 29, 2016 in Herborn, Germany. (Photo by Andreas Rentz/Getty Images)
2016 Starkey Hearing Foundation So The World May Hear Awards Gala
ST PAUL, MN - JULY 17: Johnny Depp and Alice Cooper from The Hollywood Vampires perform at the 2016 Starkey Hearing Foundation "So the World May Hear" awards gala at the St Paul RiverCentre on July 17, 2016 in St Paul, Minnesota. (Photo by Adam Bettcher/Getty Images for Starkey Hearing Foundation)
ANAHEIM, CA - JANUARY 21: Musicians Alice Cooper, Robert DeLeo , Johnny Depp and Joe Perry perform onstage at the TEC Awards during NAMM Show 2017 at the Anaheim Hilton on January 21, 2017 in Anaheim, California. (Photo by Jesse Grant/Getty Images for NAMM)
The 58th GRAMMY Awards – Arrivals
LOS ANGELES, CA - FEBRUARY 15: (L-R) Actor-musician Johnny Depp, musician Joe Perry, and singer Alice Cooper of the Hollywood Vampires attend The 58th GRAMMY Awards at Staples Center on February 15, 2016 in Los Angeles, California. (Photo by Jason Merritt/Getty Images)
The 58th GRAMMY Awards – Roaming Show
LOS ANGELES, CA - FEBRUARY 15: Actor/musician Johnny Depp (L) and musician Joe Perry of Hollywood Vampires perform onstage during The 58th GRAMMY Awards at Staples Center on February 15, 2016 in Los Angeles, California. (Photo by Larry Busacca/Getty Images for NARAS)
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The NAMM Show 2017 – TEC Awards
ANAHEIM, CA - JANUARY 21: Actor Johhny Depp and musician Joe Perry perform onstage at the TEC Awards during NAMM Show 2017 at the Anaheim Hilton on January 21, 2017 in Anaheim, California. (Photo by Jesse Grant/Getty Images for NAMM)
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Walking along Boston's historic Freedom Trail and part of Boston's original coastline, children will experience the historical sites that played a key role in American independence: Faneuil Hall, the Old State House and the Old South Meeting House.
Learning about the Boston Massacre on the site where it occurred brings a new dimension to the study of American history.
Stops also include the site of the first public school in America and the oldest burying ground in Boston.
This tour covers ten sites in downtown Boston but is 30 minutes shorter and faster-paced than our Heart of the Freedom Trail tour.
Our guides love to point out the fun and interesting attractions along the route such as a 1743 weathervane, the Royal Lion and Unicorn, along with statues of Benjamin Franklin, and a Democrat donkey.
Our guides will help your child learn about our Boston's role in the American Revolution and discover the materials from which a city is built.
This tour fulfills elements of the Massachusetts State Curriculum Frameworks, and is a perfect activity for school groups, or any group of children wanting to explore downtown Boston.
Please contact us to arrange a tour for your school or community group.
General Admission $12; Save $2 when you buy online; Free for children under 6 years old and Boston By Foot members.
Meet your guide in front of Faneuil Hall at the Samuel Adams statue, Boston.


This specialization focuses on the principles underlying the practice of ecological agriculture. When coupled with the Major in Environmental Biology, agriculture as a managed ecosystem that responds to the laws of community ecology is examined; when combined with the Major Agro-Environmental Sciences and the specialization in Professional Agrology, this specialization focuses more directly on the practice of ecological agriculture and conforms with the eligibility requirements of the Ordre des agronomes du Québec. It is suitable for students wishing to farm and do extension and government work, and those intending to pursue postgraduate work in this field.


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Home 🌿 Regional 🌿 North America 🌿 Jamaica 🌿
Why Different Countries Are Relaxing Their Cannabis Laws
Submitted by Marijuana News on Tue, 06/01/2021 - 10:28
As the first European country to legalize cannabis, Luxembourg has called on other European countries to relax their drug laws, specifically cannabis production and consumption. According to the European state, the continent's drug policy has not worked over the last few decades, and forbidding everything made it more attractive for people to find new ways of skirting laws.
The country's relaxed laws will see residents over 18 years old able to buy cannabis for recreational use starting from 2020. The state will establish a cannabis agency to regulate all production and distribution. What's more, minors between ages 12 and 17 will not face criminal charges if caught in possession of five grams or less of the drug. However, those who break the law will receive harsh penalties.
5 Countries To Visit For The Best Marijuana In World
Cannabis tourism is thriving today on account of more countries legalizing the herb. It has opened paths for enthusiasts to travel far and wide worldwide to enjoy marijuana while embracing the picturesque views. While most countries allow tourists to use the herb, not all can offer the best marijuana.
Does your dream vacation include a good amount of high-grade marijuana? Read on to know the countries that produce the best marijuana you can visit to have a magical time.
Which are the Best Countries for Marijuana Travel?
Like every other marijuana lover, you must be searching for the countries that offer the best marijuana in the world. If you are looking for your next marijuana adventure destination, you've reached the right place.
Foreign assets could be next on the block for cash-hungry cannabis companies
Submitted by Marijuana News on Fri, 01/10/2020 - 10:24
Two years ago, Canadian cannabis companies were racing to scoop up international assets, from swaths of fertile land in southern Africa to cultivation licences in Jamaica and everything in between.
Now, with fears of a cash crunch looming over the industry, some of the same producers who spent tens of millions to build an international presence have started dialling back, putting projects on hold or divesting of their foreign operations altogether.
And it's a trend that some pot analysts expect will only intensify over the next 12 months.
5 Top holiday destinations for cannabis lovers
It's a well-known fact that cannabis fans are always ready for an adventure and trying out new stuff. That's exactly why weed destinations are one of the fastest-growing trends on Earth!
So, put your day-dreams into high gear and check this list of some of the best destinations for a cannabis holiday on the planet!
1. Colorado, USA
Colorado was the first US state to legalize the recreational use and sale of cannabis. Namely, the US represents the largest market for medicinal cannabis; seeing how the government also supports the cultivation of cannabis, it's grown all around the state.
Jamaica makes first shipment of medical marijuana to Canada
Jamaica has made its first shipment of medical marijuana extract oil to Canada.
In making the announcement, Minister of Industry, Commerce, Agriculture and Fisheries Audley Shaw, "Jamaica is uniquely positioned to be a global player and we are committed to providing the leadership and resources required for opening the international markets including Canada and Europe for our licensed and regulated Jamaican companies."
The shipment was authorised through an import permit issued by the Government of Canada through Health Canada for Jamaica and an export permit issued by the Ministry of Health in Jamaica.
$260m ganja study - Jamaica eyeing investment in medicinal marijuana market in Canada
The Jamaica Medical Cannabis Corporation (JMMC) is investing US$2 million (J$264,000,000) into research on local ganja strains in order to ascertain with scientific accuracy their medicinal potential, over the next 10 years.
Professor Errol Morrison, director general of the National Commission on Science and Technology, spoke to the enormity of the project titled 'Identification, Isolation and Conservation of Local Strains of Cannabis for Medicinal Use' during Monday's signing ceremony.
"What you are about to witness is the dedication of our scientific community to eventually [map] the scientific identification of our strain. Not a look, touch, smell, feel (but) DNA science to underpin what it is that we have been making claims for centuries," he said.
These are the top 4 marijuana stocks with international expansion plans
As cannabis legalization spreads across the North American continent, industry insiders and pot stock investors alike look to diversify their portfolios in the global marijuana trade.
With Canada on track to become the first G7 nation to legalize both recreational and medical cannabis nationally, overcrowding in the market is becoming an issue for stakeholders on all sides. It's the reason why cannabis companies are starting to look for more opportunities internationally. These are the top four marijuana stocks with international expansion plans:
Rare Jamaican cannabis strains seeding a medical marijuana takeover in Canada
Toronto-based Jamaican Medical Cannabis Collective has signed contracts to provide Jamaican cannabis to three Canadian LPs and letters of intent to supply seven more.
Lift & Co., "Canada's medical marijuana marketplace," held its biggest expo in Toronto from May 25 to 27, welcoming almost 20,000 people to the Metro Toronto Convention Centre, which was surrounded by a slight haze during the three days devoted to cannabis education, product placement and trend-watching.
Billing itself as the last before legalization, the event was filled with companies poised to hit the new recreational pot market when it finally comes to Canada. Their booths took up two levels of the convention floor.
Jamaica poised to become major location for investment in medical cannabis
Minister of Industry, Commerce, Agriculture and Fisheries Audley Shaw is confident that the way is now paved for Jamaica to play a leading role in the rapidly growing medical cannabis industry.
According to Shaw, Jamaica is uniquely positioned to bring health and wellness to the world by developing one of its greatest assets, the herbal industry.
Shaw last week met with representatives of the Canadian Government and the Province of Ontario, as well as numerous companies and investors who shared their commitment to investing in the Jamaican cannabis industry.
Cannabis Growth Opportunity Corporation expands into Caribbean with investment in Herbs Holdings Ltd.
Cannabis Growth Opportunity Corporation (CSE: CGOC), today announced it has invested in Herbs Holdings Ltd., a large medical cannabis premium grower and retailer in Jamaica. The agreement is CGOC's first in the Caribbean and reflects the company's focus on driving long-term total return through investments in privately and publicly held companies that are aligned to its investment approach.


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4. Brian Daboll, Giants
The Giants have been excluded from the postseason ever since their infamous boat picture during the 2016 season. However, Daboll has steered the ship back in the right direction by securing a playoff berth in his first season at the helm. While Daboll has arguably not had a star-studded roster at his disposal, he's managed to extract a career year from Saquon Barkley and, even more impressively, he got Daniel Jones to play like a winning quarterback for the first time in his NFL career.
3. Kyle Shanahan, 49ers
Injuries have seemed to be a constant part of the 49ers in recent years. However, 2022 hit them with extra cruelty as they lost not only opening-day starting quarterback Trey Lance, but also his backup and longtime starter Jimmy Garoppolo. While this would be a death sentence for most, Shanahan made it work with seventh-round rookie signal-caller Brock Purdy and the NFL's stingiest defense. Despite their battle wounds, Shanahan has the 49ers thinking of championship aspirations once again.
2. Doug Pederson, Jaguars
Pederson was brought into Jacksonville to unlock Trevor Lawrence's potential and gradually turn the Jaguars into a competitor again. Pederson has done both in record time as Lawrence displayed the ability that made him a generational prospect, and the Jaguars snuck into the postseason after winning six of their last seven games. Urban Meyer may have left Jacksonville in shambles, but Pederson led a world-class cleanup effort that's reversed the club's fortunes faster than anyone could have expected.
1. Nick Sirianni, Eagles
Tim Nwachukwu / Getty Images Sport / Getty
Sirianni's body of work for 2022 wasn't technically perfect, but it was about as close as you can get to perfection. In just his second season in charge, Sirianni has gotten the Eagles home-field advantage in the playoffs after a 14-3 record. That's not all – he also had Jalen Hurts providing MVP-caliber play before a late-season injury. There have been some exceptional NFL coaching jobs this season, but none can hold a candle to what Sirianni has accomplished in Philly.
Defensive Rookie of the Year
5. Jaquan Brisker, Bears
There haven't been many bright spots for the Bears this season, but they've appeared to find a long-term contributor in their secondary with Brisker. The second-round pick has flashed as a tough, downhill safety in his first year in the big leagues. Despite being a defensive back, Brisker led the Bears in sacks with four while his 104 tackles rank second on the team.
4. Kayvon Thibodeaux, Giants
The 2022 fifth overall pick ascended into the Defensive Rookie of the Year conversation as a late bloomer. Three of Thibodeaux's four sacks have come over his last five games, plus he's added six tackles for a loss and one forced fumble in that span. It wouldn't be a surprise to see the Giants pass-rusher fighting for some more prestigious NFL defensive awards in the coming years.
3. Tariq Woolen, Seahawks
When it's all said and done, the Seahawks may have turned a fifth-round pick into one of the league's most ball-hungry cornerbacks. Exceeding expectations doesn't do Woolen's play justice; he's done victory laps over his 2022 projections. Not only are his six interceptions the most among all first-year players, and a new Seahawks rookie record, but they're also tied for most in the league.
2. Aidan Hutchinson, Lions
Gregory Shamus / Getty Images Sport / Getty
A lot of credit should be passed around for the Lions' turnaround, and Hutchinson deserves his fair share. The No. 2 overall pick is first among all rookies in sacks with 9.5, but he's proven to be a magnet for game-changing plays with his three interceptions as well.
1. Ahmad Gardner, Jets
It's hard to tell that Gardner is still just in his first NFL season when you watch him on the field. That's what makes him a shoo-in for the top rookie defensive honor. The top-five pick has locked down some of the league's premier receivers throughout the campaign, racking up two interceptions and a league-leading 20 pass defenses. He's also PFF's highest-graded cornerback, finishing ahead of the likes of Jalen Ramsey and Patrick Surtain.
Offensive Rookie of the Year
5. Chris Olave, Saints
The Saints were supposed to feature a three-headed beast at wide receiver with Olave, Michael Thomas, and Jarvis Landry. Instead, it's been a one-man show with the rookie carrying the workload thanks to injuries to Thomas and Landry. Olave has been a trustworthy security blanket for a New Orleans team that's struggled to find an offensive identity, as he's racked up 1,042 yards and three 100-yard games.
4. Kenny Pickett, Steelers
One look at the stat sheet won't have you walking away thinking Pickett is a credible Rookie of the Year contender, but his poise in do-or-die moments kept the Steelers in the playoff race right until the very end. Since Pittsburgh returned from its bye in Week 10, the Pitt product has orchestrated four game-winning drives, including memorable ones against the Raiders and Ravens.
3. Brock Purdy, 49ers
Thearon W. Henderson / Getty Images Sport / Getty
There's magic in the air in the Bay Area, and it's because of a rookie quarterback who's turning heads each week. Purdy, taken with the last pick of the 2022 draft, has become anything but irrelevant to the 49ers' title hopes. The signal-caller has thrown at least two touchdown passes in each game since taking over while also becoming the third rookie quarterback to win their first five starts. While the 49ers' defense is still the team's strong point, Purdy has been stealing the show as a great secondary act.
2. Garrett Wilson, Jets
If Wilson had better quarterback play this season, there's a strong possibility he'd take the top spot on our rankings. But even after having to catch passes from the likes of Mike White, Zach Wilson, Joe Flacco, and Chris Streveler, the rookie still managed to put up monster numbers – a testament to his talent. Wilson broke the 1,000-yard barrier with a game to spare before finishing the year with 1,103 yards.
1. Kenneth Walker, Seahawks
Offensive Rookie of the Year has been Walker's award to lose for the majority of the second half of the season. The Seahawks running back led all rookies in rushing yards (1,050) and touchdowns (9). His consistency is perhaps the biggest trait to admire as he's averaged over four yards per carry in eight of his 15 contests this season.
5. Chris Jones, Chiefs
After a slow start to the season, there wasn't a better defensive player over the last 12 weeks than Jones. Since Week 6, no one recorded more sacks than Jones' 13.5 over the final 12 games. He was even more impressive in the final month of play, recording 4.5 sacks and 11 quarterback hits over the Chiefs' last three contests. In total, his 15.5 sacks in 2022 evened a personal best and were tied for fourth most in the NFL.
4. Haason Reddick, Eagles
Mitchell Leff / Getty Images Sport / Getty
It's time for the world to stop ignoring Reddick. Perhaps the best value free-agent signing of the offseason, Reddick's play has paid dividends for the Eagles. The versatile linebacker has displayed a nose for the football with a league-leading five forced fumbles and 16 sacks, tied for second most in the NFL. In any other season, there's a good chance that Reddick's numbers would be enough to take home the DPOY honor.
3. Micah Parsons, Cowboys
The DPOY trophy will likely evade Parsons for another season after he came down to earth during the season's final stretch. The 23-year-old only mustered 1.5 sacks over his final six games, but he still ended the campaign with a career-high 13.5 sacks, three forced fumbles, three fumble recoveries, and a defensive touchdown. While the Cowboys' defense has earned massive praise around the league, there's no doubt that Parsons has been the biggest star in Dallas.
2. Myles Garrett, Browns
Garrett was nearly unblockable over the closing stretch of the season, recording six sacks over his final five games. His season total of 16 sacks matched a career high, while no other player on the Browns even reached more than three. While some other candidates on our rankings played on some impressive defenses, Cleveland's defensive performances were directly tied to Garrett's production.
1. Nick Bosa, 49ers
Selecting the 2022 DPOY will likely be the easiest decision voters make all year. It's just impossible to construct an argument that could take the trophy away from Bosa, who's had a season that outpaces the field. The 49ers pass-rusher led the NFL in sacks with 18.5 despite missing one game. His league-leading 48 quarterback hits are also 13 more than his next closest competitor, while his 19 tackles for a loss are tied for second most in the NFL. If that doesn't seal the deal, there were only three games this season in which Bosa failed to record a sack and only one contest where he couldn't register a single quarterback hit.
5. Justin Jefferson, Vikings
Stacy Revere / Getty Images Sport / Getty
If there was any non-quarterback who deserved to be in consideration for the NFL's most prestigious individual award, Jefferson has to be the pick. While he fell short of the 2,000-yard benchmark after a pedestrian final two weeks of the season, his 1,809-yard campaign and 10 100-yard-plus games still led the NFL. Whether it was the monster games or highlight-reel catches, no non-QB took the league by storm like the Vikings wideout.
4. Josh Allen, Bills
It's been another season of excellence for the Bills quarterback. With 4,000-plus yards and 35 touchdowns, as well as 762 yards and seven more scores on the ground, Allen initially had the Bills slated for the AFC's No. 1 seed. Boosting his resume for MVP includes a memorable victory against the Chiefs and Mahomes, another candidate for the top individual award. With the Wyoming product under center, the Bills haven't lost a game since Nov. 13.
3. Jalen Hurts, Eagles
Hurts' 2022 season is a reminder that life can often be cruel. The Eagles signal-caller appeared to be cruising to his first-ever MVP accolade before a shoulder injury forced him to miss two games late in the season. Despite the lost momentum, Hurts still holds a 14-1 record as a starter in 2022 with career bests in completion percentage (66.5%), passing yards (3,701), passing touchdowns (22), and rushing scores (13). While he may not be in play for MVP anymore, he could make it a forgotten point if he can lead the Eagles to a Super Bowl.
2. Joe Burrow, Bengals
He's doing it once again. With ice in his veins and natural swagger in his walk, Burrow has led the Bengals back into the mix for another Super Bowl appearance. For that, he's become a leading MVP candidate. Winners of eight in a row, Cincinnati has been carried by its star quarterback, who has had to do it without Ja'Marr Chase and Joe Mixon for stretches due to injury absences. His play over the eight-game win streak is what's elevated him near the top of our rankings as he's thrown 18 touchdowns to just six interceptions while also compiling a 99.6 passer rating.
1. Patrick Mahomes, Chiefs
Jeff Bottari / Getty Images Sport / Getty
Perhaps the one objective truth about the 2022 NFL season is that there was no better player in the NFL than Mahomes. Though many have likely become desensitized to the superstar's ability, it shouldn't take away from what he's been able to accomplish in a Chiefs offense that was briefly questioned following the offseason loss of Tyreek Hill. Mahomes' numbers this season are his best since his first MVP campaign in 2018, and for that reason, there should be no shock when he takes home his second MVP honor later this year. The 27-year-old threw for a whopping 5,250 yards, fourth most in NFL history, and also led the league with 41 touchdown passes.
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Hiraeth. It's a word the Welsh use, describing the feeling of homesickness, but not just the yearning of one's home town. Rather, hiraeth can mean the deep yearning one has for a home they can't return to (or never really had to begin with), or the pain of not being able to reconnect with past loves or comforts. Hence, it's a word that doesn't translate well to the English language. You are probably wondering why I'm bringing up that word in this here review. If something ever evoked the feelings of hiraeth in the form of music, London's "emokrust" collective Morrow supplied the soundtrack in their incredible debut, Covenant of Teeth.
If, like me, you shuddered at Morrow's self-described genre, relax and free your mind a bit. We're not talking the stereotype of love songs slowed down, or grunged-up coming-of-age stories. Yet, for all the negative connotations that descriptor brings, "emokrust" fits somewhat. Honestly, if you wanted to be lazy and provocative, you could label this post-metal if it makes you feel better. After all, it does tie to Neurosis in spirit, but even then the label is a bit damning, as opener "Fathom" is the closest to sounding like them. It takes about three and a half minutes to launch, but once the song properly starts, it's a tidal wave of methodical riffs, passionate vocals ranging from low roars to piercing female shrieks, plodding d-beats, and a beautifully somber cello that wafts in like the remnants of a pleasant dream.
It's that cello that places Morrow above their contemporaries, giving these four songs a blanket of sadness and longing over a bed of sludgy post-metal. Closer "Cleaved Fang," possibly the most somber on the entire album, opens with Nicole's beautiful cello melody over a strummed guitar. Also of note are the lyrics, as main vocalist Alex penned some rather wrenching poetry ("Disperse in the clap of resilient hands/We sing in the eyes that we've painted on/We drew into the bark and let ourselves be/Ruled by the whims of whilom revery (for too long)"). "Forgiving Grin" lurches with intent, rumbling angrily with disgustingly thick bass, urgent riffing, and some rather unsettling screams. Speaking of screaming, the list of guest vocalists reads like a "who's who" of crust and grindcore, featuring contributions by members of Wildspeaker, Masakari, Archivist, and Knifedoutofexistence, among others.
The one complaint I have with Covenant of Teeth is the production. While David's instrumentation (translated: he plays all of the guitar, bass, and drums on here) sounds great, there are times when the vocals are a bit buried in the mix, such as parts of "The Norr." The more ambient parts, such as the intro to "Fathom," could also use a bit of a volume increase. Otherwise, I'm impressed by the sheer fact that this is a debut album, as I've not had 40 minutes fly by so quick while listening. And despite the songs' lengths, there's not a dull moment to be had, as the stories are given their proper time to start, build, climax, and end properly.
Covenant of Teeth is at once morosely somber and defiantly proud. Morrow took the dirt and grime of the downtrodden and made a work of sad beauty in their debut. In the ache of darkness, that is when the piercing of light is the strongest. Morrow supplied the soundtrack to that light. Damn good job.


text:
Q: Filtering an ElementsCollection I'm trying to create a function to filter an ElementsCollection, with a condition on a child of each element instead of the element itself.
Here's what I came up with:
 public static ElementsCollection filterByChild(ElementsCollection elementsCollection, String childCssSelector,
        Condition condition) {

        Predicate<SelenideElement> childHasConditionPredicate = element -> element.$(childCssSelector).has(condition);
        elementsCollection.removeIf(childHasConditionPredicate);
        return elementsCollection;
    }

When calling this function like this:
myCollection = SelenideHelpers.filterByChild(myCollection, "a", Condition.text("http://www.link.com");

I'm getting the following error message:
java.lang.UnsupportedOperationException: Cannot remove elements from web page

I did not found any relevant informations on this error message that could be applied to my code. I would like to know why is this message appearing.

A: Check how SelenideElementIterator is designed:
@Override
public void remove() {
  throw new UnsupportedOperationException("Cannot remove elements from web page");
}

To make it work you need to create your custom condition like:
import com.codeborne.selenide.Condition;
import com.codeborne.selenide.ElementsCollection;
import org.openqa.selenium.By;
import org.openqa.selenium.WebElement;

import static com.codeborne.selenide.Selenide.$$;

public static Condition hasChildWithCondition(final By locator, final Condition condition) {
    return new Condition("hasChildWithCondition") {
        @Override
        public boolean apply(WebElement element) {
            return element.findElements(locator).stream().anyMatch(child -> condition.apply(child));
        }

        public String toString() {
            return this.name
        }
    };
}

and then use it to filter:
ElementsCollection collection = $$(".parent");
Condition hasChild = hasChildWithCondition(By.cssSelector("a"), Condition.text("http://www.link.com"));
collection.filterBy(hasChild);

redpajama_set_name: RedPajamaStackExchange


text:
BLACK TEA BLEND
Named after one of the most beautiful cities in Sri Lanka, Kandy brings together full and flavory Dimbula with highly aromatic and intense Uva and lightly scented high-grown Nuwara Eliya. A tea made for sipping with pleasure all day.
Malt, carob, honeysuckle
Carton [15 Sachets] Pantry Filler [100 Sachets] (out of stock) Loose Leaf Pack [4oz] (out of stock)
Carton [15 Sachets] Pantry Filler [100 Sachets] Loose Leaf Pack [4oz]
Carton [15 Sachets] - $12.99 USD Pantry Filler [100 Sachets] - Sold Out Loose Leaf Pack [4oz] - Sold Out
I bought this tea for my dad, who was born and raised in Sri Lanka and who has brothers who manage tea estates. He didn't think this tea had a great flavor. He said the leaves should be thinner. I tried it and I agree. It's not as flavorful as it should be. I love the Lord Bergamot tea but I won't buy this one again.
Ricky J.
Reliably Satisfying
Kandy is a reliably satisfying tea. I drink my tea plain, and enjoy Kandy's balanced, yet engaging flavor. It's a great, no frills, everyday tea to start the day.
Suzanne M.
My favorite of the black blends!
Love it !
James D.
A Taste of Sri Lanka
We were just in Sri Lanka for several weeks, and Kandy tea has the complexity that is representative of the special blends proudly served by each hotel.
Breakfast Delight
Really like this morning Kandy treat. I drink my tea plain, and this is a nice, smooth and a relaxing black. Sometimes, even an early afternoon pick me up needs some Kandy.
A blend of Ceylon Dimbula, Uva and Nuwara Eliya full leaf teas.
Blend Numerology
Number of cashew merchants per kilometer on the road to Kandy in Sir Lanka.
For best flavor, bring spring or freshly drawn filtered water to a boil (212 degrees). Steep five minutes while pausing to reflect on the private joys of your own tea ceremony.
Select an Ingredient:
ceylon dimbula
ceylon nuwara eliya
ceylon uva
Select an Ingredient: ceylon dimbula ceylon nuwara eliya ceylon uva
Sri Lankan Black Tea
The Dimbula region is directly opposite the Uva region in Sri Lanka. Dimbulas are often called "Westerns" in the tea trade. They have a reddish amber color in the cup, with a medium to full body, slightly fruity flavor and mineral notes. Ceylon Dimbulas are often used in medium bodied blends, Earl Grey formulas and other flavored teas. The best Dimbula teas are produced from December to February.
Central Province
The Central Province, true to its name, is located in the heart of Sri Lanka. It is said that in its capital city of Kandy, the tooth of the Buddha resides in a temple, which alone makes this place worth visiting. Here at Smith, just as holy, are the many breathtaking high elevation tea gardens that make a significant contribution to the total output of high grade Sri Lankan teas, which we look to buy between the months of December to February.
A well known, yet somewhat under-appreciated, tea from the area situated between Uva and Dimbula. Grown and processed at elevations above 1500 meters, Nuwara Eliyas have a very light color and body similar to some first flush Darjeelings. While their body and cup color are light, the flavors can be intense and floral, which add brightness and character to blends.
The Central Province, true to its name, is located in the heart of Sri Lanka. It is said that in its capital city of Kandy, the tooth of the Buddha resides in a temple, which alone makes this place worth visiting. Here at Smith, just as holy, are the many breathtaking high elevation tea gardens that make a significant contribution to the total output of high grade Sri Lankan tea, which we look to buy between the months of December to February.
Situated 1100 meters above sea level on the island of Sri Lanka, the Uva region produces teas of distinctly different character from their Ceylonese siblings. Uvas are astringent, intensely floral and slightly sharp in flavor with a golden cup color. They add "bite" and freshness to blends.
Uva Province
Uva Province is located in the soutestern part of Sri Lanka and is the second least populated portion of the island. It makes up for this with an abundance of exceptional tea gardens and wonderfule scenic overviews, like Lipton's Seat, where one can have a fresh cup of tea from the Dambethenna Estate and a front row seat to harvesting in the surrounding tea fields. We buy our teas during the peak harvest moths of June through September.


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Join me for some daughter-rescuing action! Feel free to comment on this post directly or head off to my Twitch Page to chat with me as I play!
During the last Nintendo Direct, I will admit that they sold me on the New Nintendo 3DS XL. It was a combination of the shiny new features and the gorgeous design of the special Majora's Mask Edition of the system that made me immediately go out and preorder the handheld. Now that I have it in my hands, the question becomes whether or not the new features make a big difference to the system. Exactly how new does the New Nintendo 3DS XL feel? Let's go through each of the new features one at a time to find out.
Join me for some Space Jellyfish-shooting action! Feel free to comment on this post directly or head off to my Twitch Page to chat with me as I play!
I've been meaning to do a Bonus Scare video of this one for a while, but never got around to it. Since I'm out of the country right now, I thought it would be a great time to finally take a look at Among the Sleep. Now join me on this clearly Rugrats–inspired acid trip through the world from the eyes of an infant.
Join me for some more crimson head-avoiding action! Feel free to comment on this post directly or head off to my Twitch Page to chat with me as I play!
From the beginning, it was easy to see that the StreetPass feature on the Nintendo 3DS was one of the more innovative and interesting features the handheld brought to the table. Since then, it has received updates in the way of some new games and a seemingly never-ending set of puzzle pieces to collect. This has me carrying my handheld around any time I know I'm going to be near others who may make that green light, indicating a new pass, turn on. AVAdventure Productions feels the same way and is attempting to take it to the next level with a one day round trip bus tour from Washington D.C. up to the Nintendo World Store in New York City.


text:
PFI hosts webinar on standards program tailored toward retailers
By Katie Fletcher | February 19, 2016
On Feb. 17, Pellet Fuels Institute hosted a webinar on its standards program, with information specifically for pellet retailers to familiarize participants with the program, including the difference between the quality mark and other labels, and why it matters to customers. The speakers on the webinar included John Shimek with Hearth and Home Technologies, Chris Wiberg with Timber Products Inspection, John Crouch with the Hearth, Patio and Barbecue Association and Jennifer Hedrick with PFI.
Prior to the creation of the PFI standards program, no certification program for pellet fuel existed. Crouch began the webinar by explaining how the program came to be. Triggered by the EPA, the PFI created a third-party, independent regulation of pellet fuel, and it's transitioned from the fuel standards set in 1995 to a nationally recognized quality management program for grading pellet fuels. Currently, 12 companies have qualified for the program, with 20 plants throughout the U.S. and Energex has its Canadian facility qualified. Hedrick, outgoing PFI executive director, stated during the webinar that at the end of 2015 the program represented 700,000 tons of product and more is expected in 2016. "From conversations that I've had with auditing agencies and manufacturers who are in the process of enrolling in the program, we anticipate well over 1 million tons of product qualified through the PFI standards program in 2016," she said. "It continues to grow, and it's gained a wider range of acceptance and understanding."
Hedrick briefly commented about stepping down as executive director by ensuring webinar participants that PFI is finalizing a transition plan to ensure that the programs and services PFI offers to its members and the larger community remain intact and that the major programs, like the PFI standards program, move forward steadily and efficiently.
Last year, the EPA announced changes to their new source performance standards (NSPS) from 1998 for residential wood heaters, which will impact pellet manufacturers, retailers, stove manufactures and consumers. The new rules require that any new non-commercial wood burning appliance sold in the U.S. utilize fuel that has been graded through an EPA-authorized standards program (PFI, ENplus, CANplus). For pellet stoves, boilers and furnaces, the rule requires consumers to only use the grade of fuel that the appliance was tested for. Also, manufacturers will be required to state that their products have been tested with fuel from a particular grading program and indicate that in their owners' manuals. According to PFI, fuel producers can continue to produce and sell product that isn't grade, but it can only be burned in appliances already in use, and retailers will focus on using labeled fuel for best results.
The webinar was targeted at keeping retailers informed as more customers ask for pellets with the quality mark on the bag. Wiberg, manager of Timber Products Inspection, focused his presentation on understanding the PFI quality mark and grade criteria, as well as the overall structure of the program, program documents, facility requirements and third party oversight. "PFI is the issuer, maintainer and promoter for the standard," Wiberg said when explaining the structure of the program. "Ultimately, the PFI standards program, developed by the PFI standards committee and approved through the board of directors, is passed over to the American Lumber Standard Committee through the form of an agreement where ALSC is the implementer and the enforcer. Their job is to accredit auditors and laboratories so that we have qualified third-party auditors and labs to oversee the densified fuel producers."
He adds that it's the auditing agencies and labs who work directly with the pellet producers to fulfill program requirements. In his presentation, Wiberg refers to a number of important program documents including the PFI Residential/Commercial Densified Fuel QA/QC Handbook or "the densified fuel producer's bible, so to speak, for implementing the quality control assurance and quality control components of the program," he said.
The PFI quality mark has a number of rules associated with it. The mark provides a registration number and must be displayed on the front lower third of the bag. The mark must state the material, additives (which may not exceed 2 percent), higher heating valued as-received and must reflect a minimum Btu guarantee.
Amongst the various requirements of a production facility, producers must develop a written in-house QA/QC program, based on the PFI QA/QC handbook and PFI specification; select an auditing agency and lab; demonstrate compliance with certification system components; and conduct QA/QC testing as necessary to verify continued compliance with grade criteria. "It really takes producers at least a couple of months to fulfill the requirements of the program," Wiberg said.
Once producers are ready to demonstrate compliance, accredited auditors visit facilities and in-house testing is done. Monthly audits typically take an hour or two for the regional auditor to do spot checks of the process, look at feedstock, final product storage areas and obtain a sample. Wiberg said one sample per 1,000 tons of product is taken. He adds that one caveat is if a producer sets up an onsite lab that has a certain number specified tests and can verify compliance, sampling frequency can be reduced to once every 5,000 tons.
Wiberg concludes his comments by encouraging those listening that if they want a level of quality guaranteed, then ask for it—it comes down to the mark and what's incorporated into it. "Stove manufactures are now required to do their testing with PFI—or other programs included—but quality-marked fuel that is under a grading program approved by the EPA and, in this case, ultimately what they test on has to appear in their owner's manual, so matching up a PFI quality mark with what's in your owner's manual is an important thing to teach to the consumer and to all levels of the supply chain."
Shimek, senior vice president with HHT, rounded off the webinar by providing the perspective of a stove manufacturer. "The real value in this is by using EPA-certified fuels in our appliances you're going to get a better performing product that is going to mean less maintenance for the consumers, less problems and in the end happier customers," he said. "We are taking the position that we are strongly encouraging dealers and consumers to use the grade fuel that the appliance was tested and certified to. It is the only way to ensure the customer gets the performance and service they're expecting."
More about the PFI standards program can be found here.
"The PFI leadership has invested quite a bit of time and financial resources—elbow grease—into this program over the years, and that commitment remains," Hedrick said. "We're seeing more and more fuel manufacturers take interest in the program and are taking the steps to become qualified for the program. I think it's a really exciting time and staff leadership and others I've talked to are really encouraged by all of it."
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