challenges, and issues related to the particularities of the GPU
architecture and a synthesis on the different implementation
strategies used in the literature. The implementation of parallel
challenges, and issues related to the particularities of the GPU
architecture and a synthesis on the different implementation
strategies used in the literature. The implementation of parallel
GPUs is not straightforward. The traditional models used in CPUs
must be rethought to meet the new requirements of GPU
architectures. This chapter is organized as follows. Combinatorial
GPUs is not straightforward. The traditional models used in CPUs
must be rethought to meet the new requirements of GPU
architectures. This chapter is organized as follows. Combinatorial
methods are introduced in Section~\ref{ch8:sec:optim}. The main
traditional parallel models used for metaheuristics are recalled
in Section~\ref{ch8:sec:paraMeta}.
Section~\ref{ch8:sec:challenges} highlights the main challenges
related to the GPU implementation of metaheuristics. A
state-of-the-art of GPU-based parallel
methods are introduced in Section~\ref{ch8:sec:optim}. The main
traditional parallel models used for metaheuristics are recalled
in Section~\ref{ch8:sec:paraMeta}.
Section~\ref{ch8:sec:challenges} highlights the main challenges
related to the GPU implementation of metaheuristics. A
state-of-the-art of GPU-based parallel
summarized in Section~\ref{ch8:sec:state}. In Section~\ref{ch8:sec:frameworks}, the main developed GPU-based
frameworks for metaheuristics are described. Finally, a case study
is presented in Section~\ref{ch8:sec:case} and some concluding
summarized in Section~\ref{ch8:sec:state}. In Section~\ref{ch8:sec:frameworks}, the main developed GPU-based
frameworks for metaheuristics are described. Finally, a case study
is presented in Section~\ref{ch8:sec:case} and some concluding
It consists in finding optimal configuration(s) among a finite set of possible configurations
(or solutions) of a given combinatorial optimization problem (COP). The set of all possible solutions noted $S$ is called solution space or search space. Each solution in $S$ is defined by its real cost calculated by an objective function. COPs are generally defined as follows~\cite{blumMeta}:\\ %(Definition~\ref{def:cops})
It consists in finding optimal configuration(s) among a finite set of possible configurations
(or solutions) of a given combinatorial optimization problem (COP). The set of all possible solutions noted $S$ is called solution space or search space. Each solution in $S$ is defined by its real cost calculated by an objective function. COPs are generally defined as follows~\cite{blumMeta}:\\ %(Definition~\ref{def:cops})
and iteratively improves it by exploring its neighborhood in the
search space. The most known methods in this class are local
search methods that include \emph{simulated
and iteratively improves it by exploring its neighborhood in the
search space. The most known methods in this class are local
search methods that include \emph{simulated
search}}~\cite{stutzle2006ILSforQAP}, and \emph{variable
neighborhood search}~\cite{HansenMladenovic1997VNS}.\\
search}}~\cite{stutzle2006ILSforQAP}, and \emph{variable
neighborhood search}~\cite{HansenMladenovic1997VNS}.\\
-models for metaheuristics can be distinguished~\cite{talbi2009mfdti}: \emph{algorithmic-level}\index{Metaheuristics!algorithmic-level parallelism},
-\emph{iteration-level}\index{Metaheuristics!iteration-level parallelism}, and \emph{solution-level} as illustrated in Figure~\ref{ch8:fig:paraMeta}. \\
+models for metaheuristics can be distinguished~\cite{talbi2009mfdti}: \emph{algorithmic-level}\index{metaheuristics!algorithmic-level parallelism},
+\emph{iteration-level}\index{metaheuristics!iteration-level parallelism}, and \emph{solution-level} as illustrated in Figure~\ref{ch8:fig:paraMeta}. \\
start with identical or different solutions (s-metaheuristics
case) or populations (p-metaheuristics case). Their parameter
settings such as the size of tabu list for tabu
start with identical or different solutions (s-metaheuristics
case) or populations (p-metaheuristics case). Their parameter
settings such as the size of tabu list for tabu
same or different. The parallel processes may evolve independently
or in a cooperative manner. In cooperative parallel models, the
algorithms exchange information related to the search during
evolution in order to find better and more robust solutions.}
same or different. The parallel processes may evolve independently
or in a cooperative manner. In cooperative parallel models, the
algorithms exchange information related to the search during
evolution in order to find better and more robust solutions.}
-\item{In the iteration-level\index{Metaheuristics!iteration-level
-parallelism} parallel model, the focus is on the parallelization
+\item{In the iteration-level parallel model, the focus is on the parallelization
of each iteration of the metaheuristic. Indeed, metaheuristics are
generally iterative search processes. Moreover, the most
resource-consuming part of a metaheuristic is the evaluation of
the generated solutions at each iteration. For s-metaheuristics
of each iteration of the metaheuristic. Indeed, metaheuristics are
generally iterative search processes. Moreover, the most
resource-consuming part of a metaheuristic is the evaluation of
the generated solutions at each iteration. For s-metaheuristics
annealing, variable neighborhood search), the evaluation and
generation of the neighborhood is the most time-consuming step of
the algorithm particularly when it comes to dealing with large
neighborhood sets. In this parallel model, the neighborhood is
decomposed into partitions, and each partition is evaluated in a
parallel way. For p-metaheuristics (e.g., evolutionary
annealing, variable neighborhood search), the evaluation and
generation of the neighborhood is the most time-consuming step of
the algorithm particularly when it comes to dealing with large
neighborhood sets. In this parallel model, the neighborhood is
decomposed into partitions, and each partition is evaluated in a
parallel way. For p-metaheuristics (e.g., evolutionary
parallel model arises naturally since these metaheuristics deal
with a population of independent solutions. In evolutionary
parallel model arises naturally since these metaheuristics deal
with a population of independent solutions. In evolutionary
-algorithm\index{Metaheuristics!evolutionary~algorithm}s, for
-instance, the iteration-level\index{Metaheuristics!iteration-level
-parallelism} model consists of decomposing the whole population
+algorithms, for
+instance, the iteration-level model consists of decomposing the whole population
parallel model, the focus is on the parallelization of the
evaluation of a single solution. This model is useful when the
objective function and/or the constraints are time and/or memory
consuming. Unlike the two previous parallel models, the
parallel model, the focus is on the parallelization of the
evaluation of a single solution. This model is useful when the
objective function and/or the constraints are time and/or memory
consuming. Unlike the two previous parallel models, the
not straightforward. The parallel models have to be rethought to
meet the new requirements of the GPU architecture. Several major
issues have to be taken into account both at design and
not straightforward. The parallel models have to be rethought to
meet the new requirements of the GPU architecture. Several major
issues have to be taken into account both at design and
metaheuristics on GPU, the different threads may access multiple
data structures from multiple memory spaces. These memories have
different sizes and access latencies. Nevertheless, faster
metaheuristics on GPU, the different threads may access multiple
data structures from multiple memory spaces. These memories have
different sizes and access latencies. Nevertheless, faster
per thread, one individual per thread, single population per
threads block, one ant per thread, etc.) must be defined to ensure
a maximum occupancy of the GPU and
per thread, one individual per thread, single population per
threads block, one ant per thread, etc.) must be defined to ensure
a maximum occupancy of the GPU and
According to the used metaheuristic and to the handled problem, the data
values may have different types and different ranges of their values. The data
According to the used metaheuristic and to the handled problem, the data
values may have different types and different ranges of their values. The data
synchronization issue is caused by both the GPU architecture and
the synchronization requirements of the implemented method.
Indeed, GPUs are based on a multicore architecture organized into
synchronization issue is caused by both the GPU architecture and
the synchronization requirements of the implemented method.
Indeed, GPUs are based on a multicore architecture organized into
another challenging issue in GPU-based
metaheuristics~\cite{cecilia, pugace, audreyANT}. Generally,
metaheuristics contain irregular loops and conditional
another challenging issue in GPU-based
metaheuristics~\cite{cecilia, pugace, audreyANT}. Generally,
metaheuristics contain irregular loops and conditional
(s-metaheuristics), and the population (p-metaheuristics) in the
same block. In addition, the decision to apply a crossover or a
mutation on an individual in a genetic
(s-metaheuristics), and the population (p-metaheuristics) in the
same block. In addition, the decision to apply a crossover or a
mutation on an individual in a genetic
operations. Threads of the same warp have to execute
instructions simultaneously leading to different branches whereas
in an SIMD model the threads of a same warp execute the same
operations. Threads of the same warp have to execute
instructions simultaneously leading to different branches whereas
in an SIMD model the threads of a same warp execute the same
The performance of GPU-based metaheuristics in terms of execution
time could be improved by choosing the most appropriate parallel
The performance of GPU-based metaheuristics in terms of execution
time could be improved by choosing the most appropriate parallel
-model (algorithmic-level\index{Metaheuristics!algorithmic-level
-parallelism}, instruction-level,
-solution-level\index{Metaheuristics!solution-level~parallelism}).
+model (algorithmic-level, instruction-level,
+solution-level).
Moreover, an efficient decomposition of the metaheuristic and an
efficient assignment of code portions between the CPU and GPU
should be adopted. The objective is to take benefit from the GPU
computing power without affecting the efficiency and the behavior
of the metaheuristic and without losing performance in CPU/GPU
Moreover, an efficient decomposition of the metaheuristic and an
efficient assignment of code portions between the CPU and GPU
should be adopted. The objective is to take benefit from the GPU
computing power without affecting the efficiency and the behavior
of the metaheuristic and without losing performance in CPU/GPU
memory accesses. In order to decide which part of the
metaheuristic will be executed on which component, one should
perform a careful analysis on the serial code of the
memory accesses. In order to decide which part of the
metaheuristic will be executed on which component, one should
perform a careful analysis on the serial code of the
then offload them to the GPU, while the remaining
tasks still run on the CPU in a serial way. \\
then offload them to the GPU, while the remaining
tasks still run on the CPU in a serial way. \\
memory which is a slow memory making the memory transfer between
the CPU and GPU time-consuming which can significantly degrade the
performance of the application. Accesses to this memory should be
memory which is a slow memory making the memory transfer between
the CPU and GPU time-consuming which can significantly degrade the
performance of the application. Accesses to this memory should be
\section{State-of-the-art parallel metaheuristics on GPUs}
\label{ch8:sec:state}
After more than two decades of research by the combinatorial optimisation
\section{State-of-the-art parallel metaheuristics on GPUs}
\label{ch8:sec:state}
After more than two decades of research by the combinatorial optimisation
The first works on metaheuristic algorithms implemented on GPUs
started on old graphics cards before the appearance of modern GPUs
equipped with high-level programming interfaces such as CUDA and
OpenCL. Among these pioneering works we cite the work of Wong et al.~\cite{wongOldGPU2006} dealing with the
implementation
The first works on metaheuristic algorithms implemented on GPUs
started on old graphics cards before the appearance of modern GPUs
equipped with high-level programming interfaces such as CUDA and
OpenCL. Among these pioneering works we cite the work of Wong et al.~\cite{wongOldGPU2006} dealing with the
implementation
is implemented on old GPU architectures. Yu et al.~\cite{yu2005} and
Li et al.~\cite{li2007} proposed a full parallelization of genetic
is implemented on old GPU architectures. Yu et al.~\cite{yu2005} and
Li et al.~\cite{li2007} proposed a full parallelization of genetic
shader libraries based on Direct3D and OpenGL.\\
Such architectures are based on preconfigured pipelined stages
shader libraries based on Direct3D and OpenGL.\\
Such architectures are based on preconfigured pipelined stages
more explicitly, how to calculate the memory index of each
solution associated to each CUDA thread's \textit{id}.
%For 1-Hamming neighborhoods, as there is exactly n solutions in the neighborhood, the mapping of this neighborhood to CUDA threads is obvious: the CPU host offloads to GPU exactly $n$ threads, and each thread id is associated to one index in the binary vector. In the case of 2-Hamming and 3-Hamming neighborhoods, each thread id should be mapped respectively to two and three indexes in the candidate vector.
more explicitly, how to calculate the memory index of each
solution associated to each CUDA thread's \textit{id}.
%For 1-Hamming neighborhoods, as there is exactly n solutions in the neighborhood, the mapping of this neighborhood to CUDA threads is obvious: the CPU host offloads to GPU exactly $n$ threads, and each thread id is associated to one index in the binary vector. In the case of 2-Hamming and 3-Hamming neighborhoods, each thread id should be mapped respectively to two and three indexes in the candidate vector.
-The three neighborhoods are implemented and experimented on the Permuted Perceptron Problem (PPP) using a tabu search\index{Metaheuristics!tabu~search} algorithm (TS). Accelerations from $9.9 \times$ to $18.5 \times$ are obtained on different problem sizes.\\ % The experiments are performed on an Intel Xeon 8 cores 3GHz coupled with an NVIDIA GTX 280 card.\\
+The three neighborhoods are implemented and experimented on the Permuted Perceptron Problem (PPP) using a tabu search\index{metaheuristics!tabu search} algorithm (TS). Accelerations from $9.9 \times$ to $18.5 \times$ are obtained on different problem sizes.\\ % The experiments are performed on an Intel Xeon 8 cores 3GHz coupled with an NVIDIA GTX 280 card.\\
In the same context, Deevacq et al.~\cite{audreyANT}
proposed two parallelization strategies inspired by the multi-walk
parallelization strategy, of a 3-opt iterated local
In the same context, Deevacq et al.~\cite{audreyANT}
proposed two parallelization strategies inspired by the multi-walk
parallelization strategy, of a 3-opt iterated local
over a CPU/GPU architecture. In the first strategy, each Local
Search (LS) is associated to a unique CUDA thread and improves a
unique solution by generating its neighborhood. The second
over a CPU/GPU architecture. In the first strategy, each Local
Search (LS) is associated to a unique CUDA thread and improves a
unique solution by generating its neighborhood. The second
The same strategy is used by Luong et al.
in~\cite{luongMultiStart} to implement multistart parallel local
search algorithms (a special case of the
The same strategy is used by Luong et al.
in~\cite{luongMultiStart} to implement multistart parallel local
search algorithms (a special case of the
parallelism: several LS algorithms are managed by the CPU and the
neighborhood evaluation step of each algorithm is parallelized on
the GPU (each GPU thread is associated with one neighbor and
executes the same evaluation function kernel). The advantage of
such a model is that it allows a high occupancy of the GPU
parallelism: several LS algorithms are managed by the CPU and the
neighborhood evaluation step of each algorithm is parallelized on
the GPU (each GPU thread is associated with one neighbor and
executes the same evaluation function kernel). The advantage of
such a model is that it allows a high occupancy of the GPU
quantity of data to store and to communicate between CPU and
GPU. A second proposition for implementing the same model on GPU
consists of implementing the whole LS processes on GPU with each
GPU thread being associated to a unique LS algorithm. This solves
the communication issue encountered in the first model. In
quantity of data to store and to communicate between CPU and
GPU. A second proposition for implementing the same model on GPU
consists of implementing the whole LS processes on GPU with each
GPU thread being associated to a unique LS algorithm. This solves
the communication issue encountered in the first model. In
due to uncoalesced memory accesses. The proposed approaches are
implemented on the quadratic assignment problem (QAP) using CUDA.
The acceleration rates obtained for the
due to uncoalesced memory accesses. The proposed approaches are
implemented on the quadratic assignment problem (QAP) using CUDA.
The acceleration rates obtained for the
$12\times$ (for different
QAP benchmark sizes). \\
Janiak et al.~\cite{Janiak_et_al_2008} implemented two
algorithms for TSP and the flow-shop scheduling problem (FSP).
These algorithms are based on a multistart tabu
$12\times$ (for different
QAP benchmark sizes). \\
Janiak et al.~\cite{Janiak_et_al_2008} implemented two
algorithms for TSP and the flow-shop scheduling problem (FSP).
These algorithms are based on a multistart tabu
algorithms exploit multicore CPU and GPU. A full parallelization
on GPU is adopted using shader libraries where each thread is
algorithms exploit multicore CPU and GPU. A full parallelization
on GPU is adopted using shader libraries where each thread is
However, even though their experiments report that the use of GPU
speedups the serial execution almost $16 \times$, the mapping of
However, even though their experiments report that the use of GPU
speedups the serial execution almost $16 \times$, the mapping of
requires a large number of local search algorithms to
cover the memory access latency. The same mapping policy is adopted by Zhu et al. in~\cite{zhu_et_al_2008} (one thread is associated to one local search) solving the quadratic assignment problem but using the CUDA toolkit instead of shader libraries.\\
requires a large number of local search algorithms to
cover the memory access latency. The same mapping policy is adopted by Zhu et al. in~\cite{zhu_et_al_2008} (one thread is associated to one local search) solving the quadratic assignment problem but using the CUDA toolkit instead of shader libraries.\\
of using such a heterogeneous architecture is how to distribute
tasks between the CPU cores and the GPU in such a way to have
optimal performances. Among the three traditional parallel models
of using such a heterogeneous architecture is how to distribute
tasks between the CPU cores and the GPU in such a way to have
optimal performances. Among the three traditional parallel models
-(solution-level\index{Metaheuristics!solution-level~parallelism},
-iteration-level\index{Metaheuristics!iteration-level parallelism},
-and algorithmic-level\index{Metaheuristics!algorithmic-level
-parallelism}), the authors point out that the most convenient
+(solution-level,
+iteration-level
+and algorithmic-level), the authors point out that the most convenient
-iteration-level\index{Metaheuristics!iteration-level parallelism}
-and algorithmic-level\index{Metaheuristics!algorithmic-level
-parallelism} models. Several CPU threads execute several instances
+iteration-level
+and algorithmic-level models. Several CPU threads execute several instances
of the same S-metaheuristic in parallel while the GPU device is
associated to one CPU core and used to accelerate the
neighborhood calculation of several S-metaheuristics at the same
of the same S-metaheuristic in parallel while the GPU device is
associated to one CPU core and used to accelerate the
neighborhood calculation of several S-metaheuristics at the same
used on CPUs based on the task parallelism. A different
implementation approach is proposed by Paul in~\cite{gerald2012}
to implement a simulated
used on CPUs based on the task parallelism. A different
implementation approach is proposed by Paul in~\cite{gerald2012}
to implement a simulated
for the QAP on GPUs. Indeed, the author used a preinitialized
matrix \emph{delta} in which the incremental evaluation of simple
swap moves are calculated and stored relative to the initial
for the QAP on GPUs. Indeed, the author used a preinitialized
matrix \emph{delta} in which the incremental evaluation of simple
swap moves are calculated and stored relative to the initial
supercomputers, clusters, and computational grids. Three main
classes of p-metaheuristics are considered in this section:
evolutionary
supercomputers, clusters, and computational grids. Three main
classes of p-metaheuristics are considered in this section:
evolutionary
-algorithm\index{Metaheuristics!evolutionary~algorithm}s (EAs), ant
-colony\index{Metaheuristics!ant~colony~optimization} optimization
-(ACO\index{Metaheuristics!ant~colony~optimization}), and particle
-swarm optimization\index{Metaheuristics!particle swarm
+algorithms (EAs), ant
+colony optimization
+(ACO), and particle
+swarm optimization\index{metaheuristics!particle swarm
In~\cite{kannan}, Kannan and Ganji present a CUDA implementation
of the drug discovery application Autodock (molecular docking
application). Autodock uses a genetic
In~\cite{kannan}, Kannan and Ganji present a CUDA implementation
of the drug discovery application Autodock (molecular docking
application). Autodock uses a genetic
docking positions of a ligand to a protein. The most
time-consuming task in Autodock is the fitness function
evaluation. The fitness function used for a docking problem
docking positions of a ligand to a protein. The most
time-consuming task in Autodock is the fitness function
evaluation. The fitness function used for a docking problem
description of the problem-specific components (fitness function,
problem representation, etc) in EASEA. The code is then compiled
to obtain a ready-to-use evolutionary
description of the problem-specific components (fitness function,
problem representation, etc) in EASEA. The code is then compiled
to obtain a ready-to-use evolutionary
Libraries to produce C++ or JAVA written EA codes.
In~\cite{maitre2009}, the authors proposed an extension of EASEA
to produce CUDA code from the EASEA files. This extension has been
Libraries to produce C++ or JAVA written EA codes.
In~\cite{maitre2009}, the authors proposed an extension of EASEA
to produce CUDA code from the EASEA files. This extension has been
real problem (molecular structure prediction). In order to
maximize the GPU occupation, very large populations are used (from
$2000$ to $20000$). Even though transferring such large
real problem (molecular structure prediction). In order to
maximize the GPU occupation, very large populations are used (from
$2000$ to $20000$). Even though transferring such large
-populations from the CPU to the GPU device memory at every generation is very costly, the authors report important speedups on the two problems on a GTX260 card: $105 \times$ is reported for the benchmark function while for the real problem the reported speedup is $60 \times$. This may be best explained by the complexity of the fitness functions. Nevertheless, there is no indication in the paper about the memory management\index{GPU Challenges!memory~management} of the populations on GPU.\\
+populations from the CPU to the GPU device memory at every generation is very costly, the authors report important speedups on the two problems on a GTX260 card: $105 \times$ is reported for the benchmark function while for the real problem the reported speedup is $60 \times$. This may be best explained by the complexity of the fitness functions. Nevertheless, there is no indication in the paper about the memory management of the populations on GPU.\\
The master-slave model is efficient when the fitness function is
highly time intensive. Nevertheless, it requires the use of
The master-slave model is efficient when the fitness function is
highly time intensive. Nevertheless, it requires the use of
The coarse-grained model is used by Pospichal et al.
in~\cite{pospichal10} to implement a parallel genetic
The coarse-grained model is used by Pospichal et al.
in~\cite{pospichal10} to implement a parallel genetic
when only population evaluation is performed on GPU. Each
population island is mapped with a CUDA thread block and each
thread is responsible for a unique individual. Subpopulations are
when only population evaluation is performed on GPU. Each
population island is mapped with a CUDA thread block and each
thread is responsible for a unique individual. Subpopulations are
The same strategy is also adopted by Tsutsui and Fujimoto
in~\cite{tsutsuiGAQAP} to implement a coarse-grained genetic
The same strategy is also adopted by Tsutsui and Fujimoto
in~\cite{tsutsuiGAQAP} to implement a coarse-grained genetic
the QAP. Initially, several subpopulations are created on CPU and
transferred to the global memory. The subpopulations are organized
in the global memory into blocks of $8$ individuals in such a way
the QAP. Initially, several subpopulations are created on CPU and
transferred to the global memory. The subpopulations are organized
in the global memory into blocks of $8$ individuals in such a way
QAP benchmarks from the QAPLIB~\cite{burkard1991qaplib}. The GPU
implementation reached speedups of $2.9\times$ to $12.6 \times$
compared to a single core implementation of a coarse-grained
QAP benchmarks from the QAPLIB~\cite{burkard1991qaplib}. The GPU
implementation reached speedups of $2.9\times$ to $12.6 \times$
compared to a single core implementation of a coarse-grained
parallel model used is a hierarchical model based on two levels: each
thread in a block transforms a unique individual and a different
population is assigned to each block. The algorithm is run
parallel model used is a hierarchical model based on two levels: each
thread in a block transforms a unique individual and a different
population is assigned to each block. The algorithm is run
GraphCell, to solve the independent task scheduling problem on GPU
architectures. In CGAs, the population is arranged into a
two-dimensional toroidal grid where only neighboring solutions are
GraphCell, to solve the independent task scheduling problem on GPU
architectures. In CGAs, the population is arranged into a
two-dimensional toroidal grid where only neighboring solutions are
population is set to $32^2$. When the size of the population is
too small, there are not enough computations to cover the overhead
created by the call of kernel functions, CPU/GPU
population is set to $32^2$. When the size of the population is
too small, there are not enough computations to cover the overhead
created by the call of kernel functions, CPU/GPU
synchronization, and access to global memory. Finally, an
interesting review on GPU parallel computation in bio-inspired
algorithms is proposed by Arenas et al.
synchronization, and access to global memory. Finally, an
interesting review on GPU parallel computation in bio-inspired
algorithms is proposed by Arenas et al.
accelerating the tour construction step performed by each ant by
taking a task-based parallelism approach, with pheromone
deposition on the CPU.\\
In~\cite{cecilia}, Cecilia et al. present a GPU-based
implementation of
accelerating the tour construction step performed by each ant by
taking a task-based parallelism approach, with pheromone
deposition on the CPU.\\
In~\cite{cecilia}, Cecilia et al. present a GPU-based
implementation of
the two steps (tour construction and pheromone update) are
parallelized on the GPU. A data parallelism approach is used to
enhance the performance of the tour construction step. The
the two steps (tour construction and pheromone update) are
parallelized on the GPU. A data parallelism approach is used to
enhance the performance of the tour construction step. The
In another work, Tsutsui and Fujimoto~\cite{tsutsui} propose a
hybrid algorithm combining
In another work, Tsutsui and Fujimoto~\cite{tsutsui} propose a
hybrid algorithm combining
on GPU to solve the QAP. A solution of QAP is represented as a
permutation of ${1,2,..,n}$ with $n$ being the size of the
problem. The TS algorithm is based on the 2-opt neighborhood
(swapping of two elements $(i,j)$ in the permutation). The authors
point out that the move cost of each neighbor depends on the
couple $(i,j)$. Two groups of moves are formed according to the
on GPU to solve the QAP. A solution of QAP is represented as a
permutation of ${1,2,..,n}$ with $n$ being the size of the
problem. The TS algorithm is based on the 2-opt neighborhood
(swapping of two elements $(i,j)$ in the permutation). The authors
point out that the move cost of each neighbor depends on the
couple $(i,j)$. Two groups of moves are formed according to the
-move cost. In order to avoid thread divergence\index{GPU
-Challenges!thread~divergence} within the same warp, the
+move cost. In order to avoid thread divergence\index{GPU!thread divergence} within the same warp, the
neighborhood evaluation is parallelized in such a way to assign
only moves of the same cost to each thread warp. This strategy is
called MATA for Move-cost Adjusted Thread Assignment. Concerning
neighborhood evaluation is parallelized in such a way to assign
only moves of the same cost to each thread warp. This strategy is
called MATA for Move-cost Adjusted Thread Assignment. Concerning
-the memory management\index{GPU Challenges!memory~management}, all
-the data of the ACO\index{Metaheuristics! ant~colony~optimization}
+the memory management\index{GPU!memory management}, all
+the data of the ACO\index{metaheuristics!ant colony optimization}
(population, pheromone matrix), QAP matrices, and tabu list are
placed on the global memory of the GPU. Shared memory is used only
for working data common to all threads in a given block.
All the
steps of the hybrid algorithm
(population, pheromone matrix), QAP matrices, and tabu list are
placed on the global memory of the GPU. Shared memory is used only
for working data common to all threads in a given block.
All the
steps of the hybrid algorithm
pheromone update, construct solutions, applying TS) are
implemented as kernel functions on the GPU. The GPU/CPU
communications are only used to transfer the best-so-far solution
pheromone update, construct solutions, applying TS) are
implemented as kernel functions on the GPU. The GPU/CPU
communications are only used to transfer the best-so-far solution
illustrated in Figure~\ref{ch8:fig:classification}. The design
level regroups the three classes of parallel models used in
metaheuristics
illustrated in Figure~\ref{ch8:fig:classification}. The design
level regroups the three classes of parallel models used in
metaheuristics
-(solution-level\index{Metaheuristics!solution-level~parallelism},
-iteration-level\index{Metaheuristics!iteration-level parallelism},
-algorithmic-level\index{Metaheuristics!algorithmic-level
-parallelism}) with examples for s-metaheuristics, EAs,
-ACO\index{Metaheuristics!ant~colony~optimization} and PCO. This
+(solution-level,
+iteration-level,
+algorithmic-level) with examples for s-metaheuristics, EAs,
+ACO and PCO. This
classification is principally built from the reviewed
state-of-the-art works in the previous section. The
implementation level refers to the way these parallel design
classification is principally built from the reviewed
state-of-the-art works in the previous section. The
implementation level refers to the way these parallel design
models at solution level consist of parallelizing a time intensive
atomic task of the algorithm. Generally, it consists of the
fitness evaluation~\cite{kannan}. Nevertheless, crossover
models at solution level consist of parallelizing a time intensive
atomic task of the algorithm. Generally, it consists of the
fitness evaluation~\cite{kannan}. Nevertheless, crossover
%data parallelism in SA-matrix to parallelize
\subsubsection*{GPU thread mapping for iteration-level parallelism}
%data parallelism in SA-matrix to parallelize
\subsubsection*{GPU thread mapping for iteration-level parallelism}
Iteration-level parallelism consists of parallelizing the tasks
performed independently on different solutions. Different mapping
strategies are adopted in the reviewed works to implement these
models.\\
In Figure \ref{ch8:fig:classification}, the first example of
Iteration-level parallelism consists of parallelizing the tasks
performed independently on different solutions. Different mapping
strategies are adopted in the reviewed works to implement these
models.\\
In Figure \ref{ch8:fig:classification}, the first example of
parallelism is the parallel evaluation of neighborhoods in
s-metaheuristics. In most of the reviewed works, a per-thread
mapping approach is used: each solution of the neighborhood is
parallelism is the parallel evaluation of neighborhoods in
s-metaheuristics. In most of the reviewed works, a per-thread
mapping approach is used: each solution of the neighborhood is
%pheromone update data parallelism matrices
\subsubsection*{GPU thread mapping for algorithmic-level parallelism}
%pheromone update data parallelism matrices
\subsubsection*{GPU thread mapping for algorithmic-level parallelism}
-\index{GPU-based Metaheuristics!GPU-thread mapping}
-Algorithmic-level parallelism consists of launching several self-contained algorithms in parallel. In the previously reviewed works two algorithmic-level\index{Metaheuristics!algorithmic-level parallelism} models have been used: the multistart model and the island model (parallel EAs).\\
+Algorithmic-level parallelism consists of launching several self-contained algorithms in parallel. In the previously reviewed works two algorithmic-level models have been used: the multistart model and the island model (parallel EAs).\\
The implementation of the multistart model is based on two
different mapping strategies~\cite{luongMultiStart, audreyANT}:
The implementation of the multistart model is based on two
different mapping strategies~\cite{luongMultiStart, audreyANT}:
are placed on CPU and the neighborhood evaluation of each LS is
parallelized on GPU using per-thread mapping strategy (one thread
per solution). This consists of a hierarchical parallel model
are placed on CPU and the neighborhood evaluation of each LS is
parallelized on GPU using per-thread mapping strategy (one thread
per solution). This consists of a hierarchical parallel model
-combining algorithmic-level\index{Metaheuristics!algorithmic-level
-parallelism} parallelism (multistart) with
-iteration-level\index{Metaheuristics!iteration-level parallelism}
+combining algorithmic-level parallelism (multistart) with
+iteration-level
parallelism (master-worker).\\
In the island model, the same mapping is used in all the reviewed
parallelism (master-worker).\\
In the island model, the same mapping is used in all the reviewed
implementation of p-metaheuristics on GPU. The three frameworks
are presented in more detail in the following.
implementation of p-metaheuristics on GPU. The three frameworks
are presented in more detail in the following.
-\subsection{PUGACE\index{GPU-based frameworks!PUGACE}: framework for implementing evolutionary computation on GPUs}
-PUGACE\index{GPU-based frameworks!PUGACE} is a generic framework
+\subsection{PUGACE: framework for implementing evolutionary computation on GPUs}
+PUGACE is a generic framework
for easy implementation of cellular evolutionary algorithms on
GPUs implemented using C and CUDA. It is based on the frameworks
MALLBA and JCell (a framework for cellular algorithms). The
authors justified the choice of cellular evolutionary
for easy implementation of cellular evolutionary algorithms on
GPUs implemented using C and CUDA. It is based on the frameworks
MALLBA and JCell (a framework for cellular algorithms). The
authors justified the choice of cellular evolutionary
feedback found in the literature concerning its efficient
implementation on GPUs compared to other parallel models for EAs
(island, master-slave). The main standard evolutionary operators
feedback found in the literature concerning its efficient
implementation on GPUs compared to other parallel models for EAs
(island, master-slave). The main standard evolutionary operators
crossover, and mutation operators (PMX, swap, 2-exchange,
etc.). Different problem encoding is also supported. The framework
is organized as a set of modules in which the different
crossover, and mutation operators (PMX, swap, 2-exchange,
etc.). Different problem encoding is also supported. The framework
is organized as a set of modules in which the different
individual is associated to a unique CUDA thread. The function
evaluation and mutation are done on the GPU while selection and
replacement are maintained on the CPU. In order to avoid thread
individual is associated to a unique CUDA thread. The function
evaluation and mutation are done on the GPU while selection and
replacement are maintained on the CPU. In order to avoid thread
the same CUDA thread block at the crossover step (because of the
probability of application which may give different results from
one thread to the other), the decision of whether to apply a
the same CUDA thread block at the crossover step (because of the
probability of application which may give different results from
one thread to the other), the decision of whether to apply a
framework ParadisEO-MO-GPU\index{GPU-based
frameworks!ParadisEO-MO-GPU} for parallel local search
metaheuristics (s-metaheuristics) on GPUs. It focuses on the
framework ParadisEO-MO-GPU\index{GPU-based
frameworks!ParadisEO-MO-GPU} for parallel local search
metaheuristics (s-metaheuristics) on GPUs. It focuses on the
parallel model of s-metaheuristics which consists of exploring in
parallel the neighborhood of a problem solution on GPU. The
framework, implemented using C++ and CUDA, is an extension of the
parallel model of s-metaheuristics which consists of exploring in
parallel the neighborhood of a problem solution on GPU. The
framework, implemented using C++ and CUDA, is an extension of the
for the design and implementation of metaheuristics on GPUs. Until
now, the metaheuristics supported by LibCUDAOptimize are: scatter
search, differential evolution, and particle swarm
for the design and implementation of metaheuristics on GPUs. Until
now, the metaheuristics supported by LibCUDAOptimize are: scatter
search, differential evolution, and particle swarm
Nevertheless, the library is designed in such a way to allow
further extensions for other metaheuristics and it is still in
development phase by the authors. The parallelization strategy
Nevertheless, the library is designed in such a way to allow
further extensions for other metaheuristics and it is still in
development phase by the authors. The parallelization strategy
method for solving the Quadratic 3-dimensional Assignment Problem
(Q3AP) will be presented. The local search method is an Iterated
method for solving the Quadratic 3-dimensional Assignment Problem
(Q3AP) will be presented. The local search method is an Iterated
consists of executing iteratively the embedded local search, each
iteration which starts from a disrupted local optima reached by
the previous local search process. The disruption heuristic is a
consists of executing iteratively the embedded local search, each
iteration which starts from a disrupted local optima reached by
the previous local search process. The disruption heuristic is a
\subsection{Iterated tabu search algorithm for the Q3AP}
To tackle large-sized instances of the Q3AP and speed up the
\subsection{Iterated tabu search algorithm for the Q3AP}
To tackle large-sized instances of the Q3AP and speed up the
-search process, a parallel ILS\index{Metaheuristics!iterated local
-search} algorithm has been designed. The local search embedded in
-the ILS is a TS\index{Metaheuristics!tabu~search}. A TS
+search process, a parallel ILS algorithm has been designed. The local search embedded in
+the ILS is a TS. A TS
procedure~\cite{Glover1989TS} starts from an initial feasible
solution and tries, at each step, to move to a neighboring
solution that minimizes the fitness (for a minimization case). If
procedure~\cite{Glover1989TS} starts from an initial feasible
solution and tries, at each step, to move to a neighboring
solution that minimizes the fitness (for a minimization case). If
escape local optima. However, this strategy may generate cycles,
i.e., previous moves can be selected again. To avoid cycles, the
TS manages a short-term memory that contains the moves that have
escape local optima. However, this strategy may generate cycles,
i.e., previous moves can be selected again. To avoid cycles, the
TS manages a short-term memory that contains the moves that have
local search algorithm are the efficient distribution of the
search process between the CPU and the GPU minimizing the data
transfer between them, the hierarchical memory
local search algorithm are the efficient distribution of the
search process between the CPU and the GPU minimizing the data
transfer between them, the hierarchical memory
capacity constraints of GPU memories, and the thread
synchronization. All these issues must be regarded when designing
parallel LS models to allow
capacity constraints of GPU memories, and the thread
synchronization. All these issues must be regarded when designing
parallel LS models to allow
To go back to our problem (i.e., Q3AP), we propose in
Algorithm~\ref{ch8:algoITS} an iterated tabu
To go back to our problem (i.e., Q3AP), we propose in
Algorithm~\ref{ch8:algoITS} an iterated tabu
parallel model of LS methods presented in Section
\ref{ch8:sec:paraMeta} (Fig. \ref{ch8:fig:paraMeta}). This
algorithm can be seen as a cooperative model between the CPU and
parallel model of LS methods presented in Section
\ref{ch8:sec:paraMeta} (Fig. \ref{ch8:fig:paraMeta}). This
algorithm can be seen as a cooperative model between the CPU and
not change during all the execution of the LS algorithm.
Therefore, their associated memory is copied only once during all
the execution. Third, comes the parallel
not change during all the execution of the LS algorithm.
Therefore, their associated memory is copied only once during all
the execution. Third, comes the parallel
in which each neighboring solution is generated, evaluated, and
copied into the neighborhood fitnesses structure (from lines 10 to
14). Fourth, since the order in which candidate neighbors are
in which each neighboring solution is generated, evaluated, and
copied into the neighborhood fitnesses structure (from lines 10 to
14). Fourth, since the order in which candidate neighbors are
In this section, some experimental results related to the approach
presented in Section \ref{ch8:ITS-Q3APSection} are reported. We
recall that the approach is a GPU-based iterated tabu
In this section, some experimental results related to the approach
presented in Section \ref{ch8:ITS-Q3APSection} are reported. We
recall that the approach is a GPU-based iterated tabu
generation/evaluation step of the TS process is executed on GPU.
The ILS is used to improve the quality of successive local optima
provided by TS methods. This is achieved by perturbing the local
generation/evaluation step of the TS process is executed on GPU.
The ILS is used to improve the quality of successive local optima
provided by TS methods. This is achieved by perturbing the local
& & \tiny{$529.6$} & & & \tiny{$341.1$} & \tiny{$6.6$} & & \tiny{$4.0$} \\ \hline
\end{tabular}
\caption{Results of the GPU-based iterated tabu search for
& & \tiny{$529.6$} & & & \tiny{$341.1$} & \tiny{$6.6$} & & \tiny{$4.0$} \\ \hline
\end{tabular}
\caption{Results of the GPU-based iterated tabu search for
a case study on implementing large neighborhood local search
methods on GPUs for solving large benchmarks of the quadratic
three-dimensional assignment problem (Q3AP). \\
Implementing parallel
a case study on implementing large neighborhood local search
methods on GPUs for solving large benchmarks of the quadratic
three-dimensional assignment problem (Q3AP). \\
Implementing parallel
-GPU threads, thread divergence\index{GPU
-Challenges!thread~divergence}, and synchronization. Actually, most
+GPU threads, thread divergence, and synchronization. Actually, most
of metaheuristics have been implemented on GPU using different
implementation strategies. In this chapter, a two-level
classification of the reviewed works has been proposed: design
of metaheuristics have been implemented on GPU using different
implementation strategies. In this chapter, a two-level
classification of the reviewed works has been proposed: design
metaheuristic tasks to parallelize and the GPU threads. Indeed,
the choice of a given mapping strategy strongly influences the
other challenges (memory usage, communication, thread
metaheuristic tasks to parallelize and the GPU threads. Indeed,
the choice of a given mapping strategy strongly influences the
other challenges (memory usage, communication, thread
