Multi-swarm PSO algorithm for the Quadratic Assignment Problem: a massive parallel implementation on the OpenCL platform

This paper presents a multi-swarm PSO algorithm for the Quadratic Assignment Problem (QAP) implemented on OpenCL platform. Our work was motivated by results of time efficiency tests performed for single-swarm algorithm implementation that showed clearly that the benefits of a parallel execution platform can be fully exploited, if the processed population is large. The described algorithm can be executed in two modes: with independent swarms or with migration. We discuss the algorithm construction, as well as we report results of tests performed on several problem instances from the QAPLIB library. During the experiments the algorithm was configured to process large populations. This allowed us to collect statistical data related to values of goal function reached by individual particles. We use them to demonstrate on two test cases that although single particles seem to behave chaotically during the optimization process, when the whole population is analyzed, the probability that a particle will select a near-optimal solution grows.

[1]  Godfrey C. Onwubolu,et al.  Particle Swarm Optimization for the Assignment of Facilities to Locations , 2004 .

[2]  John E. Stone,et al.  OpenCL: A Parallel Programming Standard for Heterogeneous Computing Systems , 2010, Computing in Science & Engineering.

[3]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[4]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[5]  Piotr Szwed,et al.  OpenCL Implementation of PSO Algorithm for the Quadratic Assignment Problem , 2015, ICAISC.

[6]  Ralph Johnson,et al.  design patterns elements of reusable object oriented software , 2019 .

[7]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[8]  Jens H. Krüger,et al.  A Survey of General‐Purpose Computation on Graphics Hardware , 2007, Eurographics.

[9]  Ying Tan,et al.  GPU-based parallel particle swarm optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[10]  Franz Rendl,et al.  QAPLIB – A Quadratic Assignment Problem Library , 1997, J. Glob. Optim..

[11]  Martin Grötschel,et al.  Discrete mathematics in manufacturing , 1992 .

[12]  Aaftab Munshi,et al.  The OpenCL specification , 2009, 2009 IEEE Hot Chips 21 Symposium (HCS).

[13]  Shigeyoshi Tsutsui,et al.  ACO with Tabu Search on GPUs for Fast Solution of the QAP , 2013, Massively Parallel Evolutionary Computation on GPGPUs.

[14]  Alfonsas Misevicius,et al.  An implementation of the iterated tabu search algorithm for the quadratic assignment problem , 2012, OR Spectr..

[15]  Mikael Rönnqvist,et al.  Solution methods for the balancing of jet turbines , 1997, Comput. Oper. Res..

[16]  Monique Guignard-Spielberg,et al.  Exact solution of emerging quadratic assignment problems , 2010, Int. Trans. Oper. Res..

[17]  M. Guignard,et al.  Memory-Aware Parallelized RLT 3 for solving Quadratic Assignment Problems , 2013 .

[18]  James Kennedy,et al.  Defining a Standard for Particle Swarm Optimization , 2007, 2007 IEEE Swarm Intelligence Symposium.

[19]  A. Abraham,et al.  A Particle Swarm Approach to Quadratic Assignment Problems , 2007 .

[20]  M Dorigo,et al.  Ant colonies for the quadratic assignment problem , 1999, J. Oper. Res. Soc..

[21]  Thomas Stützle,et al.  ACO algorithms for the quadratic assignment problem , 1999 .

[22]  J. Ben Rosen,et al.  A quadratic assignment formulation of the molecular conformation problem , 1994, J. Glob. Optim..

[23]  Kuan Yew Wong,et al.  Investigating the performance of bees algorithm in solving quadratic assignment problems , 2010 .

[24]  Tapio Westerlund,et al.  A new exact discrete linear reformulation of the quadratic assignment problem , 2012, Eur. J. Oper. Res..

[25]  Jeff T. Linderoth,et al.  Solving large quadratic assignment problems on computational grids , 2002, Math. Program..

[26]  Esperanza García Gonzalo,et al.  The PSO family: deduction, stochastic analysis and comparison , 2009, Swarm Intelligence.

[27]  Maurice Clerc,et al.  Discrete Particle Swarm Optimization, illustrated by the Traveling Salesman Problem , 2004 .

[28]  Ashish Tiwari,et al.  A greedy genetic algorithm for the quadratic assignment problem , 2000, Comput. Oper. Res..

[29]  Matteo Fischetti,et al.  Three Ideas for the Quadratic Assignment Problem , 2012, Oper. Res..

[30]  M H Cole,et al.  A GENETIC ALGORITHM APPROACH TO DOOR ASSIGNMENTS IN BREAKBULK TERMINALS , 2001 .

[31]  V. Deineko,et al.  The Quadratic Assignment Problem: Theory and Algorithms , 1998 .

[32]  Pierre Collet,et al.  Generic Local Search (Memetic) Algorithm on a Single GPGPU Chip , 2013, Massively Parallel Evolutionary Computation on GPGPUs.

[33]  É. Taillard.  COMPARISON OF ITERATIVE SEARCHES FOR THE QUADRATIC ASSIGNMENT PROBLEM. , 1995 .

[34]  Wojciech Chmiel,et al.  A comparison of nature inspired algorithms for the quadratic assignment problem , 2017 .

[35]  Jacek M. Zurada,et al.  Artificial Intelligence and Soft Computing , 2014, Lecture Notes in Computer Science.

[36]  Ogier Maitre.  Genetic Programming on GPGPU Cards Using EASEA , 2013, Massively Parallel Evolutionary Computation on GPGPUs.