A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem

In this paper, we present a hybrid genetic-hierarchical algorithm for the solution of the quadratic assignment problem. The main distinguishing aspect of the proposed algorithm is that this is an innovative hybrid genetic algorithm with the original, hierarchical architecture. In particular, the genetic algorithm is combined with the so-called hierarchical (self-similar) iterated tabu search algorithm, which serves as a powerful local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm. The results of the conducted computational experiments demonstrate the promising performance and competitiveness of the proposed algorithm.

[1]  A. N. Elshafei,et al.  Hospital Layout as a Quadratic Assignment Problem , 1977 .

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

[3]  Rene Victor Valqui Vidal,et al.  SOLVING THE QUADRATIC ASSIGNMENT PROBLEM , 1993 .

[4]  Adnan Acan,et al.  A great deluge and tabu search hybrid with two-stage memory support for quadratic assignment problem , 2015, Appl. Soft Comput..

[5]  Alfonsas Misevicius,et al.  Some Further Experiments with Crossover Operators for Genetic Algorithms , 2018, Informatica.

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

[7]  Ziying Zhang,et al.  A hybrid method integrating an elite genetic algorithm with tabu search for the quadratic assignment problem , 2020, Inf. Sci..

[8]  Thomas Stützle,et al.  Iterated Robust Tabu Search for MAX-SAT , 2003, Canadian Conference on AI.

[9]  Doaa El-Shahat,et al.  Integrating the whale algorithm with Tabu search for quadratic assignment problem: A new approach for locating hospital departments , 2018, Appl. Soft Comput..

[10]  Lin-Yu Tseng,et al.  A Hybrid Metaheuristic for the Quadratic Assignment Problem , 2006, Comput. Optim. Appl..

[11]  Alfonsas Misevicius,et al.  Expansion of the minimum-inbreeding seed orchard design to operational scale , 2015, Tree Genetics & Genomes.

[12]  Weihang Zhu,et al.  SIMD tabu search for the quadratic assignment problem with graphics hardware acceleration , 2010 .

[13]  Eranda Çela,et al.  The quadratic assignment problem : theory and algorithms , 1999 .

[14]  Mitat Uysal,et al.  Migrating Birds Optimization: A new metaheuristic approach and its performance on quadratic assignment problem , 2012, Inf. Sci..

[15]  Alfonsas Misevicius,et al.  An improved hybrid genetic algorithm: new results for the quadratic assignment problem , 2004, Knowl. Based Syst..

[16]  Elwood S. Buffa,et al.  A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities , 1963 .

[17]  Michal Czapinski,et al.  An effective Parallel Multistart Tabu Search for Quadratic Assignment Problem on CUDA platform , 2013, J. Parallel Distributed Comput..

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

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

[20]  Deepu Philip,et al.  A quick convergent artificial bee colony algorithm for solving quadratic assignment problems , 2019, Comput. Ind. Eng..

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

[22]  John W. Dickey,et al.  Campus building arrangement using topaz , 1972 .

[23]  Habibollah Haron,et al.  A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem , 2015, Comput. Intell. Neurosci..

[24]  Wen-Chyuan Chiang,et al.  Intelligent local search strategies for solving facility layout problems with the quadratic assignment problem formulation , 1998, Eur. J. Oper. Res..

[25]  Ji Ung Sun,et al.  A novel approach to combine the hierarchical and iterative techniques for solving capacitated location-routing problem , 2018 .

[26]  Zakir Hussain Ahmed,et al.  A multi-parent genetic algorithm for the quadratic assignment problem , 2015 .

[27]  Mohammed Essaid Riffi,et al.  Incorporating a modified uniform crossover and 2-exchange neighborhood mechanism in a discrete bat algorithm to solve the quadratic assignment problem , 2017 .

[28]  Handbook of Heuristics , 2018 .

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

[30]  Zvi Drezner,et al.  The alpha male genetic algorithm , 2018 .

[31]  Eranda C Ela,et al.  Assignment Problems , 1964, Comput. J..

[32]  T. L. Ward,et al.  Solving Quadratic Assignment Problems by ‘Simulated Annealing’ , 1987 .

[33]  Panos M. Pardalos,et al.  A computational comparison of local search heuristics for solving quadratic assignment problems , 1993 .

[34]  Mohammed Essaid Riffi,et al.  Penguins Search Optimization Algorithm to Solve Quadratic Assignment Problem , 2017, BDCA'17.

[35]  Thomas E. Vollmann,et al.  An Experimental Comparison of Techniques for the Assignment of Facilities to Locations , 1968, Oper. Res..

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

[37]  Zvi Drezner,et al.  Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods , 2005, Ann. Oper. Res..

[38]  Anand Subramanian,et al.  Optimizing single-finger keyboard layouts on smartphones , 2020, Comput. Oper. Res..

[39]  Thomas Stützle,et al.  Iterated local search for the quadratic assignment problem , 2006, Eur. J. Oper. Res..

[40]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[41]  Gilbert Laporte,et al.  Balancing hydraulic turbine runners: A quadratic assignment problem , 1988 .

[42]  Alfonsas Misevicius.  Testing of Hybrid Genetic Algorithms for Structured Quadratic Assignment Problems , 2009, Informatica.

[43]  Andrea Roli,et al.  Leveraging saving-based algorithms by master-slave genetic algorithms , 2011, Eng. Appl. Artif. Intell..

[44]  Mika Nyströem.  Solving Certain Large Instances of the Quadratic Assignment Problem: Steinberg's Examples , 1999 .

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

[46]  Alfonsas Misevicius,et al.  An improved hybrid genetic algorithm: new results for the quadratic assignment problem , 2004, Knowl. Based Syst..

[47]  Panos M. Pardalos,et al.  A local search algorithm for the quadratic assignment problem , 1992 .

[48]  Gerald Paul,et al.  An efficient implementation of the simulated annealing heuristic for the quadratic assignment problem , 2011, ArXiv.

[49]  P. Shylo.  Solving the Quadratic Assignment Problem by the Repeated Iterated Tabu Search Method , 2017 .

[50]  Tansel Dökeroglu,et al.  A novel multistart hyper-heuristic algorithm on the grid for the quadratic assignment problem , 2016, Eng. Appl. Artif. Intell..

[51]  Tansel Dökeroglu,et al.  Hybrid teaching-learning-based optimization algorithms for the Quadratic Assignment Problem , 2015, Comput. Ind. Eng..

[52]  Alfonsas Misevicius,et al.  A Tabu Search Algorithm for the Quadratic Assignment Problem , 2005, Comput. Optim. Appl..

[53]  Tansel Dökeroglu,et al.  Artificial bee colony optimization for the quadratic assignment problem , 2019, Appl. Soft Comput..

[54]  David Connolly.  An improved annealing scheme for the QAP , 1990 .

[55]  Michael J. Brusco,et al.  Using Quadratic Assignment Methods to Generate Initial Permutations for Least-Squares Unidimensional Scaling of Symmetric Proximity Matrices , 2000, J. Classif..

[56]  Babacar Mbaye Ndiaye,et al.  A greedy evolutionary hybridization algorithm for the optimal network and quadratic assignment problem , 2020, Operational Research.

[57]  Aida Mustapha,et al.  Crossover and mutation operators of genetic algorithms , 2017 .

[58]  Jiunn-Chin Wang,et al.  A Multistart Simulated Annealing Algorithm for the Quadratic Assignment Problem , 2012, 2012 Third International Conference on Innovations in Bio-Inspired Computing and Applications.

[59]  Panos M. Pardalos,et al.  GRASP with Path-Relinking for the Quadratic Assignment Problem , 2004, WEA.

[60]  Umut Tosun,et al.  A New Recombination Operator for the Genetic Algorithm Solution of the Quadratic Assignment Problem , 2014, ANT/SEIT.

[61]  Charles Fleurent,et al.  Genetic Hybrids for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[62]  Uğur Yüzgeç,et al.  Tournament selection based antlion optimization algorithm for solving quadratic assignment problem , 2019, Engineering Science and Technology, an International Journal.

[63]  Zvi Drezner,et al.  Finding a cluster of points and the grey pattern quadratic assignment problem , 2006, OR Spectr..

[64]  Adel Abdennour,et al.  Particle Swarm Algorithm variants for the Quadratic Assignment Problems - A probabilistic learning approach , 2016, Expert Syst. Appl..

[65]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[66]  Stefanie Seiler,et al.  Facility Layout And Location An Analytical Approach , 2016 .

[67]  Rakesh Nagi,et al.  Level 2 Reformulation Linearization Technique-Based Parallel Algorithms for Solving Large Quadratic Assignment Problems on Graphics Processing Unit Clusters , 2019, INFORMS J. Comput..

[68]  Mehrdad Amirghasemi,et al.  A Self-adaptive Nature-Inspired Procedure for Solving the Quadratic Assignment Problem , 2020 .

[69]  T. V. Geetha,et al.  A Survey on Crossover Operators , 2016, ACM Comput. Surv..

[70]  Amit Singer,et al.  Semidefinite programming approach for the quadratic assignment problem with a sparse graph , 2017, Computational Optimization and Applications.

[71]  Vassilis Zissimopoulos,et al.  On the Quality of Local Search for the Quadratic Assignment Problem , 1998, Discret. Appl. Math..

[72]  N. Jawahar,et al.  Iterated fast local search algorithm for solving quadratic assignment problems , 2008 .

[73]  Sven Rahmann,et al.  Microarray Layout as Quadratic Assignment Problem , 2006, German Conference on Bioinformatics.

[74]  Alfonsas Misevičius.  Letter: New best known solution for the most difficult QAP instance “tai100a” , 2019, Memetic Comput..

[75]  Jin-Kao Hao,et al.  Memetic search for the quadratic assignment problem , 2015, Expert Syst. Appl..

[76]  Wojciech Chmiel,et al.  Quantum-Inspired Evolutionary Approach for the Quadratic Assignment Problem , 2018, Entropy.

[77]  F. Glover,et al.  Sequential and parallel path-relinking algorithms for the quadratic assignment problem , 2005, IEEE Intelligent Systems.

[78]  Lúcia Maria de A. Drummond,et al.  A Graphics Processing Unit Algorithm to Solve the Quadratic Assignment Problem Using Level-2 Reformulation-Linearization Technique , 2017, INFORMS J. Comput..

[79]  U. Tosun,et al.  A robust Island Parallel Genetic Algorithm for the Quadratic Assignment Problem , 2013 .

[80]  Ulrich W. Thonemann,et al.  Optimizing simulated annealing schedules with genetic programming , 1996 .

[81]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[82]  Bidyut Baran Chaudhuri,et al.  A distributed hierarchical genetic algorithm for efficient optimization and pattern matching , 2007, Pattern Recognit..

[83]  Yongquan Zhou,et al.  Elite opposition-flower pollination algorithm for quadratic assignment problem , 2017, J. Intell. Fuzzy Syst..

[84]  Zvi Drezner,et al.  Biologically Inspired Parent Selection in Genetic Algorithms , 2019, Annals of Operations Research.

[85]  B. Murtagh,et al.  A heuristic procedure for solving the quadratic assignment problem , 1982 .

[86]  Alan M. Frieze,et al.  Algorithms for assignment problems on an array processor , 1989, Parallel Comput..

[87]  Zvi Drezner,et al.  The extended concentric tabu for the quadratic assignment problem , 2005, Eur. J. Oper. Res..

[88]  Mieczyslaw M. Kokar,et al.  Self Controlling Tabu Search algorithm for the Quadratic Assignment Problem , 2011, Comput. Ind. Eng..

[89]  Gurkan Ozturk,et al.  A Hybrid Genetic Algorithm for the Quadratic Assignment Problem on Graphics Processing Units , 2016 .

[90]  Zvi Drezner,et al.  A New Genetic Algorithm for the Quadratic Assignment Problem , 2003, INFORMS J. Comput..

[91]  Bilel Derbel,et al.  A Parallel Tabu Search for the Large-scale Quadratic Assignment Problem , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

[92]  Meng Joo Er,et al.  PARALLEL MEMETIC ALGORITHM WITH SELECTIVE LOCAL SEARCH FOR LARGE SCALE QUADRATIC ASSIGNMENT PROBLEMS , 2006 .

[93]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[94]  Alice E. Smith,et al.  A genetic approach to the quadratic assignment problem , 1995, Comput. Oper. Res..

[95]  Jin-Kao Hao,et al.  Breakout local search for the quadratic assignment problem , 2013, Appl. Math. Comput..

[96]  David Malah,et al.  Bounds on the performance of vector-quantizers under channel errors , 2005, IEEE Transactions on Information Theory.

[97]  Thomas Stützle,et al.  Hierarchical Iterated Local Search for the Quadratic Assignment Problem , 2009, Hybrid Metaheuristics.

[98]  Mohamed Abdel-Basset,et al.  A comprehensive review of quadratic assignment problem: variants, hybrids and applications , 2018, Journal of Ambient Intelligence and Humanized Computing.

[99]  Zvi Drezner.  Compounded genetic algorithms for the quadratic assignment problem , 2005, Oper. Res. Lett..

[100]  Emad El-Sharkawy,et al.  Enhanced Cuckoo Search Algorithm with SPV Rule for Quadratic Assignment Problem , 2017 .

[101]  Martin Pelikan,et al.  Image segmentation using a genetic algorithm and hierarchical local search , 2012, GECCO '12.

[102]  Fred Glover,et al.  Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory , 1999, INFORMS J. Comput..

[103]  Alfonsas Misevicius,et al.  A Modified Simulated Annealing Algorithm for the Quadratic Assignment Problem , 2003, Informatica.

[104]  Bernd Freisleben,et al.  Fitness landscape analysis and memetic algorithms for the quadratic assignment problem , 2000, IEEE Trans. Evol. Comput..

[105]  Panos M. Pardalos,et al.  Quadratic Assignment Problem , 1997, Encyclopedia of Optimization.

[106]  Anmar Abuhamdah,et al.  Applying the big bang-big crunch metaheuristic to large-sized operational problems , 2020, International Journal of Electrical and Computer Engineering (IJECE).

[107]  Abdel Nasser,et al.  A Survey of the Quadratic Assignment Problem , 2014 .

[108]  Nizar Rokbani,et al.  A Hybrid Hierarchical Heuristic-ACO With Local Search Applied to Travelling Salesman Problem, AS-FA-Ls , 2020, Int. J. Syst. Dyn. Appl..

[109]  Yiliang Xu,et al.  A GA-ACO-local search hybrid algorithm for solving quadratic assignment problem , 2006, GECCO.

[110]  Belén Melián-Batista,et al.  A Hybrid Biased Random Key Genetic Algorithm for the Quadratic Assignment Problem , 2016, Inf. Process. Lett..

[111]  Mauro Dell'Amico,et al.  Solution of large weighted equicut problems , 1998, Eur. J. Oper. Res..

[112]  Mauro Dell'Amico,et al.  The single-finger keyboard layout problem , 2009, Comput. Oper. Res..

[113]  Rainer E. Burkard,et al.  Entwurf von Schreibmaschinentastaturen mittels quadratischer Zuordnungsprobleme , 1977, Math. Methods Oper. Res..

[114]  Babak Abedin,et al.  Website structure improvement: Quadratic assignment problem approach and ant colony meta-heuristic technique , 2008, Appl. Math. Comput..

[115]  Sigeru Omatu,et al.  Efficient Genetic Algorithms Using Simple Genes Exchange Local Search Policy for the Quadratic Assignment Problem , 2000, Comput. Optim. Appl..

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

[117]  Panos M. Pardalos,et al.  A Greedy Randomized Adaptive Search Procedure for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[118]  Zvi Drezner,et al.  Enhancing the performance of hybrid genetic algorithms by differential improvement , 2013, Comput. Oper. Res..

[119]  Mario Inostroza-Ponta,et al.  A memetic algorithm for the quadratic assignment problem with parallel local search , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

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

[121]  F. Rendl,et al.  A thermodynamically motivated simulation procedure for combinatorial optimization problems , 1984 .

[122]  Zakir Hussain Ahmed,et al.  A hybrid algorithm combining lexisearch and genetic algorithms for the quadratic assignment problem , 2018 .

[123]  L. Darrell Whitley,et al.  A Hybrid Genetic Algorithm for the Quadratic Assignment Problem , 2000, GECCO.

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

[125]  Matthew J. Saltzman,et al.  A Level-3 Reformulation-Linearization Technique-Based Bound for the Quadratic Assignment Problem , 2012, INFORMS J. Comput..

[126]  Robert Schaefer,et al.  An agent-based model of hierarchic genetic search , 2012, Comput. Math. Appl..

[127]  Franz Rendl,et al.  Bounds for the quadratic assignment problem using the bundle method , 2007, Math. Program..

[128]  Leon Steinberg,et al.  The Backboard Wiring Problem: A Placement Algorithm , 1961 .

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

[130]  Wojciech Chmiel,et al.  Evolutionary algorithm using conditional expectation value for quadratic assignment problem , 2019, Swarm Evol. Comput..

[131]  Kien Ming Ng,et al.  A parallel water flow algorithm with local search for solving the quadratic assignment problem , 2019 .

[132]  Yagmur Aksan,et al.  A stagnation-aware cooperative parallel breakout local search algorithm for the quadratic assignment problem , 2017, Comput. Ind. Eng..

[133]  Alexander P. Topchy,et al.  COMBINED GENETIC AND LOCAL SEARCH ALGORITHM FOR THE QUADRATIC ASSIGNMENT PROBLEM , 2000 .

[134]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.