Restart strategies for GRASP with path-relinking heuristics

GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i1, i2, …} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem.

[1]  W. R. Schucany,et al.  Handbook of Parallel Computing and Statistics , 2008 .

[2]  Panos M. Pardalos,et al.  Randomized heuristics for the Max-Cut problem , 2002, Optim. Methods Softw..

[3]  Eric Horvitz,et al.  Dynamic restart policies , 2002, AAAI/IAAI.

[4]  Eugeniusz Nowicki,et al.  An Advanced Tabu Search Algorithm for the Job Shop Problem , 2005, J. Sched..

[5]  Mauricio G. C. Resende,et al.  GRASP with path relinking heuristics for the antibandwidth problem , 2011, Networks.

[6]  Jeffery L. Kennington,et al.  Interfaces in Computer Science and Operations Research , 1997 .

[7]  Celso C. Ribeiro,et al.  Path-relinking intensification methods for stochastic local search algorithms , 2012, J. Heuristics.

[8]  Fred Glover,et al.  Tabu Search and Adaptive Memory Programming — Advances, Applications and Challenges , 1997 .

[9]  Toshihide Ibaraki,et al.  Metaheuristics : progress as real problem solvers , 2005 .

[10]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.

[11]  David Zuckerman,et al.  Optimal Speedup of Las Vegas Algorithms , 1993, Inf. Process. Lett..

[12]  Panos M. Pardalos,et al.  GRASP with path relinking for the weighted MAXSAT problem , 2007, ACM J. Exp. Algorithmics.

[13]  Mauricio G. C. Resende,et al.  Grasp: An Annotated Bibliography , 2002 .

[14]  Celso C. Ribeiro,et al.  GRASP with Path-Relinking: Recent Advances and Applications , 2005 .

[15]  M. Resende,et al.  Greedy Randomized Adaptive Search Procedures. , 2003 .

[16]  I. V. Sergienko,et al.  Optimization Parallelizing for Discrete Programming Problems , 2004 .

[17]  Mauricio G. C. Resende,et al.  An Annotated Bibliography of Grasp Part Ii: Applications , 2022 .

[18]  F. Glover,et al.  Fundamentals of Scatter Search and Path Relinking , 2000 .

[19]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[20]  Celso C. Ribeiro,et al.  Scatter Search and Path-Relinking: Fundamentals, Advances, and Applications , 2010 .

[21]  Oleg V. Shylo,et al.  On algorithm portfolios and restart strategies , 2011, Oper. Res. Lett..

[22]  Michel Gendreau,et al.  Handbook of Metaheuristics , 2010 .

[23]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[24]  Mauricio G. C. Resende,et al.  An Annotated Bibliography of Grasp Part I: Algorithms , 2022 .

[25]  Celso C. Ribeiro,et al.  A GRASP with path‐relinking for private virtual circuit routing , 2003, Networks.

[26]  Rafael Martí,et al.  GRASP and Path Relinking for 2-Layer Straight Line Crossing Minimization , 1999, INFORMS J. Comput..

[27]  Panos M. Pardalos,et al.  Restart strategies in optimization: parallel and serial cases , 2011, Parallel Comput..

[28]  Gintaras Palubeckis,et al.  Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem , 2004, Ann. Oper. Res..

[29]  Mauricio G. C. Resende,et al.  GRASP with path-relinking for the generalized quadratic assignment problem , 2011, J. Heuristics.

[30]  Panos M. Pardalos,et al.  Handbook of applied optimization , 2002 .

[31]  Panos M. Pardalos,et al.  Parallel computing in global optimization , 2006 .