Speeding up continuous GRASP

Continuous GRASP (C-GRASP) is a stochastic local search metaheuristic for finding cost-efficient solutions to continuous global optimization problems subject to box constraints (Hirsch et al., 2007). Like a greedy randomized adaptive search procedure (GRASP), a C-GRASP is a multi-start procedure where a starting solution for local improvement is constructed in a greedy randomized fashion. In this paper, we describe several improvements that speed up the original C-GRASP and make it more robust. We compare the new C-GRASP with the original version as well as with other algorithms from the recent literature on a set of benchmark multimodal test functions whose global minima are known. Hart's sequential stopping rule (1998) is implemented and C-GRASP is shown to converge on all test problems.

[1]  Michael J. Hirsch,et al.  A continuous GRASP to determine the relationship between drugs and adverse reactions , 2007 .

[2]  Rafael Martí,et al.  Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions , 2005, J. Glob. Optim..

[3]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

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

[5]  Patrick Siarry,et al.  Enhanced simulated annealing for globally minimizing functions of many-continuous variables , 1997, TOMS.

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

[7]  Pablo Moscato,et al.  Handbook of Applied Optimization , 2000 .

[8]  Michael J. Hirsch,et al.  Solving systems of nonlinear equations with continuous GRASP , 2009 .

[9]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[10]  C. Ribeiro,et al.  Essays and Surveys in Metaheuristics , 2002, Operations Research/Computer Science Interfaces Series.

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

[12]  M. Fukushima,et al.  Minimizing multimodal functions by simplex coding genetic algorithm , 2003 .

[13]  Masao Fukushima,et al.  Tabu Search directed by direct search methods for nonlinear global optimization , 2006, Eur. J. Oper. Res..

[14]  C. Dorea.  Stopping rules for a random optimization method , 1990 .

[15]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[16]  Panos M. Pardalos,et al.  A Collection of Test Problems for Constrained Global Optimization Algorithms , 1990, Lecture Notes in Computer Science.

[17]  Z. Michalewicz,et al.  Genocop III: a co-evolutionary algorithm for numerical optimization problems with nonlinear constraints , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[18]  Panos Pardalos,et al.  Sensor Registration in a Sensor Network by Continuous GRASP , 2006, MILCOM 2006 - 2006 IEEE Military Communications conference.

[19]  Panos M. Pardalos,et al.  Global optimization by continuous grasp , 2007, Optim. Lett..

[20]  William E. Hart.  Sequential Stopping Rules for Random Optimization Methods with Applications to Multistart Local Search , 1998, SIAM J. Optim..

[21]  Masao Fukushima,et al.  Hybrid simulated annealing and direct search method for nonlinear unconstrained global optimization , 2002, Optim. Methods Softw..

[22]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.