Bayesian stopping rules for multistart global optimization methods
Mathematical Programming: Series A and B
Stopping rules for a random optimization method
SIAM Journal on Control and Optimization
SIAM Journal on Optimization
Experimental Evaluation of Heuristic Optimization Algorithms: A Tutorial
Journal of Heuristics
A Parallel GRASP Heuristic for the 2-Path Network Design Problem (Research Note)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
A Hybrid Heuristic for the p-Median Problem
Journal of Heuristics
Networks
Bayesian Stopping Rules for Greedy Randomized Procedures
Journal of Global Optimization
Efficient parallel cooperative implementations of GRASP heuristics
Parallel Computing
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The main drawback of most metaheuristics is the absence of effective stopping criteria. Most implementations stop after performing a given maximum number of iterations or a given maximum number of consecutive iterations without improvement in the best known solution value, or after the stabilization of the set of elite solutions found along the search. We propose probabilistic stopping rules for randomized metaheuristics such as GRASP and VNS. We first show experimentally that the solution values obtained by GRASP fit a Normal distribution. Next, we use this approximation to obtain an online estimation of the number of solutions that might be at least as good as the best known at the time of the current iteration. This estimation is used to implement effective stopping rules based on the trade off between solution quality and the time needed to find a solution that might improve the best found to date. This strategy is illustrated and validated by a computational study reporting results obtained with some GRASP heuristics.