Adaptive Sample Size and Importance Sampling in Estimation-based Local Search for Stochastic Combinatorial Optimization: A complete analysis

Metaheuristics and local search algorithms have received considerable attention as promising methods for tackling stochastic combinatorial optimization problems. However, in stochastic settings, these algorithms are usually simple extensions of the versions that are originally designed for deterministic optimization and often they lack rigorous integration with techniques that handle the stochastic character. In this paper, we discuss two generally applicable procedures that can be integrated into metaheuristics and local search algorithms that use Monte Carlo evaluation for estimating the solution cost. The first is an adaptive sampling procedure that selects the appropriate size of the sample to be used in Monte Carlo evaluation; the second is a procedure that adopts the importance sampling technique in order to reduce the variance of the cost estimator. We illustrate our approach and assess its performance using an estimation-based local search algorithm for the probabilistic traveling salesman problem. Experimental results show that an integration of the two procedures into the estimation-based local search increases significantly its effectiveness in cases where the variance of the cost estimator is high.