Adaptive sample size and importance sampling in estimation-based local search for the probabilistic traveling salesman problem

The probabilistic traveling salesman problem is a paradigmatic example of a stochastic combinatorial optimization problem. For this problem, recently an estimation-based local search algorithm using delta evaluation has been proposed. In this paper, we adopt two well-known variance reduction procedures in the estimation-based local search algorithm: 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 importance sampling to reduce the variance involved in the cost estimation. We investigate several possible strategies for applying these procedures to the given problem and we identify the most effective one. Experimental results show that a particular heuristic customization of the two procedures increases significantly the effectiveness of the estimation-based local search.