Investigation of ant colony optimization with Levy flight technique for a class of stochastic combinatorial optimization problem

Abstract

The demand for efficient solutions to optimization problems with uncertain and stochastic data is increasing. Probabilistic traveling salesman problem (PTSP) is a class of Stochastic Combinatorial Optimization Problems (SCOPs) involving partially unknown information about problem data with a known probability distribution. It consists to minimize the expected length of the tour where each customer requires a visit only with a given probability, at which customers who do not need a tour are just ignored without further optimization. Since the PTSP is NP-hard, the usage of metaheuristic methods is necessary to solve the problem. In this paper, we present the Ant Colony Optimization (ACO) algorithm combined with the Levy Flight mechanism (LFACO), which is based on Levy distribution to balance searching space and speed global optimization. Experimental results on a large number of instances show that the proposed Levy ACO algorithm on the probabilistic traveling salesman problem allows to obtain better results compared with the classical ACO algorithm.