Estimation-based ant colony optimization and local search for the probabilistic traveling salesman problem

Abstract

The use of ant colony optimization for solving stochastic optimization problems has received a significant amount of attention in recent years. In this paper, we present a study of enhanced ant colony optimization algorithms for tackling a stochastic optimization problem, the probabilistic traveling salesman problem. In particular, we propose an empirical estimation approach to evaluate the cost of the solutions constructed by the ants. Moreover, we use a recent estimation-based iterative improvement algorithm as a local search. Experimental results on a large number of problem instances show that the proposed ant colony optimization algorithms outperform the current best algorithm tailored to solve the given problem, which also happened to be an ant colony optimization algorithm. As a consequence, we have obtained a new state-of-the-art ant colony optimization algorithm for the probabilistic traveling salesman problem.

Estimation-based metaheuristics for the probabilistic traveling salesman problem

“…First, we developed 2.5-opt-EEais Balaprakash et al, 2009a), a new state-of-the-art iterative improvement algorithm for the PTSP that uses an estimation-based approach to compute the cost difference between two solutions. Second, we showed that the integration of two PTSP-specific algorithmic components, 2.5-opt-EEais as local search and an estimation-based approach to evaluate the solution cost of artificial ants, into an ant colony optimization (ACO) algorithm ) is highly beneficial in terms of computation time and solution quality (Balaprakash et al, 2009b). Here, we extend our work to metaheuristics that are known to have high performance on the related traveling salesman problem (TSP).…”

“…ACO/F-Race (Birattari et al, 2005) is an improved variant of S-ACOa, in which the number of realizations for each comparison is determined on-line based on the F-Race procedure (Birattari et al, 2002;Birattari, 2009). Recently, in Balaprakash et al (2009b), we extended ACS with our effective estimation-based iterative improvement algorithm, 2.5-opt-EEais (Balaprakash et al, 2009a) and an ANOVA-Race procedure. This procedure is based on a parametric statistical test for multiple comparisons to determine the number of realizations.…”

“…As an ACO algorithm for the PTSP, we choose ACS-EE (Balaprakash et al, 2009b), a recent state-of-the-art ACO algorithm for the PTSP. It is an extension of the ant colony system (ACS) algorithm (Dorigo and Gambardella, 1997) designed for the TSP.…”

F-Race and Iterated F-Race: An Overview

“…The resulting algorithm is called ACO/F-Race and it uses F-Race to determine the best of a set of candidate solutions generated by the ACO algorithm. In later work by Balaprakash et al [3] on the application of estimation-based ACO algorithms to the probabilistic traveling salesman problem the Friedman test is replaced by an ANOVA.…”

New Approximation-Based Local Search Algorithms for the Probabilistic Traveling Salesman Problem

“…Starting point for our work is a state-of-the-art local search algorithm for the PTSP which uses the 2.5-opt neighbourhood and a sampling-based approximation for the difference between the expected costs of two neighbouring solutions. It is called 2.5-opt-EEs and a detailed description can be found in [7] with some extensions in [3].…”