Path-Guided Mutation for Stochastic Pareto Local Search Algorithms

Stochastic Pareto local search (SPLS) methods are local search algorithms for multi-objective combinatorial optimization problems that restart local search from points generated using a stochastic process. Examples of such stochastic processes are Brownian motion (or random processes), and the ones resulting from the use of mutation and recombination operators. We propose a path-guided mutation operator for SPLS where an individual solution is mutated in the direction of the path to another individual solution in order to restart a PLS. We study the exploration of the landscape of the bi-objective Quadratic assignment problem (bQAP) using SPLSs that restart the PLSs from: i) uniform randomly generated solutions, ii) solutions generated from best-so-far local optimal solutions with uniform random mutation and iii) with path-guided mutation. Experiments on a bQAP with a large number of facilities and high correlation between the flow matrices show that using mutation, and especially path-guided mutation, is beneficial for performance of SPLS. The performance of SPLSs is partially explained using their dynamical behavior like the probability of escaping the local optima and the speed of enhancing the Pareto front.