Scatter Search and Path Relinking: Advances and Applications

Abstract

Scatter search (SS) is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies for combining solution vectors that have proved effective in a variety of problem settings. Path relinking (PR) has been suggested as an approach to integrate intensification and diversification strategies in a search scheme. The approach may be viewed as an extreme (highly focused) instance of a strategy that seeks to incorporate attributes of high quality solutions, by creating inducements to favor these attributes in the moves selected. The goal of this paper is to examine SS and PR strategies that provide useful alternatives to more established search methods. We describe the features of SS and PR that set them apart from other evolutionary approaches, and that offer opportunities for creating increasingly more versatile and effective methods in the future. Specific applications are summarized to provide a clearer understanding of settings where the methods are being used. Recent applications of both methods (and of selected component strategies within them) that have proved highly successful are:

New heuristic algorithms for the windy rural postman problem

“…The Scatter Search process tries to capture information not contained separately in the original solutions, takes advantage of improving methods, and makes use of strategy instead of randomization to carry out component steps. Our implementation is based on the description given in [8].…”

Usage of Exact Algorithms to Enhance Stochastic Local Search Algorithms

“…Other metaheuristics that could profit from such combinations are ant colony optimization [38], e.g. by optimizing partial solutions or extending partial solutions in an optimal way, or scatter search [53], in a way analogous to what is described for the genetic algorithms.…”

Efficient parallel cooperative implementations of GRASP heuristics

“…Information gathered from good solutions can be used to implement more effective memory-based heuristics. Path-relinking was originally proposed by Glover [12] as an intensification strategy exploring trajectories connecting elite solutions obtained by tabu search or scatter search [11,13]. Starting from one or more elite solutions, path-relinking generates paths leading toward other elite solutions and explores them in the search for better solutions.…”