Scatter Search and Path Relinking: Foundations and Advanced Designs

Abstract

Scatter Search and its generalized form Path Relinking, are evolutionary methods that have been successfully applied to hard optimization problems. Unlike genetic algorithms, they operate on a small set of solutions and employ diversification strategies of the form proposed in Tabu Search, which give precedence to strategic learning based on adaptive memory, with limited recourse to randomization. The fundamental concepts and principles were first proposed in the 1970s as an extension of formulations, dating back to the 1960s, for combining decision rules and problem constraints. (The constraint combination approaches, known as surrogate constraint methods, now independently provide an important class of relaxation strategies for global optimization.) The Scatter Search framework is flexible, allowing the development of alternative implementations with varying degrees of sophistication. Path Relinking, on the other hand, was first proposed in the context of the Tabu Search metaheuristics, but it has been also applied with a variety of other methods. This chapter’s goal is to provide a grounding in the essential ideas of Scatter Search and Path Relinking, together with pseudo-codes of simple versions of these methods, that will enable readers to create successful applications of their own.