Principles of scatter search

Scatter search is an evolutionary method that has been successfully applied to hard optimization problems. The fundamental concepts and principles of the method were first proposed in the 1970s, based on formulations dating back to the 1960s for combining decision rules and problem constraints. In contrast to other evolutionary methods like genetic algorithms, scatter search is founded on the premise that systematic designs and methods for creating new solutions afford significant benefits beyond those derived from recourse to randomization. It uses strategies for search diversification and intensification that have proved effective in a variety of optimization problems. This paper provides the main principles and ideas of scatter search and its generalized form path relinking. We first describe a basic design to give the reader the tools to create relatively simple implementations. More advanced designs derive from the fact that scatter search and path relinking are also intimately related to the tabu search (TS) metaheuristic, and gain additional advantage by making use of TS adaptive memory and associated memory-exploiting mechanisms capable of being tailored to particular contexts. These and other advanced processes described in the paper facilitate the creation of sophisticated implementations for hard problems that often arise in practical settings. Due to their flexibility and proven effectiveness, scatter search and path relinking can be successfully adapted to tackle optimization problems spanning a wide range of applications and a diverse collection of structures, as shown in the papers of this volume.