A Template for Scatter Search and Path Relinking

Scatter search and its generalized form called path relinking are evolutionary methods that have 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, these methods use strategies for combining solution vectors that have proved effective for scheduling, routing, financial product design, neural network training, optimizing simulation and a variety of other problem areas. These approaches can be implemented in multiple ways, and offer numerous alternatives for exploiting their basic ideas. We identify a template for scatter search and path relinking methods that provides a convenient and "user friendly" basis for their implementation. The overall design can be summarized by a small number of key steps, leading to versions of scatter search and path relinking that are fully specified upon providing a handful of subroutines. Illustrative forms of these subroutines are described that make it possible to create methods for a wide range of optimization problems. Highlights of these components include new diversification generators for zero-one and permutation problems (extended by a mapping-by-objective technique that handles additional classes of problems), together with processes to avoid generating or incorporating duplicate solutions at various stages (related to the avoidance of cycling in tabu search) and a new method for creating improved solutions. *** UPDATED AND EXTENDED: February 1998 *** Previous version appeared in Lecture Notes in Computer Science, 1363, J.K. Hao, E. Lutton, E. Ronald, M. Schoenauer, D. Snyers (Eds.), 13-54, 1997. This research was supported in part by the Air Force Office of Scientific Research Grant #F49620-97-1-0271.