Tabu search for nonlinear and parametric optimization (with links to genetic algorithms)

Abstract

In spite of the widespread importance of nonlinear and parametric optimization, many standard solution methods allow a large gap between local optimality and global optimality, inviting consideration of metaheuristics capable of reducing such gaps. We identify ways to apply the tabu search metaheuristic to nonlinear optimization problems from both continuous and discrete settings. The step beyond strictly combinatorial settings enlarges the domain of problems to which tabu search is typically applied. We show how tabu search can be coupled with directional search and scatter search approaches to solve such problems. In addition, we generalize standard weighted combinations (as employed in scatter search) to include structured weighted combinations capable of satisfying specified feasibility conditions (e.g., mapping weighted combinations of scheduling, partitioning and covering solutions into new solutions of the same type). The outcome suggests ways to exploit potential links between scatter search and genetic algorithms, and also provides a basis for integrating genetic algorithms with tabu search.