Designing effective improvement methods for scatter search: an experimental study on global optimization

Scatter search (SS) is a metaheuristic framework that explores solution spaces by evolving a set of reference points. These points (solutions) are initially generated with a diversification method and the evolution of these reference points is induced by the application of four methods: subset generation, combination, improvement and update. In this paper, we consider the application of the SS algorithm to the unconstrained global optimization problem and study its performance when coupled with different improvement methods. Specifically, we design and implement new procedures that result by combining SS with eight different improvement methods. We also propose an SS procedure (on the space of parameters) to determine the values of the key search parameters used to create the combined methods. We finally study whether improvement methods of different quality have a direct effect on the performance of the SS procedure, and whether this effect varies depending on attributes of the function that is minimized. Our experimental study reveals that the improvement method is a key element in an effective SS method for global optimization, and finds that the best improvement methods for high-dimensional functions are the coordinate method and two versions of scatter search itself. More significantly, extensive computational tests conducted with 12 leading methods from the literature show that our resulting method outperforms competing methods in the quality of both average solutions and best solutions obtained.