Multi-objectivization Inspired Metaheuristics for the Sum-of-the-Parts Combinatorial Optimization Problems

Multi-objectivization is a term used to describe strategies developed for optimizing single-objective problems by multi-objective algorithms. This paper focuses on multi-objectivizing the sum-of-the-parts combinatorial optimization problems, which include the traveling salesman problem, the unconstrained binary quadratic programming and other well-known combinatorial optimization problem. For a sum-of-the-parts combinatorial optimization problem, we propose to decompose its original objective into two sub-objectives with controllable correlation. Based on the decomposition method, two new multi-objectivization inspired single-objective optimization techniques called non-dominance search and non-dominance exploitation are developed, respectively. Non-dominance search is combined with two metaheuristics, namely iterated local search and iterated tabu search, while non-dominance exploitation is embedded within the iterated Lin-Kernighan metaheuristic. The resultant metaheuristics are called ILS+NDS, ITS+NDS and ILK+NDE, respectively. Empirical studies on some TSP and UBQP instances show that with appropriate correlation between the sub-objectives, there are more chances to escape from local optima when new starting solution is selected from the non-dominated solutions defined by the decomposed sub-objectives. Experimental results also show that ILS+NDS, ITS+NDS and ILK+NDE all significantly outperform their counterparts on most of the test instances

Solving Multimodal Problems via Multiobjective Techniques with Application to Phase Equilibrium Detection

Abstract — For solving multimodal problems by means of evolutionary algorithms, one often resorts to multistarts or niching methods. The latter approach the question: ‘What is elsewhere?’ by an implicit second criterion in order to keep populations distributed over the search space. Induced by a practical problem that appears to be simple but is not easily solved, a multiobjective algorithm is proposed for solving multimodal problems. It employs an explicit diversity criterion as second objective. Experimental comparison with standard methods suggests that the multiobjective algorithm is fast and reliable and that coupling it with a local search technique is straightforward and leads to enormous quality gain. The combined algorithm is still fast and may be especially valuable for practical problems with costly target function evaluations. I