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

TL;DR

This paper introduces novel multi-objectivization inspired metaheuristics for sum-of-the-parts combinatorial problems, demonstrating improved performance by decomposing objectives and leveraging non-dominated solutions to escape local optima.

Contribution

It proposes a new decomposition method for sum-of-the-parts problems and develops three metaheuristics that incorporate non-dominance search and exploitation techniques.

Findings

Metaheuristics outperform their counterparts on most test instances.

Appropriate correlation between sub-objectives enhances the ability to escape local optima.

Decomposition into sub-objectives improves solution quality and search efficiency.

Abstract

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.