Multi-Objectivizing Sum-of-the-Parts Combinatorial Optimization Problems by Random Objective Decomposition

Multi-objectivization is a term used to describe strategies developed for optimizing single-objective problems by multi-objective algorithms. This paper focuses on the multi-objectivization of the sum-of-the-parts Combinatorial Optimization Problems (COPs), which include the Traveling Salesman Problem (TSP), the Unconstrained Binary Quadratic Programming (UBQP) and other well-known COPs. For a sum-of-the-parts COP, we propose to decompose its original objective into two sub-objectives with controllable correlation. Based on the decomposition method, two new multi-objectivization techniques called Non-Dominance Search (NDS) and Non-Dominance Exploitation (NDE) are developed, respectively. NDS is combined with the Iterated Local Search (ILS) metaheuristic (with fixed neighborhood structure), while NDE is embedded within the Iterated Lin-Kernighan (ILK) metaheuristic (with varied neighborhood structure). The resultant metaheuristics are called ILS+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 and ILK+NDE both significantly outperform their counterparts on most of the test instances.

EB-GLS: An Improved Guided Local Search Based on the Big Valley Structure

Local search is a basic building block in memetic algorithms. Guided Local Search (GLS) can improve the efficiency of local search. By changing the guide function, GLS guides a local search to escape from locally optimal solutions and find better solutions. The key component of GLS is its penalizing mechanism which determines which feature is selected to penalize when the search is trapped in a locally optimal solution. The original GLS penalizing mechanism only makes use of the cost and the current penalty value of each feature. It is well known that many combinatorial optimization problems have a big valley structure, i.e., the better a solution is, the more the chance it is closer to a globally optimal solution. This paper proposes to use big valley structure assumption to improve the GLS penalizing mechanism. An improved GLS algorithm called Elite Biased GLS (EB-GLS) is proposed. EB-GLS records and maintains an elite solution as an estimate of the globally optimal solutions, and reduces the chance of penalizing the features in this solution. We have systematically tested the proposed algorithm on the symmetric traveling salesman problem. Experimental results show that EB-GLS is significantly better than GLS.