Multiple Local Searches to Balance Intensification and Diversification in a Memetic Algorithm for the Linear Ordering Problem

Abstract

The Linear Ordering problem (LOP) is an NP-hard problem, which has been solved using different metaheuristic approaches. The best solution for this problem is a memetic algorithm, which uses the traditional approach of hybridizing a genetic algorithm with a single local search; on the contrary, in this paper we present a memetic solution hybridized with multiple local searches through all the memetic process. Experimental results show that using the best combination of local searches, instead of a single local search, the performance for XLOLIB instances is improved by 11.46% in terms of quality of the solution. For the UB-I instances, the proposed algorithm obtained a 0.12% average deviation from the best known solutions, achieving 17 new best known solutions. A Wilcoxon test was performed, ranking the proposed memetic algorithm as the second best solution of the state of the art for LOP. The results show that the multiple local searches approach can be more effective to get a better control in balancing intensification/diversification than the single local search approach.