An effective hybrid harmony search for the asymmetric travelling salesman problem

ABSTRACT This article is part of a study aiming to adapt the Harmony Search (HS) algorithm to the asymmetric travelling salesman problem. The population-based approach of the HS algorithm and its weak exploitation mechanism constituted a good reason for starting the research on improving the method, by applying the approach found in other population-based metaheuristics characterized by the same imperfection. The proposed HS is supplemented with the mechanism allowing the efficiency of the exploitation process to be increased by combining the algorithm with hill climbing. The proposed approach assumes modifying the solutions at three different places, affecting the HS exploration and exploitation mechanism in different ways. As a result, the appropriate approach to the effective design of hybrid harmony search is recommended. In addition, by measuring the actual time of the method's execution, the recommended ratio of time devoted to local search and the creation of harmonies was determined.