A comparative study of different local search application strategies in hybrid metaheuristics

This paper presents results of a comparative study with the objective to identify the most effective and efficient way of applying a local search method embedded in a hybrid algorithm. The hybrid metaheuristic employed in this study is called “DE–HS–HJ” because it is comprised of two cooperative metaheusitic algorithms, i.e., differential evolution (DE) and harmony search (HS), and one local search (LS) method, i.e., Hooke and Jeeves (HJ) direct search. Eighteen different ways of using HJ local search were implemented and all of them were evaluated with 19 problems, in terms of six performance indices, covering both accuracy and efficiency. Statistic analyses were conducted accordingly to determine the significance in performance differences. The test results show that overall the best three LS application strategies are applying local search to every generated solution with a specified probability and also to each newly updated solution (NUS + ESP), applying local search to every generated solution with a specified probability (ESP), and applying local search to every generated solution with probability and also to the updated current global best solution (EUGbest + ESP). ESP is found to be the best local search application strategy in terms of success rate. Integrating it with NUS further improve the overall performance. EUGbest + ESP is the most efficient and it is also able to achieve high level of accuracy (the fourth place in terms of success rate with an average above 0.9).

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► This paper is the first comprehensive comparative study of local search application strategies in hybrid metaheuristic algorithms.
► The hybrid metaheuristic algorithm employed in the study is state-of-the-art, composed of two cooperative metaheuristic algorithms (differential evolution and harmony search) enhanced by the Hooke and Jeeves local search.
► The top three best out of 18 different strategies are identified based on the results obtained in testing a suite of 19 problems. The results are expected to be useful for deciding how to design a hybrid metaheuristic algorithm.