Best Polynomial Harmony Search with Best β-Hill Climbing Algorithm

Abstract

Harmony Search Algorithm (HSA) is an evolutionary algorithm which mimics the process of music improvisation to obtain a nice harmony. The algorithm has been successfully applied to solve optimization problems in different domains. A significant shortcoming of the algorithm is inadequate exploitation when trying to solve complex problems. The algorithm relies on three operators for performing improvisation: memory consideration, pitch adjustment, and random consideration. In order to improve algorithm efficiency, we use roulette wheel and tournament selection in memory consideration, replace the pitch adjustment and random consideration with a modified polynomial mutation, and enhance the obtained new harmony with a modified β-hill climbing algorithm. Such modification can help to maintain the diversity and enhance the convergence speed of the modified HS algorithm. β-hill climbing is a recently introduced local search algorithm that is able to effectively solve different optimization problems. β-hill climbing is utilized in the modified HS algorithm as a local search technique to improve the generated solution by HS. Two algorithms are proposed: the first one is called PHSβ–HC and the second one is called Imp. PHSβ–HC. The two algorithms are evaluated using 13 global optimization classical benchmark function with various ranges and complexities. The proposed algorithms are compared against five other HSA using the same test functions. Using Friedman test, the two proposed algorithms ranked 2nd (Imp. PHSβ–HC) and 3rd (PHSβ–HC). Furthermore, the two proposed algorithms are compared against four versions of particle swarm optimization (PSO). The results show that the proposed PHSβ–HC algorithm generates the best results for three test functions. In addition, the proposed Imp. PHSβ–HC algorithm is able to overcome the other algorithms for two test functions. Finally, the two proposed algorithms are compared with four variations of differential evolution (DE). The proposed PHSβ–HC algorithm produces the best results for three test functions, and the proposed Imp. PHSβ–HC algorithm outperforms the other algorithms for two test functions. In a nutshell, the two modified HSA are considered as an efficient extension to HSA which can be used to solve several optimization applications in the future.

Keywords

• harmony search algorithm
• evolutionary algorithms
• hill climbing
• polynomial mutation
• β-hill climbing
• 68w50
• 68t20
• 90c59