A dynamic self-adaptive harmony search algorithm for continuous optimization problems

In solving global optimization problems for continuous functions, researchers often rely on metaheuristic algorithms to overcome the computational drawbacks of the existing numerical methods. A metaheuristic is an evolutionary algorithm that does not require the functions in the problem to satisfy specific conditions or mathematical properties. A recently proposed metaheuristic is the harmony search algorithm, which was inspired by the music improvisation process and has been applied successfully in the solution of various global optimization problems. However, the overall performance of this algorithm and its convergence properties are quite sensitive to the initial parameter settings. Several improvements of the harmony search algorithm have been proposed to incorporate self-adaptive features. In these modified versions of the algorithm, the parameters are automatically tuned during the optimization process to achieve superior results. This paper proposes a new dynamic and self-adaptive harmony search algorithm in which two of the optimization parameters, the pitch adjustment rate and the bandwidth, are auto-tuned. These two parameters have substantial influence on the quality of the final solution. The proposed algorithm utilizes two new quality measures to dynamically drive the optimization process: the current best-to-worst ratio of the harmony memory fitness function and the improvisation acceptance rate. The key difference between the proposed algorithm and most competing methods is that the values of the pitch adjustment rate and bandwidth are determined independently of the current improvisation count and therefore vary dynamically rather than monotonically. The results demonstrate the superiority of the proposed algorithm over various other recent methods based on several common benchmarking functions.