An improved differential evolution algorithm for numerical optimization problems

Abstract

Differential evolution algorithm has gained popularity in solving complex optimization problems because of its simplicity and efficiency. However, it has several drawbacks, such as slow convergence rate, high sensitivity to the values of control parameters, and easiness of getting trapped into local optima. In order to overcome these drawbacks, this paper integrates three novel strategies into the original differential evolution. First, a population improvement strategy based on a multi-level sampling mechanism is used to accelerate the convergence and increase the diversity of the population. Second, a new self-adaptive mutation strategy balances the exploration and exploitation abilities of the algorithm by dynamically determining an appropriate value of the mutation parameters; this improves the search ability and helps the algorithm to escape from local optima when it gets stuck. Third, a new selection strategy guides the search to avoid local optima. Twelve benchmark functions of different characteristics are used to validate the performance of the proposed algorithm. The experimental results show that the proposed algorithm performs significantly better than the original DE in terms of the ability to locate the global optimum, convergence speed and scalability. In addition, the proposed algorithm is able to find the global optimal solutions on 8 out of 12 benchmark functions while 7 other well-established metaheuristic algorithms, namely NBOLDE, ODE, DE, SaDE, JADE, PSO and GA, can obtain only 6, 2, 1, 1, 1, 1 and 1 functions respectively.