Cε-LDE: A lightweight variant of differential evolution algorithm with combined ε constrained method and Lévy flight for constrained optimization problems

Abstract

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named Cε-LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed Cε-LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of Cε-LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that Cε-LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme.