QUATRE-PM: QUasi-Affine TRansformation Evolution With Perturbation Mechanism

Abstract

Differential Evolution(DE) is a widely used technique to tackle complex optimization problems owing to its easy-implementation and excellent performance, nevertheless, the inborn weakness of the crossover operation has not been solved even in the recent state-of-the-art DE algorithms. There are two commonly used crossover schemes in DE, the exponential crossover and binomial crossover. The exponential crossover is actually a combination of 1-point and 2-point crossover schemes originated with Genetic Algorithm (GA), and it has positional bias because of the dependence on parameter separation. The binomial crossover tackles the positional bias by separating each dimension separately and treating them independently, however, bias still exists from a higher dimensional view, we name it selection bias, and that is the reason why the QUATRE algorithm was proposed. The evolution matrix is the primary component of the QUATRE algorithm which solves the selection bias of DE, however, the previous QUATRE variants still suffer the adaptation of the evolution matrix and can not be able to escape some local optima in complex optimization. Therefore, this paper proposes a new QUATRE with better adaptations of evolution matrix and control parameter, moreover, a perturbation mechanism is firstly proposed for the enhancement of population diversity. The main contributions of our algorithm can be summarized as follows. First, a new generation of evolution matrix is proposed, which can obtain better adaptation to the landscape of the objectives and help the algorithm jump out some local optima. Second, novel adaptations of control parameters are also proposed by incorporating historical memory mechanism and population reduction. Third, a new perturbation mechanism is proposed to enhance the population diversity. In order to validate the proposed algorithm, intensive experiments are conducted under 88 benchmark functions from the universal CEC2013, CEC2014, and CEC2017 test suites in comparison with several excellent DE variants and QUATRE variants, and the results support our superiority.

Keywords

• Differential evolution
• evolution matrix
• parameter adaptation
• perturbation mechanism
• QUATRE algorithm