Incorporating Objective Function Information Into the Feasibility Rule for Constrained Evolutionary Optimization

Abstract

When solving constrained optimization problems by evolutionary algorithms, an important issue is how to balance constraints and objective function. This paper presents a new method to address the above issue. In our method, after generating an offspring for each parent in the population by making use of differential evolution (DE), the well-known feasibility rule is used to compare the offspring and its parent. Since the feasibility rule prefers constraints to objective function, the objective function information has been exploited as follows: if the offspring cannot survive into the next generation and if the objective function value of the offspring is better than that of the parent, then the offspring is stored into a predefined archive. Subsequently, the individuals in the archive are used to replace some individuals in the population according to a replacement mechanism. Moreover, a mutation strategy is proposed to help the population jump out of a local optimum in the infeasible region. Note that, in the replacement mechanism and the mutation strategy, the comparison of individuals is based on objective function. In addition, the information of objective function has also been utilized to generate offspring in DE. By the above processes, this paper achieves an effective balance between constraints and objective function in constrained evolutionary optimization. The performance of our method has been tested on two sets of benchmark test functions, namely, 24 test functions at IEEE CEC2006 and 18 test functions with 10-D and 30-D at IEEE CEC2010. The experimental results have demonstrated that our method shows better or at least competitive performance against other state-of-the-art methods. Furthermore, the advantage of our method increases with the increase of the number of decision variables.

Composite Differential Evolution for Constrained Evolutionary Optimization

“…In [8], Wang et al made use of DE/rand-to-best/1/bin to introduce information of objective function into the population. Meanwhile, DE/current-to-rand/1 is used to cope with rotated optimization problems.…”

“…, and x t r 4 from the population; 8 Randomly choose a F value from F pool and a CR value from CR pool ; , and x t r 2 from the population ; 13 Randomly choose a F value from F pool and a CR value from CR pool ;…”

“…As shown in Algorithm 1, three offspring will be generated for each target vector. Moreover, similar to [8], we establish two parameter pools F pool and CR pool for the scaling factor F and the crossover control parameter CR, respectively.…”

“…As a result, a variety of constrained EAs has been proposed [8], [9], [10]. A constrained EA includes two main components: 1) search algorithm and 2) constraint-handling technique.…”

Economic and Emission Dispatch Using Ensemble Multi-Objective Differential Evolution Algorithm

“…It is a greedy mechanism [50].The advantage of the principle is that it has the ability to motivate the population to the feasible regions and accelerate the optimization. In addition, the method does not need any penalty parameters, which makes it attractive.…”