Promising infeasibility and multiple offspring incorporated to differential evolution for constrained optimization

Abstract

In this paper, we incorporate a diversity mechanism to the differential evolution algorithm to solve constrained optimization problems without using a penalty function. The aim is twofold: (1) to allow infeasible solutions with a promising value of the objective function to remain in the population and also (2) to increase the probabilities of an individual to generate a better offspring while promoting collaboration of all the population to generate better solutions. These goals are achieved by allowing each parent to generate more than one offspring. The best offspring is selected using a comparison mechanism based on feasibility and this child is compared against its parent. To maintain diversity, the proposed approach uses a mechanism successfully adopted with other evolutionary algorithms where, based on a parameter Sr a solution (between the best offspring and the current parent) with a better value of the objective function can remain in the population, regardless of its feasibility. The proposed approach is validated using test functions from a well-known benchmark commonly adopted to validate constrainthandling techniques used with evolutionary algorithms. The statistical results obtained by the proposed approach are highly competitive (based on quality, robustness and number of evaluations of the objective function) with respect to other constraint-handling techniques, either based on differential evolution or on other evolutionary algorithms, that are representative of the state-of-the-art in the area. Finally, a small set of experiments were made to detect sensitivity of the approach to its parameters.

Saving evaluations in differential evolution for constrained optimization

“…¤ £ well-known benchmark problems for constrained optimization. Details of each problem can be found in [4]. A summary of their main features are presented in Table 1.…”

“…From previous research [4] and some observations, we found, based on the DE mutation and crossover operator, that the offspring generated using them is located near one of the three random individuals selected for reproduction (about ¢ ¡ of the time) instead of being close to its parent. See rows 9 to 17 in Figure 1 for details.…”

“…Mezura-Montes et al [4] proposed a novel approach based on DE to solve constrained optimization problems called Diversity Differential Evolution (DDE). This constraint-handling technique consists on a comparison method based on feasibility.…”

Constrained Optimization with Evolutionary Algorithms: A Comprehensive Review

“…SR is proved to be efficient and highly competitive with other methods (Yu & Gen, 2010). As a general concept of constraint handling SR have been accompanied with other evolutionary algorithms including DE (Mezura-Montes, Velázquez-Reyes, & Coello Coello, 2005) and ACO (Leguizamon & Coello Coello, 2007).…”

An Evolutionary Approach to Solve a Novel Mechatronic Multiobjective Optimization Problem

“…a set of solutions is randomly generated). We selected Differential Evolution [17] because of several reasons: (1) it is an EA which has provided very competitive results when compared with respect to traditional EAs such as genetic algorithms and evolution strategies in real-world problems [6], (2) it is very simple to implement [17] and (3) its parameters for the crossover and mutation operators generally do not require a careful fine-tuning [13].…”