Surrogate-Assisted Differential Evolution with an Adaptive Evolution Control Based on Feasibility to Solve Constrained Optimization Problems

Abstract

This paper presents an adaptive evolution control based on the feasibility of solutions, which is used with the nearest-neighbor regression surrogate model, to approximate the objective function value and the sum of constraint violation when solving constrained numerical optimization problems. The search algorithm used is the "differential evolution with combined variants'' (DECV) and the constrainthandling technique adopted is the set of feasibility rules. The approach is compared against one state-of-the-art algorithm that employs the same surrogate model with an adaptive evolution control, as well. Twenty-four well-known test problems are solved in the experiments. From the obtained results, it is found that the evolution control based on the feasibility of solutions reduces the number of evaluations in the expensive model, particularly in problems with inequality constraints.

An enhanced surrogate-assisted differential evolution for constrained optimization problems

“…The SADE-kNN method presented in [38] employed the binary tournament selection technique proposed by Deb [51]. Other methods recently presented in the literature also employed the DE algorithm associated with some of the CHTs described above, including for instance SA-DECV [21] and SA-DECV_SR [56]. These works presented methods that couple DE with the k-NN surrogate model to approximate both the values of the objective function and the sum of constraint violations.…”

“…This way, the average number of evaluations considering all 25 runs (nfe) increases to 83,177.22. This does not accurately represent the performance of the algorithm: although it was able to reach the optimum with a small number of evaluations in most of the runs (21), the stagnation in the other 4 runs drastically increases the value of this metric (nfe).…”

“…They may comprise polynomial approximation models [5,6]; radial basis functions [7][8][9][10]; response surface models [11]; artificial neural networks [12]; Gaussian process [13,14]; Kriging [15]; Support Vector Machines [16], and similarity-based models such as the nearest-neighbor algorithms [17][18][19]. Particularly, the 𝒌-NN model presents many advantages in terms of good performance and ease of implementation, as reported in [19][20][21].…”

“…The goal of reducing computational costs was also sought in [24] where the fitness function has been approximated by an online multi-layer neural network, and in [25] that presented a surrogate-assisted PSO algorithm. Surrogate models have also been employed to initialize the population of candidate solutions in evolutionary operators such as mutation and crossover [26,27], and to calculate approximations for the sum of violation terms [21]. The IEEE Congress on Evolutionary Computation (CEC) competitions have presented many articles that solve computationally expensive functions by employing metamodels with EAs.…”