Fitness-Distance-Constraint (FDC) based guide selection method for constrained optimization problems

In the optimization of constrained type problems, the main difficulty is the elimination of the constraint violations in the evolutionary search process. Evolutionary algorithms are designed by default according to the requirements of unconstrained and continuous global optimization problems. Since there are no constraint functions in these type of problems, the constraint violations are not considered in the design of the guiding mechanism of evolutionary algorithms. In this study, two new methods were introduced to redesign the evolutionary algorithms in accordance with the requirements of constrained optimization problems. These were (i) constraint space-based, called Fitness-Distance-Constraint (FDC), selection method and (ii) dynamic guiding mechanism. Firstly, thanks to the FDC guide selection method, the constraint violation values of the individuals in the population were converted into score values and the individuals who increase the diversity in the search process were selected as guide. On the other hand, in dynamic guiding mechanism, the FDC method was applied in case of constraint violation, otherwise the default guide selection method was used The proposed methods were used to redesign the guiding mechanism of adaptive guided differential evolution (AGDE), a current evolutionary algorithm, and the FDC-AGDE algorithm was designed. The performance of the FDC-AGDE was tested on eleven different constrained real-world optimization problems. The results of the FDC-AGDE and AGDE were evaluated using the Friedman and Wilcoxon test methods. According to Wilcoxon pairwise results, the FDC-AGDE showed better performance than the AGDE in nine of the eleven problems and equal performance in two of the eleven problems. Moreover, the proposed algorithm was compared with the competitive and up-to-date MHS algorithms in terms of the results of Friedman test, Wilcoxon test, feasibility rate, and success rate. According to Friedman test results, the first three algorithms were the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms with the score of 2.69, 4.05, and 4.34, respectively. According to the mean values of the success rates obtained from the eleven problems, the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms ranked in the first three with the success rates of 67%, 48% and 28%, respectively. Consequently, the FDC-AGDE algorithm showed a superior performance comparing with the competing MHS algorithms. According to the results, it is expected that the proposed methods will be widely used in the constrained optimization problems in the future.