Fitness-Distance-Constraint in Constrained Optimization

Fitness-Distance-Constraint (FDC): A New Guide Selection Method for Meta-Heuristic Search Algorithms in solving Constrained Optimization

Dear researchers, Fitness-Distance-Constraint (FDC) is a guide selection method specially developed for the optimization of constrained problems. With the FDC method, the guidance mechanism in meta-heuristic search algorithms is designed specifically for constrained problems. With the FDC method, for the first time, distances in the constraint space were used in the design of the guidance mechanism in MHS algorithms.

Dear researchers, different terminologies are used for the design of the guidance mechanism in different types of MHS algorithms. In evolutionary algorithms such as GA, DE, FDB-AGDE, LSHADE processes such as mating pool creation and selection of parents are defined as guide selection. In algorithms such as ABC, NSM-TLABC, TLBO, the selection of followers, trackers, teachers, and students is actually the process of determining the solution candidates that guide the search process. Population members used in exploitation and exploration convergence equations in other types of MHS algorithms are actually guides in the search process.

Dear researchers, if you use the distances in the constraint space to determine the guides used in the convergence equations, you will be applying the hypothesis where we introduced in the FDC study. We recommend that the implementation of the FDC has been combined with other guide selection methods and dynamic strategies have been developed. The application of FDC in MHS algorithms is described below.

For solving Constrained Optimization Problems (COPs), you can used the Fitness-Distance-Constraint (FDC) selection method to redesign the selection mechanism of the MHS algorithm. The method is very easy to implement. You can use different strategies in applying the FDC method. Here, we developed three strategies for applying the FDC method to a MHS algorithm. While Strategy-1 and Strategy-2 are different applications of the FDC method, Strategy-3 is hybrid version of these two strategies. Besides, the Fitness-Constraint (FC) method, which is a different application of the FDC method, was also presented in the study. You can reach the detailed information about these strategies from the article.

In the source codes of the method, two different FC/FDC scripts were given and their explanation were presented as below:

Fitness_Constraint_v1: Used with the Strategy-1.

Fitness_Constraint_v2: Used with the Strategy-2.

Fitness_Distance_Constraint_v1: Used with the Strategy-1.

Fitness_Distance_Constraint_v2: Used with the Strategy-2.

We also tested the proposed FDC method on the AGDE algorithm. We have presented the best seven of the case studies which were created from using these strategies. We have also shared the codes of seven case studies created with the AGDE algorithm explained as below:

AGDE_Case1: The Strategy-1 and FDC method were used.

AGDE_Case2: The Strategy-1 and FC method were used.

AGDE_Case3: The Strategy-2 and FDC method were used.

AGDE_Case4: The Strategy-2 and FDC method were used.

AGDE_Case5: The Strategy-3 was used.

AGDE_Case6: The Strategy-3 was used.

AGDE_Case7: The Strategy-3 was used.

We proposed also a dynamic guide selection mechanism to implement the FDC method. In this mechanism, if there are constraint violations, the FDC method is used; otherwise, other selection methods such as Fitness-Distance Balance (FDB), randomly, probabilistic (methods such as roulette and tournament), and ordinally (ordinal selection from the population) are used.

We recommend using the FDC method for solving COPs. We hope that the FDC-AGDE algorithm will find the optimum solutions for COPs.

The article on the FDC method has been accepted but has not yet been published. When our article will be published, we will share the link of it.

Please also read the following article to learn more about guide selection methods. “Fitness-distance balance (FDB): a new selection method for meta-heuristic search algorithms”.

Please read the following article to learn also about “survivor methods” in MHS algorithms. “Development of the Natural Survivor Method (NSM) for designing an updating mechanism in metaheuristic search algorithms”.