Feasibility Preserving Constraint-Handling Strategies for Real Parameter Evolutionary Optimization

TL;DR

This paper introduces new constraint-handling strategies for evolutionary algorithms that repair infeasible solutions, demonstrating their robustness and effectiveness on large-scale problems and various applications.

Contribution

It proposes two novel single-parameter constraint-handling methods based on parent-centric and inverse parabolic probability distributions, improving feasibility preservation in EAs.

Findings

New methods outperform existing strategies in robustness and accuracy.

Effective on problems with up to 500 variables, locating solutions within 10^{-10} error.

Demonstrated on structural design and generic constrained problems.

Abstract

Evolutionary Algorithms (EAs) are being routinely applied for a variety of optimization tasks, and real-parameter optimization in the presence of constraints is one such important area. During constrained optimization EAs often create solutions that fall outside the feasible region; hence a viable constraint- handling strategy is needed. This paper focuses on the class of constraint-handling strategies that repair infeasible solutions by bringing them back into the search space and explicitly preserve feasibility of the solutions. Several existing constraint-handling strategies are studied, and two new single parameter constraint-handling methodologies based on parent-centric and inverse parabolic probability (IP) distribution are proposed. The existing and newly proposed constraint-handling methods are first studied with PSO, DE, GAs, and simulation results on four scalable test-problems under different location settings of the optimum are presented. The newly proposed constraint-handling methods exhibit robustness in terms of performance and also succeed on search spaces comprising up-to 500 variables while locating the optimum within an error of 10$^{-10}$. The working principle of the IP based methods is also demonstrated on (i) some generic constrained optimization problems, and (ii) a classic `Weld' problem from structural design and mechanics. The successful performance of the proposed methods clearly exhibits their efficacy as a generic constrained-handling strategy for a wide range of applications.