UDE-III: An Enhanced Unified Differential Evolution Algorithm for Constrained Optimization Problems

TL;DR

UDE-III is an improved differential evolution algorithm designed for constrained optimization, incorporating multiple strategies, dual populations, and novel stagnation handling to outperform previous versions on benchmark problems.

Contribution

The paper introduces UDE-III, a significantly enhanced differential evolution algorithm with new strategies and mechanisms for better performance on constrained optimization problems.

Findings

UDE-III outperforms UDE-II on CEC 2024 benchmark problems.

The integration of multiple trial vector strategies improves convergence.

Novel stagnation handling enhances algorithm robustness.

Abstract

In this paper, an enhanced unified differential evolution algorithm, named UDE-III, is presented for real parameter-constrained optimization problems (COPs). The proposed UDE-III is a significantly enhanced version of the Improved UDE (i.e., IUDE or UDE-II), which secured the 1st rank in the CEC 2018 competition on real parameter COPs. To design UDE-III, we extensively targeted the weaknesses of UDE-II. Specifically, UDE-III uses three trial vector generation strategies - DE/rand/1, DE/current-to-rand/1, and DE/current-to-pbest/1. It is based on a dual population approach, and for each generation, it divides the current population into two sub-populations. In the top sub-population, it employs all three trial vector generation strategies on each target vector. On the other hand, the bottom sub-population employs strategy adaptation and one trial vector generation strategy is implemented on each target vector. The mutation operation in UDE-III is based on ranking-based mutation. Further, it employs the parameter adaptation principle of SHADE. The constraint handling principle in UDE-III is based on a combination of the feasibility rule and epsilon-constraint handling technique. We observed that stagnation is a major weakness of UDE-II. To overcome this weakness, we took inspiration from the best-discarded vector selection (BDVS) strategy proposed in the literature and integrated a novel strategy in UDE-III to address stagnation. Additionally, unlike UDE-II, UDE-III considers the size of the two sub-populations to be a design element. Moreover, in comparison to UDE-II, UDE-III improves upon the strategy adaptation, ranking-based mutation, and the constraint handling technique. The proposed UDE-III algorithm is tested on the 28 benchmark 30D problems provided for the CEC 2024 competition on real parameter COPs. The experimental results demonstrate the superiority of UDE-III over UDE-II.