Open Access

ARTICLE

Enhanced Artificial Protozoa Optimizer via a Multi-Strategy Framework for Engineering Design Problems

Dingfeng Song¹, Haibo Wang^2,3,*, Zhiwei Ye¹, Shuhao Yang¹, Mengxuan Li¹

1 School of Computer Science and Artificial Intelligence, Hubei University of Technology, Wuhan, China
2 School of Economics and Management, Hubei University of Technology, Wuhan, China
3 Digital Economy Development Research Center, Hubei University of Technology, Wuhan, China

* Corresponding Author: Haibo Wang. Email:

Computers, Materials & Continua 2026, 89(2), 54 https://doi.org/10.32604/cmc.2026.084242

Received 18 April 2026; Accepted 03 August 2026; Issue published 15 September 2026

Abstract

The Artificial Protozoa Optimizer (APO) is a population-based metaheuristic for numerical optimization and engineering design. However, its stochastic initialization and limited local refinement can reduce performance on non-convex, discontinuous, and high-dimensional landscapes. To address these issues, this paper proposes an enhanced Artificial Protozoa Optimizer with a multi-strategy framework (EAPO). The method incorporates three mechanisms: a Symmetry-Enhanced Latin Hypercube Initialization (SELHI) strategy to improve the uniformity of the initial population, an Adaptive Phase Equilibrium Strategy (APES) to regulate the exploration–exploitation balance using iteration progress and population diversity, and an Adaptive Elite Perturbation Strategy (AEPS) to strengthen local refinement around high-quality individuals. Experiments on the CEC2005 and CEC2017 benchmark suites and five constrained engineering design problems show that EAPO improves upon the baseline APO and remains competitive with the selected comparison algorithms in solution quality, convergence behavior, and stability. Two-sided Wilcoxon rank-sum tests with Holm–Bonferroni correction indicate that many of these improvements are statistically significant. These results suggest that combining more uniform initialization, diversity-aware phase regulation, and elite-guided perturbation can improve APO on complex continuous and engineering optimization tasks.

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Keywords

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