Open Access

ARTICLE

An Improved Variant of Multi-Population Cooperative Constrained Multi-Objective Optimization (MCCMO) for Multi-Objective Optimization Problem

Muhammad Waqar Khan^1,*, Adnan Ahmed Siddiqui¹, Syed Sajjad Hussain Rizvi²

1 Faculty of Engineering Science and Technology, Hamdard University, Karachi, 74600, Pakistan
2 Faculty of Computing and Engineering Sciences, SZABIST University, Karachi, 74700, Pakistan

* Corresponding Authors: Muhammad Waqar Khan. Email: ,

(This article belongs to the Special Issue: Advancements in Evolutionary Optimization Approaches: Theory and Applications)

Computers, Materials & Continua 2026, 86(2), 1-15. https://doi.org/10.32604/cmc.2025.070858

Received 25 July 2025; Accepted 06 October 2025; Issue published 09 December 2025

Abstract

The multi-objective optimization problems, especially in constrained environments such as power distribution planning, demand robust strategies for discovering effective solutions. This work presents the improved variant of the Multi-population Cooperative Constrained Multi-Objective Optimization (MCCMO) Algorithm, termed Adaptive Diversity Preservation (ADP). This enhancement is primarily focused on the improvement of constraint handling strategies, local search integration, hybrid selection approaches, and adaptive parameter control. The improved variant was experimented on with the RWMOP50 power distribution system planning benchmark. As per the findings, the improved variant outperformed the original MCCMO across the eleven performance metrics, particularly in terms of convergence speed, constraint handling efficiency, and solution diversity. The results also establish that MCCMO-ADP consistently delivers substantial performance gains over the baseline MCCMO, demonstrating its effectiveness across performance metrics. The new variant also excels at maintaining the balanced trade-off between exploration and exploitation throughout the search process, making it especially suitable for complex optimization problems in multi-constrained power systems. These enhancements make MCCMO-ADP a valuable and promising candidate for handling problems such as renewable energy scheduling, logistics planning, and power system optimization. Future work will benchmark the MCCMO-ADP against widely recognized algorithms such as NSGA-II, NSGA-III, and MOEA/D and will also extend its validation to large-scale real-world optimization domains to further consolidate its generalizability.

---

Keywords

---