Hybrid MOCPO–AGE-MOEA for Efficient Bi-Objective Constrained Minimum Spanning Trees

The constrained bi-objective Minimum Spanning Tree (MST) problem is a fundamental challenge in network design, as it simultaneously requires minimizing both total edge weight and maximum hop distance under strict feasibility limits; however, most existing algorithms tend to emphasize one objective over the other, resulting in imbalanced solutions, limited Pareto fronts, or poor scalability on larger instances. To overcome these shortcomings, this study introduces a Hybrid MOCPO–AGE-MOEA algorithm that strategically combines the exploratory strength of Multi-Objective Crested Porcupines Optimization (MOCPO) with the exploitative refinement of the Adaptive Geometry-based Evolutionary Algorithm (AGE-MOEA), while a Kruskal-based repair operator is integrated to strictly enforce feasibility and preserve solution diversity. Moreover, through extensive experiments conducted on Euclidean graphs with 11–100 nodes, the hybrid consistently demonstrates superior performance compared with five state-of-the-art baselines, as it generates Pareto fronts up to four times larger, achieves nearly 20% reductions in hop counts, and delivers order-of-magnitude runtime improvements with near-linear scalability. Importantly, results reveal that allocating 85% of offspring to MOCPO exploration and 15% to AGE-MOEA exploitation yields the best balance between diversity, efficiency, and feasibility. Therefore, the Hybrid MOCPO–AGE-MOEA not only addresses critical gaps in constrained MST optimization but also establishes itself as a practical and scalable solution with strong applicability to domains such as software-defined networking, wireless mesh systems, and adaptive routing, where both computational efficiency and solution diversity are paramount