Collaborative Decomposition Multi-Objective Improved Elephant Clan Optimization Based on Penalty-Based and Normal Boundary Intersection
Mengjiao Wei1,*, Wenyu Liu2
1 School of Electrical Engineering, Northeast Electric Power University, Jilin, 132012, China
2 Northeast Electric Power Design Institute, Changchun, 130000, China
* Corresponding Author: Mengjiao Wei. Email: 
(This article belongs to the Special Issue: Metaheuristic-Driven Optimization Algorithms: Methods and Applications)
Computers, Materials & Continua https://doi.org/10.32604/cmc.2025.060887
Received 12 November 2024; Accepted 25 December 2024; Published online 10 February 2025
Abstract
In recent years, decomposition-based evolutionary algorithms have become popular algorithms for solving multi-objective problems in real-life scenarios. In these algorithms, the reference vectors of the Penalty-Based boundary intersection (PBI) are distributed parallelly while those based on the normal boundary intersection (NBI) are distributed radially in a conical shape in the objective space. To improve the problem-solving effectiveness of multi-objective optimization algorithms in engineering applications, this paper addresses the improvement of the Collaborative Decomposition (CoD) method, a multi-objective decomposition technique that integrates PBI and NBI, and combines it with the Elephant Clan Optimization Algorithm, introducing the Collaborative Decomposition Multi-objective Improved Elephant Clan Optimization Algorithm (CoDMOIECO). Specifically, a novel subpopulation construction method with adaptive changes following the number of iterations and a novel individual merit ranking based on NBI and angle are proposed., enabling the creation of subpopulations closely linked to weight vectors and the identification of diverse individuals within them. Additionally, new update strategies for the clan leader, male elephants, and juvenile elephants are introduced to boost individual exploitation capabilities and further enhance the algorithm’s convergence. Finally, a new CoD-based environmental selection method is proposed, introducing adaptive dynamically adjusted angle coefficients and individual angles on corresponding weight vectors, significantly improving both the convergence and distribution of the algorithm. Experimental comparisons on the ZDT, DTLZ, and WFG function sets with four benchmark multi-objective algorithms—MOEA/D, CAMOEA, VaEA, and MOEA/D-UR—demonstrate that CoDMOIECO achieves superior performance in both convergence and distribution.
Keywords
Multi-objective optimization; elephant clan optimization algorithm; collaborative decomposition; new individual selection mechanism; diversity preservation
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