Aerospace Knowledge and Technology Journal

Aerospace Knowledge and Technology Journal

Convergence analysis of pareto fronts in three-objective optimization of a bio-capsule design using relative hypervolume metric

Document Type : Research Paper

Authors
hassan Naseh 1
Hadiseh Karimaei 1
Mohammad Lesani fadafan 2
1 Assistant Professor of Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran
2 Ph.D. Student of Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran
Abstract
This paper examines the application of the Relative Hypervolume (RHV) metric as a powerful tool for assessing convergence in multi-objective optimization problems. Most engineering optimization problems lack a true Pareto front, which makes convergence assessment challenging. In this approach, the Multi-Objective Genetic Algorithm (MOGA) is executed 30 times for each problem, generating 30 approximate Pareto fronts. All solutions from these runs are then combined into a merged set, and a Pareto dominance filter is applied to identify the non-dominated solutions, allowing the determination of the true Pareto front along with its associated hypervolume. The method is applied to three three-objective optimization problems in the design of a space biocapsule. Sensitivity analysis using Latin Hypercube Sampling (LHS) and MOGA execution showed that all three problems achieved satisfactory convergence in fewer than 373 generations, which is appropriate for constrained multi-objective optimization problems and demonstrates the efficiency of the proposed approach. Results indicate that the method successfully generates high-quality three-dimensional Pareto fronts with RHV values ranging from 0.87 to 0.93. Comparison with native capsule data revealed that while some configurations were optimal, others required redesign of parameters.
Keywords
Bio-capsule
Design optimization
Tri-objective
Relative Hypervolume
Multi-Objective GA
Subjects
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Aerospace Knowledge and Technology Journal
Volume 14, Issue 1
May 2025
Pages 107-119