A Sobol-Driven Multi-Objective Whale Migration Algorithm for Engineering Optimization

Abstract

Multi-objective optimization plays an important role in modern design and complex engineering applications. However, achieving an effective balance between the convergence and diversity of Pareto-optimal solutions remains challenging. This paper proposes a Sobol-driven Multi-objective Whale Migration Algorithm (SMOWMA), which extends the Whale Migration Algorithm within a non-dominated sorting and elite-selection framework. A maximin scrambled Sobol initialization scheme is first employed to improve the distribution of the initial population. An archive-guided adaptive Student-t flight mechanism is then incorporated into the leader-whale position update to dynamically balance global exploration and local exploitation. In addition, archive crowding information and archive-entry success feedback are jointly used to adjust the search behavior according to both environmental diversity and recent search performance. SMOWMA is evaluated on five widely used multi-objective benchmark suites, namely ZDT, DTLZ, WFG, UF, and CF, using four performance indicators: generational distance (GD), inverted generational distance (IGD), spacing (SP), and hypervolume (HV). The results, together with Friedman tests and Holm-adjusted Wilcoxon tests, demonstrate that SMOWMA achieves competitive overall performance in terms of convergence, diversity, and objective-space coverage, although its relative advantage remains problem-dependent. The practical applicability of SMOWMA is further examined using multi-objective welded-beam design formulations, a bi-objective four-bar truss design problem, and a five-objective car side-impact design problem. The engineering results show that SMOWMA can obtain competitive and stable approximation sets for constrained design problems with different numbers of objectives, supporting its effectiveness and applicability in multi-objective engineering optimization.