Real-World Steel Frame Optimization Using a Hybrid Leader Selection-Based Multi-Objective Flow Direction Algorithm

Abstract

This paper presents a novel Multi-Objective Flow Direction Algorithm (MOFDA) for complex engineering optimization problems. The key innovation is a hybrid leader selection mechanism, which replaces the conventional roulette wheel selection and significantly enhances convergence and diversity in identifying Pareto-optimal solutions. The proposed MOFDA is rigorously evaluated on 31 standard benchmark problems and 11 constrained engineering design cases—including truss optimization, welded beam design, and a large-scale steel frame structure—to assess its accuracy, stability, and solution diversity comprehensively. Comparative studies with state-of-the-art multi-objective algorithms such as MOMVO, MOMSA, MSSA, and MOGNDO further highlight the strong performance of MOFDA. In addition, MOFDA is integrated into a MATLAB–SAP2000 framework and applied to the real-world structural optimization of the Dong Bai ferry terminal steel frame in Vietnam. The results show that MOFDA consistently achieves competitive or superior outcomes on benchmark functions, delivers substantial weight reduction, and improves structural efficiency in engineering applications. These findings demonstrate both the proposed approach's technical novelty and practical effectiveness. Source codes of MOFDA is publicly available at https://ceats.ou.edu.vn/us/codes.html.