Leader selection based Multi-Objective Flow Direction Algorithm (MOFDA): A novel approach for engineering design problems

Addressing complex real-world issues with conflicting objectives is a significant challenge in optimization. Practical algorithms must balance these objectives, mainly when decision-maker preferences are unclear. This paper introduces a multi-objective adaptation of the Flow Direction Algorithm (FDA) to address the shortcomings of traditional evolutionary and meta-heuristic optimization methods in multi-objective optimization (MOO). These conventional methods often fail to find Pareto optimal solutions and to represent all objectives fairly. Building on the FDA's success in single-objective tasks, we expanded its application to MOO, creating the MultiObjective Flow Direction Algorithm (MOFDA). MOFDA incorporates new mechanisms to accurately and uniformly find optimal solutions for MOO challenges. It features a fixed-size external archive to maintain Pareto optimal solutions, uses a grid mechanism to improve non-dominated solutions within this archive, and implements a leader selection process to guide searches in the multi-objective space. These strategies enable MOFDA to discover superior solutions and ensure extensive coverage of the Pareto front. We validated MOFDA's effectiveness by testing it against 27 diverse problems using seven performance metrics. The results show MOFDA's ability to outperform well-known algorithms, achieving significant convergence and broad coverage, thus demonstrating its advanced capability in multi-objective optimization. The MOFDA source code is available at: https://nimakhodadadi.com/algorithms-%2B-codes.