An Archive-Guided Equilibrium Optimizer Based on Epsilon Dominance for Multi-Objective Optimization Problems

Abstract

In real-world applications, many problems involve two or more conflicting objectives that need to be optimized at the same time. These are called multi-objective optimization problems (MOPs). To solve these problems, we introduced a guided multi-objective equilibrium optimizer (GMOEO) algorithm based on the equilibrium optimizer (EO), which was inspired by control–volume–mass balance models that use particles (solutions) and their respective concentrations (positions) as search agents in the search space. The GMOEO algorithm involves the integration of an external archive that acts as a guide and stores the optimal Pareto set during the exploration and exploitation of the search space. The key candidate population also acted as a guide, and Pareto dominance was employed to obtain the non-dominated solutions. The principal of ϵ-dominance was employed to update the archive solutions, such that they could then guide the particles to ensure better exploration and diversity during the optimization process. Furthermore, we utilized the fast non-dominated sort (FNS) and crowding distance methods for updating the position of the particles efficiently in order to guarantee fast convergence in the direction of the Pareto optimal set and to maintain diversity. The GMOEO algorithm obtained a set of solutions that achieved the best compromise among the competing objectives. GMOEO was tested and validated against various benchmarks, namely the ZDT and DTLZ test functions. Furthermore, a benchmarking study was conducted using cone-ϵ-dominance as an update strategy for the archive solutions. In addition, several well-known multi-objective algorithms, such as the multi-objective particle-swarm optimization (MOPSO) and the multi-objective grey-wolf optimization (MOGWO), were compared to the proposed algorithm. The experimental results proved definitively that the proposed GMOEO algorithm is a powerful tool for solving MOPs.