Multi-objective Geometric Mean Optimizer (MOGMO): A Novel Metaphor-Free Population-Based Math-Inspired Multi-objective Algorithm

Abstract This research introduces a novel multi-objective adaptation of the Geometric Mean Optimizer (GMO), termed the Multi-Objective Geometric Mean Optimizer (MOGMO). MOGMO melds the traditional GMO with an elite non-dominated sorting approach, allowing it to pinpoint Pareto optimal solutions through offspring creation and selection. A Crowding Distance (CD) coupled with an Information Feedback Mechanism (IFM) selection strategy is employed to maintain and amplify the convergence and diversity of potential solutions. MOGMO efficacy and capabilities are assessed using thirty notable case studies. This encompasses nineteen multi-objective benchmark problems without constraints, six with constraints and five multi-objective engineering design challenges. Based on the optimization results, the proposed MOGMO is better 54.83% in terms of GD, 64.51% in terms of IGD, 67.74% in terms of SP, 70.96% in terms of SD, 64.51% in terms of HV and 77.41% in terms of RT. Therefore, MOGMO has a better convergence and diversity for solving un-constraint, constraint and real-world application. Statistical outcomes from MOGMO are compared with those from Multi-Objective Equilibrium Optimizer (MOEO), Decomposition-Based Multi-Objective Symbiotic Organism Search (MOSOS/D), Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Multi-Verse Optimization (MOMVO) and Multi-Objective Plasma Generation Optimizer (MOPGO) algorithms, utilizing identical performance measures. This comparison reveals that MOGMO consistently exhibits robustness and excels in addressing an array of multi-objective challenges. The MOGMO source code is available at https://github.com/kanak02/MOGMO .