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This work proposes the multi-objective version of the recently proposed Multi-Verse Optimizer (MVO) called Multi-Objective Multi-Verse Optimizer (MOMVO). The same concepts of MVO are used for converging towards the best solutions in a multi-objective search space. For maintaining and improving the coverage of Pareto optimal solutions obtained, however, an archive with an updating mechanism is employed. To test the performance of MOMVO, 80 case studies are employed including 49 unconstrained multi-objective test functions, 10 constrained multi-objective test functions, and 21 engineering design multi-objective problems. The results are compared quantitatively and qualitatively with other algorithms using a variety of performance indicators, which show the merits of this new MOMVO algorithm in solving a wide range of problems with different characteristics.

This paper proposes a multi-objective Slime Mould Algorithm (MOSMA), a multi-objective variant of the recently-developed Slime Mould Algorithm (SMA) for handling the multi-objective optimization problems in industries. Recently, for handling optimization problems, several meta-heuristic and evolutionary optimization techniques have been suggested for the optimization community. These methods tend to suffer from low-quality solutions when evaluating multi-objective optimization (MOO) problems than addressing the objective functions of identifying Pareto optimal solutions' accurate estimation and increasing the distribution throughout all objectives. The SMA method follows the logic gained from the oscillation behaviors of slime mould in the laboratory experiments. The SMA algorithm shows a powerful performance compared to other well-established methods, and it is designed by incorporating the optimal food path using the positive-negative feedback system. The proposed MOSMA algorithm employs the same underlying SMA mechanisms for convergence combined with an elitist non-dominated sorting approach to estimate Pareto optimal solutions. As a posteriori method, the multi-objective formulation is maintained in the MOSMA, and a crowding distance operator is utilized to ensure increasing the coverage of optimal solutions across all objectives. To verify and validate the performance of MOSMA, 41 different case studies, including unconstrained, constrained, and real-world engineering design problems are considered. The performance of the MOSMA is compared with Multiobjective Symbiotic-Organism Search (MOSOS), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multiobjective Water-Cycle Algorithm (MOWCA) in terms of different performance metrics, such as Generational Distance (GD), Inverted Generational Distance (IGD), Maximum Spread (MS), Spacing, and Run-time. The simulation results demonstrated the superiority of the proposed algorithm in realizing high-quality solutions to all multi-objective problems, including linear, nonlinear, continuous, and discrete Pareto optimal front. The results indicate the effectiveness of the proposed algorithm in solving complicated multi-objective problems. This research will be backed up with extra online

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