Recently, a new strong optimization algorithm called marine predators algorithm (MPA) has been proposed for tackling the single-objective optimization problems and could dramatically fulfill good outcomes in comparison to the other compared algorithms. Those dramatic outcomes, in addition to our recently-proposed strategies for helping meta-heuristic algorithms in fulfilling better outcomes for the multi-objective optimization problems, motivate us to make a comprehensive study to see the performance of MPA alone and with those strategies for those optimization problems. Specifically, This paper proposes four variants of the marine predators' algorithm (MPA) for solving multi-objective optimization problems. The first version, called the multi-objective marine predators' algorithm (MMPA) is based on the behavior of marine predators in finding their prey. In the second version, a novel strategy called dominance strategy-based exploration-exploitation (DSEE) recently-proposed is effectively incorporated with MMPA to relate the exploration and exploitation phase of MPA to the dominance of the solutions - this version is called M-MMPA. DSEE counts the number of dominated solutions for each solution - the solutions with high dominance undergo an exploitation phase; the others with small dominance undergo the exploration phase. The third version integrates M-MMPA with a novel strategy called Gaussian-based mutation, which uses the Gaussian distribution-based exploration and exploitation strategy to search for the optimal solution. The fourth version uses the Nelder-Mead simplex method with M-MMPA (M-MMPA-NMM) at the start of the optimization process to construct a front of the non-dominated solutions that will help M-MMPA to find more good solutions. The effectiveness of the four versions is validated on a large set of theoretical and practical problems. For all the cases, the proposed algorithm and its variants are shown to be superior to a number of well-known multi-objective optimization algorithms.