Despite the remarkable work conducted to improve fog computing applications’ efficiency, the task scheduling problem in such an environment is still a big challenge. Optimizing the task scheduling in these applications, i.e. critical healthcare applications, smart cities, and transportation is urgent to save energy, improve the quality of service, reduce the carbon emission rate, and improve the flow time. As proposed in much recent work, dealing with this problem as a single objective problem did not get the desired results. As a result, this paper presents a new multi-objective approach based on integrating the marine predator’s algorithm with the polynomial mutation mechanism (MHMPA) for task scheduling in fog computing environments. In the proposed algorithm, a trade-off between the makespan and the carbon emission ratio based on the Pareto optimality is produced. An external archive is utilized to store the non-dominated solutions generated from the optimization process. Also, another improved version based on the marine predator’s algorithm (MIMPA) by using the Cauchy distribution instead of the Gaussian distribution with the levy Flight to increase the algorithm’s convergence with avoiding stuck into local minima as possible is investigated in this manuscript. The experimental outcomes proved the superiority of the MIMPA over the standard one under various performance metrics. However, the MIMPA couldn’t overcome the MHMPA even after integrating the polynomial mutation strategy with the improved version. Furthermore, several well-known robust multi-objective optimization algorithms are used to test the efficacy of the proposed method. The experiment outcomes show that MHMPA could achieve better outcomes for the various employed performance metrics: Flow time, carbon emission rate, energy, and makespan with an improvement percentage of 414, 27257.46, 64151, and 2 for those metrics, respectively, compared to the second-best compared algorithm