With the significant growth of multiprocessor systems (MPS) to deal with complex tasks and speed up their execution, the energy generated as a result of this growth becomes one of the significant limits to that growth. Although several traditional techniques are available to deal with this challenge, they don’t deal with this problem as multi-objective to optimize both energy and makespan metrics at the same time, in addition to expensive cost and memory usage. Therefore, this paper proposes a multi-objective approach to tackle the task scheduling for MPS based on the modified sine-cosine algorithm (MSCA) to optimize the makespan and energy using the Pareto dominance strategy; this version is abbreviated as energy-aware multi-objective MSCA (EA-M2SCA). The classical SCA is modified based on dividing the optimization process into three phases. The first phase explores the search space as much as possible at the start of the optimization process, the second phase searches around a solution selected randomly from the population to avoid becoming trapped into local minima within the optimization process, and the last searches around the best-so-far solution to accelerate the convergence. To further improve the performance of EA-M2SCA, it was hybridized with the polynomial mutation mechanism in two effective manners to accelerate the convergence toward the best-so-far solution with preserving the diversity of the solutions; this hybrid version is abbreviated as EA-MHSCA. Finally, the proposed algorithms were compared with a number of well-established multi-objective algorithms: EA-MHSCA is shown to be superior in most test cases.