This paper proposes a novel hybrid multi-objective algorithm named Multi-objective Spotted Hyena and Emperor Penguin Optimizer (MOSHEPO) for solving both convex and non-convex economic dispatch and micro grid power dispatch problems. The proposed algorithm combines two newly developed bio-inspired optimization algorithms namely Multi-objective Spotted Hyena Optimizer (MOSHO) and Emperor Penguin Optimizer (EPO). MOSHEPO contemplates many non-linear characteristics of power generators such as transmission losses, multiple fuels, valve-point loading, and prohibited operating zones along with their operational constraints, for practical operation. To evaluate the effectiveness of MOSHEPO, the proposed algorithm has been tested on various benchmark test systems and its performance is compared with other well-known approaches. The experimental results demonstrate that the proposed algorithm outperforms other algorithms with low computational efforts while solving economic and micro grid power dispatch problems.