This paper proposes a novel multiple group search optimizer (MGSO) to solve the highly constrained multiobjective power dispatch (MOPD) problem with conflicting and competing objectives. The algorithm employs a stochastic learning automata based synergistic learning to allow information interaction and credit assignment among multi-groups for cooperative search. An alternative constraint handling, which separates constraints and objectives with different searching strategies, has been adopted to produce a more uniformly-distributed Pareto-optimal front (PF). Moreover, two enhancements, namely space reduction and chaotic sequence dispersion, have also been incorporated to facilitate local exploitation and global exploration of Pareto-optimal solutions in the convergence process. Lastly, Nash equilibrium point is first introduced to identify the best compromise solution from the PF. The performance of MGSO has been fully evaluated and benchmarked on the IEEE 30-bus 6-generator system and 118-bus 54-generator system. Comparisons with previous Pareto heuristic techniques demonstrated the superiority of the proposed MGSO and confirm its capability to cope with practical multiobjective optimization problems with multiple high-dimensional objective functions.