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In this paper, a novel approach to optimally operate a day-ahead electricity market with considerations of market power is proposed. First, this approach formulates the 1-hour based optimal dispatch problem as a nonlinear constrained multi-objective optimization problem which simultaneously minimizes fuel cost, emissions and the modified Herfindahl-Hirschman index. Then the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve this optimization problem. Simulation results illustrate that this algorithm is capable of finding the Pareto-optimal front in a single run. The best operation schedule for the whole 24 hours can be chosen by taking the ramp rate constraints of generators into account. This approach can provide the market operator with much operating feasibility and thus is more realistic and feasible.