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Congestion or overload in transmission networks is alleviated by rescheduling of generators and\/or load shedding. The two objectives conflicting in nature (1) transmission line over load and (2) congestion cost are optimized in this paper. The multiobjective fuzzy evolutionary programming (FEP) and nondominated sorting genetic algorithm II methods are used to solve this problem. FEP uses the combined advantages of fuzzy and evolutionary programming (EP) techniques and gives better unique solution satisfying both objectives, whereas nondominated sorting genetic algorithm (NSGA) II gives a set of Pareto\u2010optimal solutions. The methods propose an efficient and reliable algorithm for line overload alleviation due to critical line outages in a deregulated power markets. 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