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Hybrid evolutionary algorithms are designed to generate quality solutions by combining both global and local search mechanisms. This paper presents a hybrid evolutionary algorithm with preferential local search using adaptive weights. Preferential local search identifies the promising solutions during the evolution and applies the local search on them. This process iteratively deepens as the global search progresses. The proposed algorithm uses weighted sum method with adaptive weights to combine multiple objectives into single during the local search. Adaptive weights are assigned to objective functions according to their relative positions in the objective space. This approach is applied on 10 benchmark problems and the results have been analyzed. This adaptive weight with preferential local search incorporated within the evolutionary process enhances the efficiency of the process, which is verified by the performance metrics and are validated using statistical t-test.