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This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobjective optimization algorithm to lead a decision maker (DM) to the most preferred solution of her or his choice. The progress toward the most preferred solution is made by accepting preference based information progressively from the DM after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly monotone value function, which is used for the subsequent iterations of the evolutionary multiobjective optimization (EMO) algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO-approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference-based termination criterion. Results on two- to five-objective optimization problems using the progressively interactive NSGA-II approach show the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this paper are also suggested.