In multiobjective optimization problem, a substantial number of solutions generated along the Pareto front are unacceptable to the decision maker. In this paper, we propose a variation of the concept of Pareto dominance by using a penalty based Multi Objective Genetic Algorithm which attempts to obtain the nondominated set of Pareto solutions within the acceptable region for decision maker. A Relenting Factor is used to incorporate decision maker's opinion corresponding to the aspiration for respective objective function. The proposed method is evaluated on standard benchmark test problems DTLZ1 and DTLZ2 with 2 and 3 objectives each. Results indicate that within certain limitations, the proposed method is able to converge to the true Pareto front as well as limit the solutions to region of interest to the Decision Maker.