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Constrained optimization problems (COPs) are converted into a bi-objective optimization problem first, and a novel fitness function based on achievement scalarizing function (ASF) is presented. The fitness function adopts the valuable properties of ASF and can measure the merits of individuals by the weighting distance from the ndividuals to the reference point, where the reference point and the weighting vector reflect the preference of decision makers. In the initial stage of the evolution, the main preference should be put in generating more feasible solutions, and in the later stage of the evolution, the main preference should be put in improving the objective function. For this purpose, the proper reference point and weighting vector are chosen adaptively to realize the preference in different evolutionary stages. Then a new preference based multiobjective evolutionary algorithm is proposed based on all these. The numerical experiments for four standard test functions with different characteristic illustrate that the new proposed algorithm is effective and efficient.