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A common approach to constraint handling in evolutionary optimization is to apply a penalty function to bias the search toward a feasible solution. It has been proposed that the subjective setting of various penalty parameters can be avoided using a multiobjective formulation. This paper analyzes and explains in depth why and when the multiobjective approach to constraint handling is expected to work or fail. Furthermore, an improved evolutionary algorithm based on evolution strategies and differential variation is proposed. Extensive experimental studies have been carried out. Our results reveal that the unbiased multiobjective approach to constraint handling may not be as effective as one may have assumed.