Controlling the search for a compromise solution in multi-objective optimization

Two methods for multi-objective optimization are discussed, both based upon a scalarizing function with weights incorporating the decision maker’s subjective preferential judgment: one of them minimizes the weighted Chebychev-norm distance from the ideal vector, the other maximizes a weighted geometric mean of the objective functions. By an appropriate choice of the weights the computational process homes in towards a non-dominated (efficient, Pareto-optimal) solution where the deviations of the objective-function values from the ideal values are felt to be in a proper balance. These approaches are not affected by the units of measurement expressing the performance of the feasible solutions under the respective objectives. In essence, the two methods make the concepts of the relative importance of the objective functions operational. Numerical experience with a gearbox design problem is presented at the end of the paper.