A CLOSER LOOK AT DRAWBACKS OF MINIMIZING WEIGHTED SUMS OF OBJECTIVES FOR PARETO SET GENERATION IN MULTICRITERIA OPTIMIZATION PROBLEMS

A standard technique for generating the Pareto set in multicriteria op timization problems is to minimize (convex) weighted sums of the diffe rent objectives for various different settings of the weights. However , it is well-known that this method succeeds in getting points from al l parts of the Pareto set only when the Pareto curve is convex. This a rticle provides a geometrical argument as to why this is the case. Sec ondly, it is a frequent observation that even for convex Pareto curves , an evenly distributed set of weights fails to produce an even distri bution of points from all parts of the Pareto set. This article aims t o identify the mechanism behind this observation. Roughly, the weight is related to the slope of the Pareto curve in the objective space in a way such that an even spread of Pareto points actually corresponds t o often very uneven distributions of weights. Several examples are pro vided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curv es.