This paper proposes an alternate method for nding several Pareto optimal points for a general nonlinear multicriteria optimization problem. Such points collectively capture the trade-o among the various con icting objectives. It is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the Pareto set given an evenly distributed set of parameters, a property w h i c h the popular method of minimizing weighted combinations of objective functions lacks. Further, this method can handle more than two objectives while retaining the computational e ciency of continuation-type algorithms. This is an improvement o ver continuation techniques for tracing the trade-o curve since continuation strategies cannot easily be extended to handle more than two objectives.

A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the di erent objectives for various di erent settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve i s c o n vex. This article provides a geometrical argument a s t o w h y t h i s i s t h e c a s e. Secondly, it is a frequent observation that even for convex Pareto curves, an evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. This article aims to identify the mechanism behind this observation. Roughly, t h e w eight is related to the slope of the Pareto curve in the objective space in a way such t h a t a n e v en spread of Pareto points actually corresponds to often very uneven distributions of weights. Several examples are provided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curves.

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