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Normal-Boundary Intersection: A New Approach for Generating the Trade-off Surface in Multi-objective Optimization Problems

Indraneel Das

Presented at the 1997 CRPC Annual Meeting Poster Session

Many design optimization problems occuring in practice involve minimizing not just one but several objectives or cost functions. An interesting issue here is the trade-off between minimizing the different, perhaps conflicting objectives. This trade-off is essentially captured by the Pareto curve or surface for the multicriteria optimization problem, which is the set of all points that are 'optimal' (rigorous definition exists) from a multicriteria viewpoint. Currently available methods involve parametrically combining the different cost functions into a single objective (e.g. a weighted sum of the cost functions) and minimizing this objective for various parameter settings. Each of these methods suffers from its own drawbacks, which the presentation will elaborate on. Normal-Boundary Intersection (NBI) is a new technique proposed by the speaker which attempts to remedy all the drawbacks inherent in the traditional approaches by introducing a better parametrization of the Pareto set. Some details of NBI will be presented and its particular merit of finding a uniform spread of Pareto optimal points given a 'uniform spread' of parameter settings will be focussed on.