Reference, Preference, Convexity and Efficiency - Basic Notions in Multiobjective Decision Making

Peschel, M., Ester, J., & Nguyen, T.L. (1980). Reference, Preference, Convexity and Efficiency - Basic Notions in Multiobjective Decision Making. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-80-002

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Abstract

In commonly used Pareto optimality the notions reference, preference, convexity and efficiency are interrelated and of great importance. It is shown that the usual notion of convexity on the base of straight lines is not consistent with Pareto optimality. There are many possibilities to reach all efficient points by using a parameterized set of compromise criteria.

Especially important for the decision maker's goal is to describe local wishes by corresponding reference points. It is useful to describe these reference points by preference levels or local utility fields. The method of direction diagrams helps to introduce the decision maker's imagination. The penalty scalarization method proves as a special case of direction diagrams. Direction diagrams serve for the design of good seeking procedures for efficient points expressed in terms of the control space.

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