An Implementation of the Reference Point Approach for Multiobjective Optimization

Kallio, M.J., Lewandowski, A., & Orchard-Hays, W. (1980). An Implementation of the Reference Point Approach for Multiobjective Optimization. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-80-035

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Abstract

This paper studies the reference point approach of Wierzbicki for multiobjective optimization. The method does not necessarily aim at finding an optimum under any utility function but rather it is used to generate a sequence of efficient solutions which are interesting from the decision maker's point of view. The user can interfere via suggestions of reference values for the vector of objectives. The optimization system is used to find (in a certain sense) the nearest Par-to solution to each reference objective.

The approach is expanded for adaptation of information which may accumulate on the decision maker's preferences in the course of the interactive process. In this case any Pareto point is excluded from consideration if it is not optimal under any linear utility function consistent with the information obtained. Thus, the pareto points being generated are the "nearest" ones among the rest of the pareto points.

Wierzbicki's approach is implemented on an interactive mathematical programming system called SESAME and developed by Orchard-Hays. It is now capable of handling large practical multicriteria linear programs with up to 99 objectives and 1000 to 2000 constraints. The method is tested using a forest sector model which is a moderate sized dynamic linear program with twenty criteria (two for each of the ten time periods). The approach is generally found very satisfactory. This is partly due to the simplicity of the basic idea which makes it easy to implement and use.

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