Multi-Objective Interactive Programming

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Abstract
This paper proposes a method for finding optimal, or near optimal, solutions for problems involving m objective functions, where there is an overall criterion which is a weighted sum of the m objective functions, but where the weights are, initially, unknown. The process is an interactive one, beginning with a set within which the actual weighting vector is known to lie, and progressively cutting down the size of the set until an acceptable solution is found. A by-product of the procedure is an iterative method for finding the generators of the polyhedral cones, within which the weighting vector must lie, at each stage.

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