Principles of multiobjective optimization

Abstract

The purpose of this paper is to isolate and analyze the principal ideas of multiobjective optimization (multicriterion decision making) in management/operations research. This is done without casting recriminatory aspersions on single-objective optimization or championing any one multiobjective technique. The paper first attempts to define the problem, and then discusses the fundamental ideas, many of which stem from common sense. Each idea is examined for strengths and weaknesses and two-efficiency and utility-are shown worthy of extended consideration. In the light of this analysis some general recommendations are made. Besides offering the simple advice of not dismissing single-objective optimization as a possible approach, we suggest that three broad classes of multiobjective techniques are very promising in terms of reliably and believably achieving a most preferred solution. These are: (1) partial generation of the efficient set, a rubric we use for unifying a wide spectrum of existing methods; (2) explicit utility maximization, a much overlooked approach combining multiattribute decision theory and mathematical programming and (3) implicit utility maximization, the name we use for the popular class of methods introduced by Geoffrion, Dyer and Feinberg and extended significantly by many others.