Interactive multiobjective programing in water resources: A case study

Abstract

Multiple-objective problems are ubiquitous in human affairs and are commonly attacked in a subjective way. Semops, a sequential multiobjective problem solving technique, allows the decision maker to trade off one objective versus another in an interactive manner. Semops cyclically uses a surrogate objective function based on goals and the decision maker's aspirations about achieving these goals. The algorithm, applied to a synthetic case study of regional water quality management, demonstrates that (1) a complex situation can be handled, (2) the individuality of the deckion maker's preference structure is preserved, (3) the feasible alternatives do not need to be specified a priori, (4) the concept of a satisfactory solution rather than an optimum solution is more realistic in situations involving conflicting goals. SEMOPS: AN OVERVIEWSemops is an interactive programing technique that dynamically involves the decision maker (DM) in a search process that attempts to locate a satisfactory course of action, that is, a 'satisfacturn.' The concept of a satisfactum expresses the idea that we cannot define precisely a multi-objective optimum because we may not know how to trade off one objective versus another except in a subjective way.Our research is predicated on a series of assumptions concerning the decision-making process. Specifically, we assume the following. 1. Perception is influenced by the total set of elements in a situation and the environment in which the situation is imbedded. This assumption is basically the Gestalt philosophy [KOhler, 1947]. 2. Individual preference functions or value structures cannot be expressed analytically, although it is assumed that the DM does subscribe to a set of beliefs. 3. Value structures change over time, and different 'parts' (i.e., religious convictions versus automobile preferences) may change at different rates. 4. Aspirations or desires change as a result of learning and experience. 5. The number of goals in a decision situation is usually < 7 [Johnsen, 1968]. 6. The DM normally satisfices rather than optimizes [Doffman, 1960, p. 608]. 7. A solution to a decision problem is any acceptable course of action. 837 d= A2 A1/z + z/•A: Except for the first transformation these transformations are all nonlinear functions of a criterion function that may itself be nonlinear. The critical fact in this construction is that the direction of any change in d has a consistent interpretation for all T goals. Goals and Criterion Functions Goal 1: DO level at Bowville (z• •_ A• --6 mg•l) z• = 6.5 •-(5.0.3)] r(z) = Goal 3: DO level at Plympton (zs •_ As = 6 mg/1) za = 5.2 •-[(4.42.10 -6) -(4.0.104) ß (xx --0.3) -{-(7.71.10 -•) ß (2.s. •o •).(w• -o.a)] -{-[(7.64.10 -•) .(1.28-105) ß (x2 --0.a) -{-(1.60.10 -5) ß (4.8.104 ).(w2 -0.3)] = (0-s.5) i•ONARCHI ET AL.: I•ULTIOBJECTIYE PROGRAI•IING Goal 4: percent return on equity at Pierce-Hall Cannery (z, •_ •i, = 6.5%) 102 z, -5:•-06 [(3.75.105 ) --0.6 ß 1.09-x• •'--59 Goal 5: addition to the tax rate at Bowville (z5 _• A•-1.5) r(z) = 532 ) (2...

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