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Solving Probabilistic Multiobjective Decision Problems

by Constructing Maximum Probabilistic

Deduction Graphs

**Han-Lin Li**

National Chiao-Tung University

Ta-Hsieh Rd., Hsinchu, TAIWAN, R.O.C.

An algorithm is proposed for finding the optimal alternative of multi-objective decision making problems (MODM) by using maximum probabilistic deduction graphs to accomplish deduction from alternatives to reach multi-objectives. The algorithm can effectively find an optimal set of alternatives with the budget constraint, such that the overall welfare of the decision making is maximized. The relationship among alternatives, objectives, overall welfare and possible intermediaries is first represented by a causal network. Then, we construct a probabilistic deduction graph within the causal network to accomplish the reasoning by solving a 0-1 integer programming problem. The advantages of this algorithm are: 1) It provides a systematic way to integrate MODM problems with probabilistic reasoning problems. 2) It proposes a convenient method to solve MODM problems to obtain optimal solutions.

Keywords: causal network, deduction, deduction graph, integer programming, multiobjective decision making, mutually independent or exclusive, optimization, probabilistic reasoning

Received February 1, 1990; revised January 15, 1991.

Communicated by Lin-Shan Lee.