Multiple objectives under uncertainty: An illustrative application of protrade

Abstract

A decision making method labeled Protrade has been developed to account for both multiple objectives and uncertainty aspects. This method is applied to the case study of the Black Mesa Region in Northern Arizona which is being strip mined for coal. One important concern in large-scale surface mining is the reclamation of mine spoils to bring about beneficial land uses while observing economic, social, environmental, and legal constraints. Protrade considers a set of linear objective functions with random parameters, subject to a set of physical constraints; the preferences of the decision maker are articulated in a progressive manner, and alternative solutions are generated. Nonlinear deterministic equivalents are introduced to account for uncertainty in some of the parameters involved. While nq•fi•al policy recommendations are made, this illustration of Protrade is carried out to investigate the p6te'•ial of the method for trading off multiple objectives and measures of uncertainty in water and other natural resource system design problems. generating techniques are the Weighting method [Geoffrion, 1967; Major, 1969; Hairnes, 1973], the e-constraint method [Hairnes and Nainis, 1973], adaptive search [Beeson and Meisel, 1971], multi-criteria simplex methods [Zeleny, 1974], and compromise programing [Starr and Zeleny, 1977; Duckstein and Opricovic, 1978]. Methods which rely on prior articulation of preferences are goal programing [Charnes and Cooper, 1961; Lee, 1972], utility function assessment [Raiffa, 1969; Keeney and Wood, 1977], Electre method [Roy, 1971; David and Duckstein, 1976], and surrogate worth tradeoff [Hairnes et al., 1975]. Techniques which rely on progressive articulation of preferences are the step method [Benayoun et al., 1971], sequential multiobjective problem solving [Monarchi et al., ], and the tradeoff development method [Goicoechea et al., 1976b, c]. Structuring a decision problem as a mathematical optimization problem often leads to a number of difficulties, such as described by Keeney and Wood [1977]: 1. The formulation of the objective function as a weighted linear function implies constant tradeoffs between objectives regardless of the level of each objective. This is rarely the situation.

Towards a Multi Objective Path Optimisation for Car Navigation

“…Type I -No preference articulation. Methods in this group include: probabilistic trade-offs development method (Goicoechea et al, 1979), step method (Benayoun et al, 1971), and sequential multi objective problem solving method (Monarchi et al, 1973;Goicoechea et al, 1982). Methods of this type includes the ε-constraint (Haimes, 1973), global criterion method (Salukvadze, 1974), and weighted-sum method (Zadeh, 1963).…”

DERIVING THE NONLINEAR RISK‐BENEFIT ALGORITHM FOR RESERVOIRS1

“…After selecting both the desired trade-off and the risk, the various "quantile solutions" were used in an implicit stochastic optimization approach. Goicoechea, et a!. (1979), proposed a method that considered nultiobjectives with uncertainty applied to land-use planning.…”

Dual Objective Control of Nutrient Loading into a Lake1

“…A compromise solution may be found by using "Compromise Programming" which seeks the "shortest" distance between the ideal point and the set of nondominated solutions (Zeleny, 1973). Alternatively, game theory can be applied for finding the "maximum" distance between some "status quo" point and the set of nondominated solutions (Szidarovszky, et aL, 1978;Szidarovszky, A number of other techniques could be used as well (Roy, 1971;Benayoun, et aL, 1971;Haimes, et aL, 1975Haimes, et aL, , 1980Major, 1977;Cohon, 1978;Cohon, et aL, 1979;Goicoechea, et aL, 1979Goicoechea, et aL, , 1981 but as pointed out in Zionts and Wallenius (1 975), and Gershon (1 981), it is often advantageous to choose multiobjective techniques that are simple from the viewpoints of both decision maker and computations. It is hoped that Compromise Programming is acceptable on both accounts.…”