Virtual interpolation of discrete multi-objective programming solutions with probabilistic operation

Silva, Ricardo C., Arruda, Edilson F. and Ourique, Fabrício O. (2011) Virtual interpolation of discrete multi-objective programming solutions with probabilistic operation. Controle y Automacao, 22 (4), 379-389. (doi:10.1590/S0103-17592011000400005).

Abstract

This work presents a novel framework to address the long term operation of a class of multi-objective programming problems. The proposed approach considers a stochastic operation and evaluates the long term average operating costs/profits. To illustrate the approach, a two-phase method is proposed which solves a prescribed number of K monoobjective problems to identify a set of K points in the Paretooptimal region. In the second phase, one searches for a set of non-dominated probability distributions that define the probability that the system operates at each point selected in the first phase, at any given operation period. Each probability distribution generates a vector of average long-term objectives and one solves for the Pareto-optimal set with respect to the average objectives. The proposed approach can generate virtual operating points with average objectives that need not have a feasible solution with an equal vector of objectives. A few numerical examples are presented to illustrate the proposed method.

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Contributors

Author: Edilson F. Arruda

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