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

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 mono-objective problems to identify a set of k points in the pareto-optimal 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.