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.

This work proposes a novel framework that enables one to compare distinct iterative procedures with known rates of convergence, in terms of the computational effort to be employed to reach some prescribed vicinity of the optimal solution to a given problem of interest. An algorithm is introduced that decides between two competing algorithms, which algorithm makes the best use of the computational resources for some prescribed error. Several examples are presented that illustrate the trade-offs involved in such a choice and demonstrate that choosing an algorithm over another with a higher rate of convergence can be perfectly justifiable in terms of the overall computational effort.