Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems

Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality to show the trade-off between objectives. Pareto optimality involves the identification of solutions that are not dominated by other solutions based on their respective objective functions. However, the Pareto optimality concept does not contain any information about the uncertainty of solutions. Evaluation and comparison of solutions becomes difficult when the objective functions are subjected to uncertainty. A new metric, the Pareto Uncertainty Index (PUI), is presented. This metric includes uncertainty due to the stochastic coefficients in the objective functions as part of the Pareto optimality concept to form an extended probabilistic Pareto set, we define as the p-Pareto set. The decision maker can observe and assess the randomness of solutions and compare the promising solutions according to their performance of satisfying objectives and any undesirable uncertainty. The PUI is an effective and convenient decision-making tool to compare promising solutions with multiple uncertain objectives. (C) 2020 Elsevier B.V. All rights reserved