Reliability-Based MCDM Using Objective Preferences under Variable Uncertainty.

The state-of-the-art evolutionary algorithms (EAs), developed to solve constrained multi/many-objective optimization problems (M/MaOPs), mostly deal with deterministic design variables causing no uncertainty in their implementation. However, from a practical point of view, it is imperative to consider unavoidable uncertainties in implementing design variables and parameters. In the presence of hard constraints, a slight change in one or more variables may cause a feasible optimal solution to become infeasible upon implementation and result in a failure during operation. The literature suggests reliability-based techniques for solving such M/MaOPs to obtain a Reliable Front (ReF), rather than a Pareto-optimal front (PF). A ReF is usually either a part of the PF or a completely different set of trade-off solutions dominated by the deterministic PF. However, in the presence of decision-making, computing the complete ReF may not be necessary, as the focus would be to locate only the preferred part of the ReF, dictated by the objective preference information provided by a decision-maker (DM). The proposed approach incorporates DM's preferences and variable uncertainty information a priori. The proposed Reliability-based Multi-criteria Decision-making (ReMCDM) approach uses the hybrid mean value (HMV) method for constrained handling under variable uncertainties and R-NSGA-III for preference incorporation by DMs to conduct MCDM. Results obtained by the proposed method, implemented on several benchmark and realworld engineering examples, encourage future EMO research combining constraint handling, uncertainty in decision variables, and preference incorporation.