Application and Analysis of Methods for Selecting an Optimal Solution from the Pareto-Optimal Front obtained by Multiobjective Optimization

TLDR

Process optimization often involves multiple conflicting objectives, and multiobjective optimization yields a Pareto‑optimal front of nondominated solutions that reveal trade‑offs; although widely used in chemical engineering, the problem of selecting a single optimal solution from this front has received little attention. This study identifies and implements ten candidate methods for selecting an optimal solution from the Pareto‑optimal front. The authors coded the methods in an MS Excel‑based program and applied them to benchmark and chemical‑engineering problems to compare effectiveness and similarities. The analysis shows that the preference‑by‑similarity‑to‑ideal, gray‑relational analysis, and simple additive weighting methods outperform the others in choosing a Pareto‑optimal solution.

Abstract

Process optimization often has two or more objectives which are conflicting. For such situations, multiobjective optimization (MOO) provides many optimal solutions, which are equally good from the perspective of the given objectives. These solutions, known as Pareto-optimal front and as nondominated solutions, provide deeper insights into the trade-off among the objectives and many choices for implementation. In the past 20 years, researchers have applied MOO to numerous applications in chemical engineering. However, selection of an optimal solution from the set of nondominated solutions has not received much attention in the chemical engineering literature. In the present study, 10 methods for selecting an optimal solution from the Pareto-optimal front are carefully chosen and implemented in an MS Excel-based program. Then, they are applied to the selection of an optimal solution in many benchmark or mathematical problems and chemical engineering applications, and their effectiveness and similarities are analyzed. Results of analysis indicate that, among the 10 methods studied, technique for order of preference by similarity to ideal solution, gray relational analysis, and simple additive weighting are better for choosing one of the Pareto-optimal solutions.