Assessing the Uses of NLP-based Surrogate Models for Solving Expensive Multi-Objective Optimization Problems: Application to Potable Water Chains

Abstract

In practice many multi-objective optimization problems relying oncomputationally expensive black-box model simulators of industrialprocesses have to be solved with limited computing time budget. In thiscontext, this paper proposes and explores the uses of an iterativeheuristic approach aiming at quickly providing a satisfactory accurateapproximation of the Pareto front. The approach builds, in eachiteration, a multi-objective nonlinear programming (MO-NLP) surrogateproblem model using curve fitting of objectives and constraints. Theapproximated solutions of the Pareto front are generated by applying the``epsilon-constraint method to the multi-objective surrogate problem,converting it into a desired number of single objective (SO) NLPproblems, for which mature and computationally efficient solvers exist.The proposed approach is applied to the cost versus life cycleassessment (LCA)-based environmental optimization of drinking watertreatment chains. The paper thoroughly investigates various settingschoices of the approach such as: the type of the polynomial function tobe fit, the input points, choice of weights in curve fitting, andanalytical fit. The numerical simulations results with the approach showthat a good quality approximation of Pareto front can be obtained with asignificantly smaller computational time than with the popular SPEA2state-of-the-art metaheuristic algorithm.