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 on computationally expensive black-box model simulators of industrial processes have to be solved with limited computing time budget. In this context, this paper proposes and explores the uses of an iterative heuristic approach aiming at quickly providing a satisfactory accurate approximation of the Pareto front. The approach builds, in each iteration, a multi-objective nonlinear programming (MO-NLP) surrogate problem model using curve fitting of objectives and constraints. The approximated solutions of the Pareto front are generated by applying the "-constraint method to the multi-objective surrogate problem, converting it into a desired number of single objective (SO) NLP problems, for which mature and computationally efficient solvers exist. The proposed approach is applied to the cost versus life cycle assessment (LCA)-based environmental optimization of drinking water treatment chains. The paper thoroughly investigates various settings choices of the approach such as: the type of the polynomial function to be fit, the input points, choice of weights in curve fitting, and analytical fit. The numerical simulations results with the approach show that a good quality approximation of Pareto front can be obtained with a significantly smaller computational time than with the popular SPEA2 state-of-the-art metaheuristic algorithm.