Metaheuristic and matheuristic approaches for multi-objective optimization problems in process engineering : application to the hydrogen supply chain design

Abstract

Complex optimization problems are ubiquitous in Process Systems Engineering (PSE) and are generally solved by deterministic approaches. The treatment of real case studies usually involves mixed-integer variables, nonlinear functions, a large number of constraints, and several conflicting criteria to be optimized simultaneously, thus challenging the classical methods. The main motivation of this research is therefore to explore alternative solution methods for addressing these complex multiobjective optimization problems related to the PSE area, focusing on the recent advances in Evolutionary Computation. If multiobjective evolutionary algorithms (MOEAs) have proven to be robust for the solution of multiobjective problems, their performance yet strongly depends on the constraint-handling techniques for the solution of highly constrained problems. The core of innovation of this research is the adaptation of metaheuristic-based tools to this class of PSE problems. For this purpose, a two-stage strategy was developed. First, an empirical study was performed in the perspective of comparing different algorithmic configurations and selecting the best to provide a high-quality approximation of the Pareto front. This study, comprising both academic test problems and several PSE applications, demonstrated that a method using the gradient-based mechanism to repair infeasible solutions consistently obtains the best results, in particular for handling equality constraints. Capitalizing on the experience from this preliminary numerical investigation, a novel matheuristic solution strategy was then developed and adapted to the problem of Hydrogen Supply Chain (HSC) design that encompasses the aforementioned numerical difficulties, considering both economic and environmental criteria. A MOEA based on decomposition combined with the gradient-based repair was first explored as a solution technique. However, due to the important number of mass balances (equality constraints), this approach showed a poor convergence to the optimal Pareto front. Therefore, a novel matheuristic was developed and adapted to this problem, following a bilevel decomposition: the upper level (discrete) addresses the HSC structure design problem (facility sizing and location), whereas the lower level (Linear Programming problem) solves the corresponding operation subproblem (production and transportation). This strategy allows the development of an ad-hoc matheuristic solution technique, through the hybridization of a MOEA (upper level) with a LP solver (lower level) using a scalarizing function to deal with the two objectives considered. The numerical results obtained for the Occitanie region case study highlight that the hybrid approach produces an accurate approximation of the optimal Pareto front, more efficiently than exact solution methods. Finally, the matheuristic allowed studying the HSC design problem with more realistic assumptions regarding the technologies used for hydrogen synthesis, the learning rates capturing the increasing maturity of these technologies over time and nonlinear relationships for the computation of Capital and Operational Expenditures (CAPEX and OPEX) for the hydrogen production facilities. The resulting novel model, with a non-convex, bi-objective mixed-integer nonlinear programming (MINLP) formulation, can be efficiently solved through minor modifications in the hybrid algorithm proposed earlier, which finds its mere justification in the determination of the timewise deployment of sustainable hydrogen supply chains