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

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

Métaheuristiques et matheuristiques pour des problèmes d'optimisation multi-objectifs en génie des procédés : application à la conception d'une chaîne logistique "hydrogène"

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.Les approches systémiques du Génie des Procédés font très fréquemment intervenir des problèmes complexes d'optimisation, généralement résolus par des approches déterministes. L'étude de cas réels implique des variables mixtes, des fonctions non linéaires, un grand nombre de contraintes ainsi que plusieurs critères conflictuels à optimiser simultanément, ce qui met à l'épreuve ces méthodes classiques. La motivation principale de cette recherche est donc d'explorer des méthodes alternatives pour résoudre ces problèmes d'optimisation multi-objectif complexes avec une attention particulière sur les avancées récentes des méthodes évolutionnaires. Si les algorithmes évolutionnaires multi-objectifs (MOEA) se sont avérés robustes pour la résolution de problèmes multi-objectifs, leurs performances dépendent largement des techniques de gestion des contraintes pour les problèmes fortement contraints. Le cœur de l'innovation de cette étude consiste en l'adaptation d'outils basés sur les métaheuristiques à cette classe de problèmes en Génie des Procédés. Dans ce but, la stratégie de recherche a comporté deux volets. Tout d'abord, une étude empirique a été réalisée afin de comparer différentes configurations algorithmiques et sélectionner la meilleure pour fournir des approximations de fronts de Pareto de haute qualité. Cette étude, comprenant à la fois des problèmes de test académiques et applications en Génie des Procédés, a montré qu'une méthode utilisant le gradient de contraintes pour réparer les solutions infaisables obtenait les meilleurs résultats, en particulier pour le traitement des contraintes d'égalité. En capitalisant sur l'expérience acquise lors de cette étude numérique préliminaire, la conception optimale de chaînes logistiques durables « hydrogène » (HSC), prenant en compte des critères économiques et environnementaux, est étudiée. Une méthode MOEA basée sur la décomposition et combinée à la réparation basée sur le gradient, a d'abord été exploré pour résoudre le problème. Cependant, en raison du nombre important de bilans massiques (contraintes égalité), cette approche a montré une faible convergence vers le front de Pareto optimal. Une nouvelle stratégie a donc été développée et adaptée à ce problème, à travers une reformulation en deux niveaux : le niveau supérieur (discret) traite le problème de conception de la structure de la HSC (dimensionnement et emplacement des installations), tandis que le niveau inférieur (problème de programmation linéaire) résout le sous-problème opérationnel correspondant (production et transport). Cette stratégie permet le développement d'une technique de solution matheuristique ad-hoc, par l'hybridation d'un MOEA avec un solveur LP utilisant une fonction de scalarisation pour traiter les deux objectifs considérés. Les résultats numériques obtenus pour l'étude de cas de la région Occitanie soulignent que l'approche hybride produit une bonne approximation du front de Pareto, et ce plus efficacement que les méthodes exactes. Enfin, la matheuristique a permis d'étudier le problème de conception de la HSC avec des hypothèses plus réalistes concernant les technologies utilisées pour la synthèse de l'hydrogène, les taux d'apprentissage reflétant la maturité croissante de ces technologies au fil du temps et les relations non linéaires pour le calcul des dépenses d'investissement et d'exploitation (CAPEX et OPEX) des installations de production d'hydrogène. Le nouveau modèle, qui fait intervenir une formulation bi-objectif mixte non-linéaire (MINLP), peut être résolu efficacement par l'algorithme hybride proposé

Integración másica en ecoparques industriales: optimización global mediante evolución diferencial

93 páginas. Maestría en Ingeniería de Procesos.La problemática actual referente al agotamiento de los recursos naturales ha obligado a la creación de diversas estrategias para la preservación del medio ambiente. Asía ha surgido la novedosa idea del “ecoparque industrial” bajo la premisa de que al combinar varias plantas industriales para compartir mutuamente recursos u otros materiales, energía e infraestructura, se obtienen mayores beneficios, tanto ambientales como económicos, a aquellos obtenidos si cada planta industrial trabajase por separado. En este trabajo la integración másica de procesos, y específicamente, la integración de corrientes de agua con múltiples contaminantes es estudiada. Para la optimización del proceso se utiliza un modelo matemático que describe el funcionamiento de la superestructura del ecoparque industrial, cuyo objetivo es minimizar los costos totales anuales. El problema de optimización resultante es de tipo mixto-entero no lineal (MINLP). Las técnicas de programación matemática generalmente son utilizadas para la optimización de redes de agua en ecoparques industriales. Estas técnicas permiten involucrar una cantidad elevada de plantas de fuentes y de sumideros de procesos incluyendo muchos contaminantes así como consideraciones topológicas y de operación. Sin embargo, hallar la estructura óptima del ecoparque resulta verdaderamente complicado, debido a que el problema es altamente no convexo. Además, la gran mayoría de los métodos reportados no garantizan hallar el óptimo global y utilizan procedimientos de optimización local. Por otro lado, una alternativa a los métodos de programación matemática son las técnicas metaheurísticas de búsqueda. Estas últimas no han sido exploradas aún en esta área de ingeniería de procesos y, por lo tanto su implementación y evaluación constituyen el principal objetivo de este estudio. Específicamente, se implementan diferentes versiones del algoritmo de Evolución diferencial (DE), prestando una atención particular al tratamiento de restricciones de igualdad. Los experimentos numéricos realizados demuestran que los algoritmos desarrollados aunque no alcanzan las soluciones óptimas determinadas por las técnicas de programación matemática permiten obtener resultados de buena calidad, robustamente y en tiempos de cómputo razonables.The current concern relating the depletion of natural resources, caused mainly by the industrial activity and de population growth, has demanded the creation of various strategies for the preservation of the environment. This way, the concept “eco-industrial park” has appeared. The idea behind this concept is that sharing resources or other materials energy and infrastructure between industries, the benefits, environmentally and economically, obtained to this way are higher than those if each industry worked alone. The optimal design of the eco-industrial park involves different topics of processes engineering, such as optimization and process integration. In this work water integration based and properties to characterize streams with numerous components is studied. A mathematical model describing the operation the of the eco- industrial park is used to optimize the process, which objective is to minimize the total annual costs. The resulting optimization problem is a mixed integer nonlinear programming (MINLP). Mathematical programming techniques are generally used for the optimization of water networks in eco-industrial parks. These techniques enable to considerer large problems, involving large number industries, process sources and process sinks including several pollutants, as well as topological and operational considerations. Nonetheless, the resulted problems are frequently highly nonconvex and finding the optimal configuration of the eco-industrial park can become very difficult. In Order to avoid these complications, the reported methods have used local optimization procedures and then they do not guarantee to find the global optimal solution. On the other hand, metaheuristic optimization techniques are an alternative to the mathematical programming techniques. The former techniques are not still well explored in process engineering and, thus, its implementation and evaluation are the main goal of this work. Concretely, several version of differential evolution algorithm (DE) are implemented focusing on the handing of equality constraints. The numerical experiments show that implemented algorithms even though they do not get as good solutions as those got by mathematical programming techniques they find well quality solutions, robustly and in reasonable computational time.Consejo Nacional de Ciencia y Tecnología (México)