Constraint handling strategies in Genetic Algorithms application to optimal batch plant design

Optimal batch plant design is a recurrent issue in Process Engineering, which can be formulated as a Mixed Integer Non-Linear Programming(MINLP) optimisation problem involving specific constraints, which can be, typically, the respect of a time horizon for the synthesis of various products. Genetic Algorithms constitute a common option for the solution of these problems, but their basic operating mode is not always wellsuited to any kind of constraint treatment: if those cannot be integrated in variable encoding or accounted for through adapted genetic operators, their handling turns to be a thorny issue. The point of this study is thus to test a few constraint handling techniques on a mid-size example in order to determine which one is the best fitted, in the framework of one particular problem formulation. The investigated methods are the elimination of infeasible individuals, the use of a penalty term added in the minimized criterion, the relaxation of the discrete variables upper bounds, dominancebased tournaments and, finally, a multiobjective strategy. The numerical computations, analysed in terms of result quality and of computational time, show the superiority of elimination technique for the former criterion only when the latter one does not become a bottleneck. Besides, when the problem complexity makes the random location of feasible space too difficult, a single tournament technique proves to be the most efficient one

Strategies for multiobjective genetic algorithm development: Application to optimal batch plant design in process systems engineering

This work deals with multiobjective optimization problems using Genetic Algorithms (GA). A MultiObjective GA (MOGA) is proposed to solve multiobjective problems combining both continuous and discrete variables. This kind of problem is commonly found in chemical engineering since process design and operability involve structural and decisional choices as well as the determination of operating conditions. In this paper, a design of a basic MOGA which copes successfully with a range of typical chemical engineering optimization problems is considered and the key points of its architecture described in detail. Several performance tests are presented, based on the influence of bit ranging encoding in a chromosome. Four mathematical functions were used as a test bench. The MOGA was able to find the optimal solution for each objective function, as well as an important number of Pareto optimal solutions. Then, the results of two multiobjective case studies in batch plant design and retrofit were presented, showing the flexibility and adaptability of the MOGA to deal with various engineering problems

Multiobjective optimization for multiproduct batch plant design under economic and environmental considerations

This work deals with the multicriteria cost–environment design of multiproduct batch plants, where the design variables are the size of the equipment items as well as the operating conditions. The case study is a multiproduct batch plant for the production of four recombinant proteins. Given the important combinatorial aspect of the problem, the approach used consists in coupling a stochastic algorithm, indeed a genetic algorithm (GA) with a discrete-event simulator (DES). Another incentive to use this kind of optimization method is that, there is no easy way of calculating derivatives of the objective functions, which then discards gradient optimization methods. To take into account the conflicting situations that may be encountered at the earliest stage of batch plant design, i.e. compromise situations between cost and environmental consideration, a multiobjective genetic algorithm (MOGA) was developed with a Pareto optimal ranking method. The results show how the methodology can be used to find a range of trade-off solutions for optimizing batch plant design

A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production

This paper addresses the problem of the optimal design of batch plants with imprecise demands and proposes an alternative treatment of the imprecision by using fuzzy concepts. For this purpose, we extended a multiobjective genetic algorithm (MOGA) developed in previousworks, taking into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The former is computed by comparing the fuzzy computed production time to a given fuzzy production time horizon and the latter is based on the additional fuzzy demand that the plant is able to produce. The methodology provides a set of scenarios that are helpful to the decision’s maker and constitutes a very promising framework for taken imprecision into account in new product development stage

Optimal design of batch plants under economic and ecological considerations: Application to a biochemical batch plant

This work deals with the multicriteria cost-environment design of multiproduct batch plants, where the design variables are the equipment item sizes as well as the operating conditions. The case study is a multiproduct batch plant for the production of four recombinant proteins. Given the important combinatorial aspect of the problem, the approach used consists in coupling a stochastic algorithm, indeed a Genetic Algorithm (GA) with a Discrete Event Simulator (DES). To take into account the conflicting situations that may be encountered at the earliest stage of batch plant design, i.e. compromise situations between cost and environmental considerations, a Multicriteria Genetic Algorithm (MUGA) was developed with a Pareto optimal ranking method. The results show how the methodology can be used to find a range of trade-off solutions for optimizing batch plant design

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Mixed-Integer Nonlinear Programming Optimization Strategies for Batch Plant Design Problems

Due to their large variety of applications, complex optimisation problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in non-linear functions. But among the diversity of those optimisation methods, the choice of the relevant technique for the treatment of a given problem keeps being a thorny issue. Within the Process Engineering context, batch plant design problems provide a good framework to test the performances of various optimisation methods : on the one hand, two Mathematical Programming techniques – DICOPT++ and SBB, implemented in the GAMS environment – and, on the other hand, one stochastic method, i.e. a genetic algorithm. Seven examples, showing an increasing complexity, were solved with these three techniques. The result comparison enables to evaluate their efficiency in order to highlight the most appropriate method for a given problem instance. It was proved that the best performing method is SBB, even if the GA also provides interesting solutions, in terms of quality as well as of computational time

Mutual benefits of two multicriteria analysis methodologies: A case study for batch plant design

This paper presents a MultiObjective Genetic Algorithm (MOGA) optimization framework for batch plant design. For this purpose, two approaches are implemented and compared with respect to three criteria, i.e., investment cost, equipment number and a flexibility indicator based on work in process (the so-called WIP) computed by use of a discrete-event simulation model. The first approach involves a genetic algorithm in order to generate acceptable solutions, from which the best ones are chosen by using a Pareto Sort algorithm. The second approach combines the previous Genetic Algorithm with a multicriteria analysis methodology, i.e., the Electre method in order to find the best solutions. The performances of the two procedures are studied for a large-size problem and a comparison between the procedures is then made

Integrated batch process development based on mixed-logic dynamic optimization

Specialty chemicals industry relies on batch manufacturing, since it requires the frequent adaptation of production systems to market fluctuations. To be first in the market, batch industry requires decision-support systems for the rapid development and implementation of chemical processes. Moreover, the processes should be competitive to ensure their long-term viability. General-purpose and flexible plants and the consideration of physicochemical insights to define an efficient operation are also cornerstones for the success of specialty chemical industries. Precisely, this thesis tackles the systematic development of batch processes that are efficient, economically competitive, and environmentally friendly, to assist their agile introduction into production systems in grassroots and retrofit scenarios. Synthesis of conceptual processing schemes and plant allocation subproblems are solved simultaneously, taking into account the plant design. With this purpose, an optimization-based approach is proposed, where all structural alternatives are represented in a State-Equipment Network (SEN) superstructure, following formulated into a Mixed-Logic Dynamic Optimization (MLDO) problem which is later solved to minimize an objective function. Essentially, the strength of the proposed methodology lies in the modeling strategy which combines the different kinds of decisions of the integrated problem in a unique optimization model. Accordingly, it considers: (i) synthesis and allocation alternatives combination, (ii) dynamic process performance models and dynamic control variable profiles, (iii) discrete events associated to transitions of batch phases and operations, (iv) quantitative and qualitative information, (v) material transference synchronization to ensure batch integrity between unit procedures, and (vi) batch and semicontinuous processing elements. Different strategies can be used to solve the resulting MLDO problem. A deterministic direct-simultaneous approach is first proposed. The mixed-logic problem is reformulated into a mixed-integer one, which is fully-discretized to provide a Mixed-Integer Non-Linear Programming (MINLP) that is optimized using conventional solvers. Then, a Differential Genetic Algorithm (DGA) and a hybrid approach are presented. The purpose of these evolutionary strategies is to pose solution alternatives that keep solution goodness while seek for the improvement of computational efficiency to handle industrial-size problems. The optimization-based approach is applied in retrofit scenarios to solve the simultaneous process synthesis and plant allocation, taking into account the physical restrictions of existing plant elements. The production of specialty chemicals based on a competitive reactions system in an existing reactor network is first defined through process development and improvement according to different economic scenarios, decision criteria, and plant modifications. Additionally, a photo-Fenton process is optimized to eliminate an emergent wastewater pollutant in a given pilot plant, pursuing the minimization of processing time and cost. Batch process development in grassroots scenarios is also proven to be a problem of utmost importance to deal with uncertainty in future markets. Seeking for plant flexibility in several demand scenarios, the expected profit is maximized through a two-stage stochastic formulation that includes simultaneous plant design, process synthesis, and plant allocation decisions. A heuristic solution algorithm is used to handle the problem complexity. A grassroots plant design is defined to implement the previous competitive reaction system, where decisions like the feed-forward trajectories or operating modes allow the adaptation of master recipes to different demands. Finally, an acrylic fiber production example is presented to illustrate process development decisions like the selection of tasks, technological alternatives, chemicals, and solvent reuse.La indústria de productes químics especials es basa en la fabricació discontinua, ja que permet adaptar de forma freqüent els sistemes de producció en funció de les fluctuacions de mercat. Per ser líder al sector, són necessàries eines de suport a la decisió que ajudin a l’àgil desenvolupament i implementació de nous processos. A més, aquests han de ser competitius per garantir la seva viabilitat a llarg termini. Altres peces clau per una operació eficient són l’ús de plantes flexibles així com l’estudi dels fenòmens fisicoquímics. Aquesta tesis aborda justament el desenvolupament sistemàtic de processos químics discontinus que siguin eficients, econòmicament competitius i ecològics, per contribuir a la seva ràpida introducció en els sistemes de producció, tant en escenaris de plantes existents com des de les bases. En concret, es planteja la resolució simultània de la síntesi conceptual d’esquemes de procés i l’assignació d’equips, tenint en compte el disseny de la planta. Amb aquest objectiu, es proposa una metodologia de solució basada en optimització, on les alternatives estructurals es representen en una Xarxa d’Estats i Equips (SEN per les sigles en anglès) que es formula mitjançant un problema d’Optimització Dinàmica Mixta-Lògica (MLDO per les sigles en anglès) que es resol minimitzant una funció objectiu. La solidesa de la metodologia proposada rau en la estratègia de modelat del problema MLDO, que integra els diferents tipus de decisions en un sol model d’optimització. En concret, es consideren: (i) la combinació d’alternatives de síntesi i assignació d’equips, (ii) models de procés i trajectòries de control dinàmics, (iii) esdeveniments discrets associats al canvi de fase i operació, (iv) informació quantitativa i qualitativa, (v) sincronització de transferències de material en tasques consecutives, i (vi) elements de processat discontinus i semi-continus. Existeixen diverses estratègies per resoldre el problema MLDO resultant. En aquesta tesi es proposa en primer lloc un mètode determinístic directe-simultani, on el model mixt-lògic es transforma en un mixt-enter. Aquest es discretitza al seu torn de forma completa per obtenir un problema de Programació No-Lineal Mixta-Entera (MINLP per les sigles en anglès) el qual es pot resoldre utilitzant algoritmes d’optimització convencionals. A més, es presenten un Algoritme Genètic Diferencial (DGA per les sigles en anglès) i un mètode híbrid. Totes dues estratègies esdevenen alternatives de cerca amb l’objectiu de mantenir la bondat de la solució i millorar l’eficàcia de computació per tractar problemes de dimensió industrial. La metodologia de solució proposada s’aplica al desenvolupament de processos discontinus en escenaris de plantes existents, tenint en compte les restriccions físiques dels equips. Un primer exemple aborda la manufactura de productes químics basada en un sistema de reaccions competitives. Concretament, es desenvolupa i millora el procés de producció implementat en una xarxa de reactors considerant diferents escenaris econòmics, criteris de decisió, i modificacions de planta. En un segon exemple, s’optimitza el procés foto-Fenton per ser executat en una planta pilot per eliminar contaminants emergents. Buscant integrar el desenvolupament de procés i el disseny de plantes flexibles en escenaris de base, es presenta una formulació estocàstica en dues etapes per a optimitzar el benefici esperat d’acord a diversos escenaris de demanda. Per gestionar la complexitat d’aquest problema es proposa la utilització d’una heurística. Com a exemple, es planteja el disseny d’una planta de base on implementar l’anterior sistema de reaccions competitives. Decisions com les trajectòries dinàmiques de control o la configuració d’equips permeten adaptar la recepta màster en funció de la demanda. Un darrer exemple defineix el procés de producció de fibra acrílica, il·lustrant decisions com la selecció de tasques, tecnologia, reactius o reutilització de dissolvents.La industria productos químicos especiales se basa en la fabricación discontinua, la cual permite la adaptación frecuente de los sistemas de producción en función de las fluctuaciones de mercado. Para ser líder en el sector, son necesarias herramientas de soporte a la decisión que contribuyan al ágil desarrollo e implementación de nuevos procesos. Además, éstos deben ser competitivos para garantizar su viabilidad a largo plazo. Otras piezas clave para una operación eficiente son la utilización de plantas flexibles y el estudio de los fenómenos fisicoquímicos. Esta tesis aborda justamente el desarrollo sistemático de procesos químicos discontinuos que sean eficientes, económicamente competitivos y ecológicos, para contribuir a su rápida introducción en los sistemas de producción, ya sea en escenarios de plantas existentes o desde las bases. En particular, se plantea la resoluciónsimultánea de la síntesis conceptual de esquemas de proceso y la asignación de equipos, teniendo en cuenta además el diseño de planta.Con este fin, se propone una metodología de solución basada en optimización, donde todas las alternativas estructurales se representan en una Red de Estados y Equipos (SENpor sus siglas en inglés) que se formula mediante un problema de Optimización Dinámica Mixta-Lógica (MLDO por sus siglas en inglés) que se resuelve minimizando una función objetivo. La solidez de la metodología propuesta reside en la estrategia de modelado delproblema MLDO, que integra los diferentes tipos de decisiones en un solo modelo de optimización. En concreto, se consideran: (i) la combinación de alternativas de síntesis y asignación de equipos, (ii) modelos de proceso y trayectorias de control dinámicos, (iii)eventos discretos asociados al cambio de fase y operación, (iv) información cuantitativa y cualitativa, (v) sincronización de la transferencia de material en tareas consecutivas, y(vi) elementos de procesado discontinuos y semicontinuos.Existen diversas estrategias para resolver el problema MLDO resultante. En esta tesis se propone en primer lugar un método determinístico directo-simultáneo, donde el problema mixto-lógico se reformula en un mixto-entero. A su vez, éste se discretiza de formacompleta para obtener un problema de Programación No-Lineal Mixta-Entera (MINLP por sus siglas en inglés) el cual se puede resolver mediante algoritmos de optimización convencionales. Además, se presentan un Algoritmo Genético Diferencial (DGA por sussiglas en inglés) y un método híbrido. Ambas estrategias se plantean como alternativas de búsqueda con objeto de mantener la bondad de la solución y mejorar la eficacia de computación para tratar problemas de dimensión industrial.La metodología de solución propuesta se aplica al desarrollo de procesos discontinuos en escenarios con plantas existentes, teniendo en cuenta las restricciones físicas de los equipos. Un primer ejemplo aborda la fabricación de productos químicos basada en un sistema de reacciones competitivas. En concreto, se desarrolla y mejora el proceso de producción a implementar en una red de reactores considerando diferentes escenarios económicos, criterios de decisión, y modificaciones de planta. En un segundo ejemplo,se optimiza el proceso foto-Fenton a ser ejecutado en una planta piloto para eliminar contaminantes emergentes.Persiguiendo la integración del desarrollo de proceso con el diseño de plantas flexi-bles en escenarios base, se presenta asimismo una formulación estocástica en dos etapas para optimizar el beneficio esperado de acuerdo a varios escenarios de demanda. Paramanejar la complejidad de dicho problema se propone la utilización de una heurística.Como ejemplo, se plantea el diseño de una planta de base para implementar el anterior sistema de reacciones competitivas, donde decisiones como las trayectorias dinámicas de control o la configuración de equipos permiten adaptar la receta máster en función de lademandas. Por último, se presenta un ejemplo donde se define el proceso de producción de fibra acrílica, ilustrando decisiones como la selección de tareas, alternativas tecnológicas, reactivos químicos o la reutilización de disolventes.Postprint (published version