Multiobjective Simulation Optimization Using Enhanced Evolutionary Algorithm Approaches

In today\u27s competitive business environment, a firm\u27s ability to make the correct, critical decisions can be translated into a great competitive advantage. Most of these critical real-world decisions involve the optimization not only of multiple objectives simultaneously, but also conflicting objectives, where improving one objective may degrade the performance of one or more of the other objectives. Traditional approaches for solving multiobjective optimization problems typically try to scalarize the multiple objectives into a single objective. This transforms the original multiple optimization problem formulation into a single objective optimization problem with a single solution. However, the drawbacks to these traditional approaches have motivated researchers and practitioners to seek alternative techniques that yield a set of Pareto optimal solutions rather than only a single solution. The problem becomes much more complicated in stochastic environments when the objectives take on uncertain (or noisy ) values due to random influences within the system being optimized, which is the case in real-world environments. Moreover, in stochastic environments, a solution approach should be sufficiently robust and/or capable of handling the uncertainty of the objective values. This makes the development of effective solution techniques that generate Pareto optimal solutions within these problem environments even more challenging than in their deterministic counterparts. Furthermore, many real-world problems involve complicated, black-box objective functions making a large number of solution evaluations computationally- and/or financially-prohibitive. This is often the case when complex computer simulation models are used to repeatedly evaluate possible solutions in search of the best solution (or set of solutions). Therefore, multiobjective optimization approaches capable of rapidly finding a diverse set of Pareto optimal solutions would be greatly beneficial. This research proposes two new multiobjective evolutionary algorithms (MOEAs), called fast Pareto genetic algorithm (FPGA) and stochastic Pareto genetic algorithm (SPGA), for optimization problems with multiple deterministic objectives and stochastic objectives, respectively. New search operators are introduced and employed to enhance the algorithms\u27 performance in terms of converging fast to the true Pareto optimal frontier while maintaining a diverse set of nondominated solutions along the Pareto optimal front. New concepts of solution dominance are defined for better discrimination among competing solutions in stochastic environments. SPGA uses a solution ranking strategy based on these new concepts. Computational results for a suite of published test problems indicate that both FPGA and SPGA are promising approaches. The results show that both FPGA and SPGA outperform the improved nondominated sorting genetic algorithm (NSGA-II), widely-considered benchmark in the MOEA research community, in terms of fast convergence to the true Pareto optimal frontier and diversity among the solutions along the front. The results also show that FPGA and SPGA require far fewer solution evaluations than NSGA-II, which is crucial in computationally-expensive simulation modeling applications

Multiobjective differential evolution based on fuzzy performance feedback: Soft constraint handling and its application in antenna designs

The recently emerging Differential Evolution is considered one of the most powerful tools for solving optimization problems. It is a stochastic population-based search approach for optimization over the continuous space. The main advantages of differential evolution are simplicity, robustness and high speed of convergence. Differential evolution is attractive to researchers all over the world as evidenced by recent publications. There are many variants of differential evolution proposed by researchers and differential evolution algorithms are continuously improved in its performance. Performance of differential evolution algorithms depend on the control parameters setting which are problem dependent and time-consuming task. This study proposed a Fuzzy-based Multiobjective Differential Evolution (FMDE) that exploits three performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution process. We apply the fuzzy inference rules to these metrics in order to adaptively adjust the associated control parameters of the chosen mutation strategy used in this algorithm. The proposed FMDE is evaluated on the well known ZDT, DTLZ, and WFG benchmark test suites. The experimental results show that FMDE is competitive with respect to the chosen state-of-the-art multiobjective evolutionary algorithms. The advanced version of FMDE with adaptive crossover rate (AFMDE) is proposed. The proof of concept AFMDE is then applied specifically to the designs of microstrip antenna array. Furthermore, the soft constraint handling technique incorporates with AFMDE is proposed. Soft constraint AFMDE is evaluated on the benchmark constrained problems. AFMDE with soft constraint handling technique is applied to the constrained non-uniform circular antenna array design problem as a case study

Evolutionary multiobjective optimization : review, algorithms, and applications

Programa Doutoral em Engenharia Industrial e SistemasMany mathematical problems arising from diverse elds of human activity can be formulated as optimization problems. The majority of real-world optimization problems involve several and con icting objectives. Such problems are called multiobjective optimization problems (MOPs). The presence of multiple con icting objectives that have to be simultaneously optimized gives rise to a set of trade-o solutions, known as the Pareto optimal set. Since this set of solutions is crucial for e ective decision-making, which generally aims to improve the human condition, the availability of e cient optimization methods becomes indispensable. Recently, evolutionary algorithms (EAs) have become popular and successful in approximating the Pareto set. The population-based nature is the main feature that makes them especially attractive for dealing with MOPs. Due to the presence of two search spaces, operators able to e ciently perform the search in both the decision and objective spaces are required. Despite the wide variety of existing methods, a lot of open research issues in the design of multiobjective evolutionary algorithms (MOEAs) remains. This thesis investigates the use of evolutionary algorithms for solving multiobjective optimization problems. Innovative algorithms are developed studying new techniques for performing the search either in the decision or the objective space. Concerning the search in the decision space, the focus is on the combinations of traditional and evolutionary optimization methods. An issue related to the search in the objective space is studied in the context of many-objective optimization. Application of evolutionary algorithms is addressed solving two di erent real-world problems, which are modeled using multiobjective approaches. The problems arise from the mathematical modelling of the dengue disease transmission and a wastewater treatment plant design. The obtained results clearly show that multiobjective modelling is an e ective approach. The success in solving these challenging optimization problems highlights the practical relevance and robustness of the developed algorithms.Muitos problemas matemáticos que surgem nas diversas áreas da atividade humana podem ser formulados como problemas de otimização. A maioria dos problemas do mundo real envolve vários objetivos conflituosos. Tais problemas chamam-se problemas de otimização multiobjetivo. A presença de vários objetivos conflituosos, que têm de ser otimizados em simultâneo, dá origem a um conjunto de soluções de compromisso, conhecido como conjunto de soluções ótimas de Pareto. Uma vez que este conjunto de soluções é fundamental para uma tomada de decisão eficaz, cujo objetivo em geral é melhorar a condição humana, o desenvolvimento de métodos de otimização eficientes torna-se indispensável. Recentemente, os algoritmos evolucionários tornaram-se populares e bem-sucedidos na aproximação do conjunto de Pareto. A natureza populacional é a principal característica que os torna especialmente atraentes para lidar com problemas de otimização multiobjetivo. Devido à presença de dois espaços de procura, operadores capazes de realizar a procura de forma eficiente, tanto no espaço de decisão como no espaço dos objetivos, são necessários. Apesar da grande variedade de métodos existentes, várias questões de investigação permanecem em aberto na área do desenvolvimento de algoritmos evolucionários multiobjetivo. Esta tese investiga o uso de algoritmos evolucionários para a resolução de problemas de otimização multiobjetivo. São desenvolvidos algoritmos inovadores que estudam novas técnicas de procura, quer no espaço de decisão, quer no espaço dos objetivos. No que diz respeito à procura no espaço de decisão, o foco está na combinação de métodos de otimização tradicionais com algoritmos evolucionários. A questão relacionada com a procura no espaço dos objetivos é desenvolvida no contexto da otimização com muitos objetivos. A aplicação dos algoritmos evolucionários é abordada resolvendo dois problemas reais, que são modelados utilizando abordagens multiobjectivo. Os problemas resultam da modelação matemática da transmissão da doença do dengue e do desenho ótimo de estações de tratamento de águas residuais. O sucesso na resolução destes problemas de otimização constitui um desafio e destaca a relevância prática e robustez dos algoritmos desenvolvidos

Optimisation of welding parameters to mitigate the effect of residual stress on the fatigue life of nozzle–shell welded joints in cylindrical pressure vessels.

Doctoral Degree. University of KwaZulu-Natal, Durban.The process of welding steel structures inadvertently causes residual stress as a result of thermal cycles that the material is subjected to. These welding-induced residual stresses have been shown to be responsible for a number of catastrophic failures in critical infrastructure installations such as pressure vessels, ship’s hulls, steel roof structures, and others. The present study examines the relationship between welding input parameters and the resultant residual stress, fatigue properties, weld bead geometry and mechanical properties of welded carbon steel pressure vessels. The study focuses on circumferential nozzle-to-shell welds, which have not been studied to this extent until now. A hybrid methodology including experimentation, numerical analysis, and mathematical modelling is employed to map out the relationship between welding input parameters and the output weld characteristics in order to further optimize the input parameters to produce an optimal welded joint whose stress and fatigue characteristics enhance service life of the welded structure. The results of a series of experiments performed show that the mechanical properties such as hardness are significantly affected by the welding process parameters and thereby affect the service life of a welded pressure vessel. The weld geometry is also affected by the input parameters of the welding process such that bead width and bead depth will vary depending on the parametric combination of input variables. The fatigue properties of a welded pressure vessel structure are affected by the residual stress conditions of the structure. The fractional factorial design technique shows that the welding current (I) and voltage (V) are statistically significant controlling parameters in the welding process. The results of the neutron diffraction (ND) tests reveal that there is a high concentration of residual stresses close to the weld centre-line. These stresses subside with increasing distance from the centre-line. The resultant hoop residual stress distribution shows that the hoop stresses are highly tensile close to the weld centre-line, decrease in magnitude as the distance from the weld centre-line increases, then decrease back to zero before changing direction to compressive further away from the weld centre-line. The hoop stress distribution profile on the flange side is similar to that of the pipe side around the circumferential weld, and the residual stress peak values are equal to or higher than the yield strength of the filler material. The weld specimens failed at the weld toe where the hoop stress was generally highly tensile in most of the welded specimens. The multiobjective genetic algorithm is successfully used to produce a set of optimal solutions that are in agreement with values obtained during experiments. The 3D finite element model produced using MSC Marc software is generally comparable to physical experimentation. The results obtained in the present study are in agreement with similar studies reported in the literature

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

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

Scalable multi-objective optimization

This thesis is concerned with the three open in multi-objective optimization: (i) the development of strategies for dealing with problems with many objective functions; (ii) the comprehension and solution of the model-building issues of current MOEDAs, and; (iii) the formulation of stopping criteria for multi-objective optimizers. We argue about what elements of MOEDAs should be modified in order to achieve a substantial improvement on their performance and scalability. However, in order to supply a solid ground for that discussion, some other elements are to be discussed as well. In particular, this thesis: sketches the supporting theoretical corpus and the fundamentals of MOEA and MOEDA algorithms; analyzes the scalability issue of MOEAs from both theoretical and experimental points of view; discusses the possible directions of improvement for MOEAs’ scalability, presenting the current trends of research; gives reasons of why EDAs can be used as a foundation for achieving a sizable improvement with regard to the scalability issue; examines the model-building issue in depth, hypothesizing on how it affects MOEDAs performance; proposes a novel model-building algorithm, the model-building growing neural gas (MBGNG), which fulfill the requirements for a new approach derived from the previous debate, and; introduces a novel MOEDA, the multi-objective neural EDA, that is constructed using MB-GNG as foundation. The formulation of an strategy for stopping multi-objective optimizers became obvious and necessary as this thesis was developed. The lack of an adequate stopping criterion made the rendered any experimentation that had to do with many objectives a rather cumbersome task. That is why it was compulsory to deal with this issue in order to proceed with further studies. In this regard, the thesis: provides an updated and exhaustive state-of-the-art of this matter; examines the properties and characteristics that a given stopping criterion should exhibit; puts forward a new stopping criterion, denominated MGBM, after the authors last names, that has a small computational footprint, and; experimentally validates MGBM in a set of experiments. Theoretical discussions and algorithm proposals are experimentally contrasted with current state-of-the-art approaches when required. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Muchas actividades humanas están relacionadas con la elaboración de artefactos cuyas características, organización y/o costes de producción, etc., se deben ajustar en la manera más eficiente posible. Este hecho ha creado la necesidad de tener herramientas matemáticas y computacionales capaces de tratar estos problemas, lo cual ha impulsado el desarrollo de distintas áreas de investigación interrelacionadas, como, por ejemplo, la optimización, programación matemática, investigación de operaciones, etc. El concepto de optimización se puede formular en términos matemáticos como el proceso de buscar una o más soluciones factibles que se correspondan con los valores extremos de una o varias funciones. La mayor parte de los problemas de optimización reales implican la optimización de más de una función a la vez. Esta clase de problemas se conoce como problemas de optimización multi-objetivo (POM). Existe una clase de POM que es particularmente atractivo debido a su complejidad inherente: los denominados problemas de muchos objetivos. Estos son problemas con un número relativamente elevado de funciones objetivo. Numerosos experimentos han mostrado que los métodos “tradicionales” no logran un desempeño adecuado debido a la relación intensamente exponencial entre la dimensión del conjunto objetivo y la cantidad de recursos requeridos para resolver el problema correctamente. Estos problemas tienen una naturaleza poco intuitiva y, en particular, sus soluciones son difíciles de visualizar por un tomador de decisiones humano. Sin embargo, son bastante comunes en la práctica (Stewart et al., 2008). La optimización multi-objetivo ha recibido una importante atención por parte de la comunidad dedicada a los algoritmos evolutivos (Coello Coello et al., 2007). Sin embargo, se ha hecho patente la necesidad de buscar alternativas para poder tratar con los problemas de muchos objetivos. Los algoritmos de estimación de distribución (EDAs, por sus siglas en inglés) (Lozano et al., 2006) son buenos candidatos para esa tarea. Estos algoritmos se han presentado como una revolución en el campo de la computación evolutiva. Ellos sustituyen la aplicación de operadores inspirados en la selección natural por la síntesis de un modelo estadístico. Este modelo es muestreado para generar nuevos elementos y así proseguir con la búsqueda de soluciones. Sin embargo, los EDAs multi-objetivo (MOEDAs) no han logrado cumplir las expectativas creadas a priori. El leit motif de esta tesis se puede resumir en que la causa principal del bajo rendimiento MOEDAs se debe a los algoritmos de aprendizaje automático que se aplican en la construcción de modelos estadísticos. Los trabajos existentes hasta el momento han tomado una aproximación de “caja negra” al problema de la construcción de modelos. Por esa razón, se aplican métodos de aprendizaje automático ya existentes sin modificación alguna, sin percatarse que el problema de la construcción de modelos para EDAs tiene unos requisitos propios que en varios casos son contradictorios con el contexto original de aplicación de los mencionados algoritmos. En particular, hay propiedades compartidas por la mayoría de los enfoques de aprendizaje automático que podrían evitar la obtención de una mejora sustancial en el resultado de los MOEDAs. Ellas son: el tratamiento incorrecto de los valores atípicos (outliers) en el conjunto de datos; tendencia a la pérdida de la diversidad de la población, y; exceso de esfuerzo computacional dedicado a la búsqueda de un modelo óptimo. Estos problemas, aunque ya están presentes en los EDAs de un solo objetivo, se hacen patentes al escalar a problemas de varios objetivos y, en particular, a muchos objetivos. Además, con el aumento de la cantidad de objetivos con frecuencia esta situación se ve agravada por las consecuencias de la “maldición de la dimensionalidad”. La cuestión de los valores atípicos en los datos es un buen ejemplo de como la comunidad no ha notado esta diferencia. En el contexto tradicional del aprendizaje automático los valores extremos son considerados como datos ruidosos o irrelevantes y, por tanto, deben ser evitados. Sin embargo, los valores atípicos en los datos de la construcción de modelos representan las regiones recién descubiertas o soluciones candidatas del conjunto de decisión y por lo tanto deben ser explorados. En este caso, los casos aislados debe ser al menos igualmente representados por el modelo con respecto a los que están formando grupos. Sobre la base de estos razonamientos se estructuran los principales resultados obtenidos en el desarrollo de la tesis. A continuación se enumeran brevemente los mismos mencionando las referencias principales de los mismos. Comprensión del problema de la construcción de modelos en MOEDAs (Martí et al., 2010a, 2008b, 2009c). Se analiza que los EDAs han asumido incorrectamente que la construcción de modelos es un problema tradicional de aprendizaje automático. En el trabajo se muestra experimentalmente la hipótesis. Growing Neural Gas: una alternativa viable para construcción de modelos (Martí et al., 2008c). Se propone el Model-Building Growing Neural Gas network (MB-GNG), una modificación de las redes neuronales tipo Growing Neural Gas. MB-GNG tiene las propiedades requeridas para tratar correctamente la construcción de modelos. MONEDA: mejorando el desempeño de los MOEDAs (Martí et al., 2008a, 2009b, 2010c). El Multi-objective Optimization Neural EDA (MONEDA) fue ideado con el fin de hacer frente a los problemas arriba descritos de los MOEDAs y, por lo tanto, mejorar la escalabilidad de los MOEDAs. MONEDA utiliza MB-GNG para la construcción de modelos. Gracias a su algoritmo específico de construcción de modelos, la preservación de las élites de individuos de la población y su mecanismo de sustitución de individuos MONEDA es escalable capaz de resolver POMs continuos de muchos objetivos con un mejor desepeño que algoritmos similares a un coste computacional menor. Esta propuesta fue nominada a mejor trabajo en GECCO’2008. MONEDA en problemas de alta complejidad (Martí et al., 2009d). En este caso se lleva a cabo una amplia experimentación para comprender como las características de MONEDA provocan una mejora en el desempeño del algoritmo, y si sus resultados mejoran los obtenidos de otros enfoques. Se tratan problemas de alta complejidad. Estos experimentos demostraron que MONEDA produce resultados sustancialmente mejores que los algoritmos similares a una menor coste computacional. Nuevos paradigmas de aprendizaje: MARTEDA (Martí et al., 2010d). Si bien MB-GNG y MONEDA mostraron que la vía del tratamiento correcto de la construcción de modelos era una de las formas de obtener mejores resultados, ellos no evadían por completo el punto esencial: el paradigma de aprendizaje empleado. Al combinar un paradigma de aprendizaje automático alternativo, en particular, la Teoría de Resonancia Adaptativa, se trata a este asunto desde su raíz. En este respecto se han obtenido algunos resultados preliminares alentadores. Criterios de parada y convergencia (Martí et al., 2007, 2009a, 2010e). Con la realización de los experimentos anteriores nos percatamos de la falta de de un criterio de parada adecuado y que esta es un área inexplorada en el ámbito de la investigación en algoritmos evolutivos multi-objectivo. Abordamos esta cuestión proponiendo una serie de criterios de parada que se han demostrado efectivos en problemas sintéticos y del mundo real

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided

Robust and Multi-objective Portfolio Selection

In this thesis, robust and multi-objective portfolio selection problem will be studied. New models and computational algorithms will be developed to solve the proposed models. In particularly, we have studied multi-objective portfolio selection with inexact information on investment return and covariance matrix. The problems have been transformed into easily solvable problems through theoretical analysis. Numerical experiments are presented to validate the methods

Incremental approach to particle swarm assisted function optimization

Ph.DDOCTOR OF PHILOSOPH