Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome (AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663]. We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are: minimization of the number of HIV infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.Comment: This is a preprint of a paper whose final and definite form is with 'Computational and Applied Mathematics', ISSN 0101-8205 (print), ISSN 1807-0302 (electronic). Submitted 04-Feb-2016; revised 11-June-2016 and 02-Sept-2016; accepted for publication 15-March-201

Weighted stress function method for multiobjective evolutionary algorithm based on decomposition

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a well established state-of-the-art framework. Major concerns that must be addressed when applying MOEA/D are the choice of an appropriate scalarizing function and setting the values of main control parameters. This study suggests a weighted stress function method (WSFM) for fitness assignment in MOEA/D. WSFM establishes analogy between the stress-strain behavior of thermoplastic vulcanizates and scalarization of a multiobjective optimization problem. The experimental results suggest that the proposed approach is able to provide a faster convergence and a better performance of final approximation sets with respect to quality indicators when compared with traditional methods. The validity of the proposed approach is also demonstrated on engineering problems.This work has been supported by FCT - Fundação para a Ciência e Tecnologia in the scope of the project: PEst-OE/EEI/UI0319/2014.info:eu-repo/semantics/publishedVersio

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

Combining artificial neural networks and evolution to solve multiobjective knapsack problems

The multiobjective knapsack problem (MOKP) is a combinatorial problem that arises in various applications, including resource allocation, computer science and finance. Evolutionary multiobjective optimization algorithms (EMOAs) can be effective in solving MOKPs. Though, they often face difficulties due to the loss of solution diversity and poor scalability. To address those issues, our study [2] proposes to generate candidate solutions by artificial neural networks. This is intended to provide intelligence to the search. As gradient-based learning cannot be used when target values are unknown, neuroevolution is adapted to adjust the neural network parameters. The proposal is implemented within a state-of-the-art EMOA and benchmarked against traditional search operators base on a binary crossover. The obtained experimental results indicate a superior performance of the proposed approach. Furthermore, it is advantageous in terms of scalability and can be readily incorporated into different EMOAs.(undefined

Multiobjective optimization of polymer extrusion: decision making and robustness

A Multi-Objective Evolutionary Algorithm (MOEA) is used to optimize polymer single screw extrusion. In this approach, the MOEA is linked to a modelling routine that quantifies the objectives as a function of the decision variables (i.e., operating conditions and/or screw geometry). Due to the conflicting nature of some objectives, the optimization algorithm uses a set of possible solutions to the problem that evolves during suc-cessive generations to a set of optimal solutions denoted as Pareto set. Since practical process optimization should yield a single solution, it is convenient to implement also a Decision Making (DM) strategy. Two methodologies were followed. In one case, the solutions were selected based on the preferences of a decision maker. Alternatively, the sensitivity of the solutions to small changes in the design variables was taken into account through a robustness analysis. The analysis of various case studies and the comparison with experi-mental data validated the method and demonstrates its potential.This work was supported by the Portuguese Fundação para a Ciência e Tecnologia under grant PEst-C/CTM/LA0025/2013 (Projecto Estratégico - LA 25 - 2013-2014 - Strategic Project - LA 25 - 2013-2014).info:eu-repo/semantics/publishedVersio

Neuroevolution for solving multiobjective knapsack problems

The multiobjective knapsack problem (MOKP) is an important combinatorial problem that arises in various applications, including resource allocation, computer science and finance. When tackling this problem by evolutionary multiobjective optimization algorithms (EMOAs), it has been demonstrated that traditional recombination operators acting on binary solution representations are susceptible to a loss of diversity and poor scalability. To address those issues, we propose to use artificial neural networks for generating solutions by performing a binary classification of items using the information about their profits and weights. As gradient-based learning cannot be used when target values are unknown, neuroevolution is adapted to adjust the neural network parameters. The main contribution of this study resides in developing a solution encoding and genotype-phenotype mapping for EMOAs to solve MOKPs. The proposal is implemented within a state-of-the-art EMOA and benchmarked against traditional variation operators based on binary crossovers. The obtained experimental results indicate a superior performance of the proposed approach. Furthermore, it is advantageous in terms of scalability and can be readily incorporated into different EMOAs.Portuguese “Fundação para a Ciência e Tecnologia” under grant PEst-C/CTM/LA0025/2013 (Projecto Estratégico - LA 25 - 2013-2014 - Strategic Project - LA 25 - 2013-2014

Evolving neural networks to optimize material usage in blow molded containers

In industry, there is a growing interest to optimize the use of raw material in blow molded products. Commonly, the material in blow molded containers is optimized by dividing the container into different sections and minimizing the wall thickness of each section. The definition of discrete sections is limited by the shape of the container and can lead to suboptimal solutions. This study suggests determining the optimal thickness distribution for blow molded containers as a function of geometry. The proposed methodology relies on the use of neural networks and finite element analysis. Neural networks are stochastically evolved considering multiple objectives related to the optimization of material usage, such as cost and quality. Numerical simulations based on finite element analysis are used to evaluate the performance of the container with a thickness profile determined by feeding the coordinates of mesh elements in finite element model into the neural network. The proposed methodology was applied to the design of industrial bottle. The obtained results suggested the validity and usefulness of this methodology by revealing its ability to identify the most critical regions for the application of material.FCT -Fundação para a Ciência e a Tecnologia(PEst-E/EEI/UI0319/2014)info:eu-repo/semantics/publishedVersio

Regularization-free multicriteria optimization of polymer viscoelasticity model

This paper introduces a multiobjective optimization (MOP) method for nonlinear regression analysis which is capable of simultaneously minimizing the model order and estimating parameter values without the need of exogenous regularization constraints. The method is introduced through a case study in polymer rheology modeling. Prevailing approaches in this field tackle conflicting optimization goals as a monobjective problem by aggregating individual regression errors on each dependent variable into a single weighted scalarization function. In addition, their supporting deterministic numerical methods often rely on assumptions which are extrinsic to the problem, such as regularization constants and restrictions on parameter distribution, thereby introducing methodology inherent biases into the model. Our proposed non-deterministic MOP strategy, on the other hand, aims at finding the Pareto-front of all optimal solutions with respect not only to individual regression errors, but also to the number of parameters needed to fit the data, automatically reducing the model order. The evolutionary computation approach does not require arbitrary constraints on objective weights, regularization parameters or other exogenous assumptions to handle the ill-posed inverse problem. The article discusses the method rationales, implementation, simulation experiments, and comparison with other methods, with experimental evidences that it can outperform state-of-art techniques. While the discussion focuses on the study case, the introduced method is general and immediately applicable to other problem domains.This work is funded by National Funds through FCT - Portuguese Foundation for Science and Technology, References UIDB/05256/2020 and UIDP/05256/2020 and the European project MSCA-RISE-2015, NEWEX, Reference 734205

Hybrid genetic pattern search augmented Lagrangian algorithm : application to WWTP optimization

An augmented Lagrangian algorithm is presented to solve a global optimization problem that arises when modeling the activated sludge system in a Wastewater Treatment Plant, attempting to minimize both investment and operation costs. It is a heuristic-based algorithm that uses a genetic algorithm to explore the search space for a global optimum and a pattern search method for the local search refinement. The obtained results have physical meaning and show the effectiveness of the proposed method

Optimização de um sistema de lamas activadas por um algoritmo genético

Apresenta-se, neste artigo, um problema de optimização relacionado com um processo biológico de tratamento de águas residuais. A formulação matemática que surge da modelação de um sistema de lamas activadas de uma ETAR é optimizado, em termos de custos de investimento e custos operacionais, através de um algoritmo genético. É usado o modelo ASM1 para as lamas activadas, um dos modelos matemáticos mais difundidos e aceites pela comunidade científica. Para o sedimentador secundário é usado um modelo que combina as normas ATV e o modelo da dupla exponencial. Trata-se de uma formulação matemática de elevada complexidade. O modelo está disponível em MatLab e AMPL, e foi resolvido por uma heurística que garante convergência para um óptimo global do problema. Esta heurística baseia-se num algoritmo genético que implementa elitismo