Increasing the density of available pareto optimal solutions

The set of available multi-objective optimization algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due to the computational cost - to use a population large enough to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem

Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems

This is the final version. Available from MIT Press via the DOI in this recordFor offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data and an optimizer, e.g. a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to provide uncertainty information. However, building GPRs becomes computationally expensive when the size of the dataset is large. Using sparse GPRs reduces the computational cost of building the surrogates. However, sparse GPRs are not tailored to solve offline data-driven MOPs, where good accuracy of the surrogates is needed near Pareto optimal solutions. Treed GPR (TGPR-MO) surrogates for offline data-driven MOPs with continuous decision variables are proposed in this paper. The proposed surrogates first split the decision space into subregions using regression trees and build GPRs sequentially in regions close to Pareto optimal solutions in the decision space to accurately approximate tradeoffs between the objective functions. TGPR-MO surrogates are computationally inexpensive because GPRs are built only in a smaller region of the decision space utilizing a subset of the data. The TGPR-MO surrogates were tested on distance-based visualizable problems with various data sizes, sampling strategies, numbers of objective functions, and decision variables. Experimental results showed that the TGPR-MO surrogates are computationally cheaper and can handle datasets of large size. Furthermore, TGPR-MO surrogates produced solutions closer to Pareto optimal solutions compared to full GPRs and sparse GPRs.Academy of Finlan

Traffic engineering approaches using multicriteria optimization techniques

Nowadays, network planning and management tasks can be of high complexity, given the numerous inputs that should be consid- ered to effectively achieve an adequate configuration of the underlying network. This paper presents an optimization framework that helps net- work administrators in setting the optimal routing weights of link state protocols according to the required traffic demands, contributing in this way to improve the service levels quality provided by the network infras- tructure. Since the envisaged task is a NP-hard problem, the framework resorts to Evolutionary Computation as the optimization engine. The fo- cus is given to the use of multi-objective optimization approaches given the flexibility they provide to network administrators in selecting the ad- equate solutions in a given context. Resorting to the proposed optimiza- tion framework the administrator is able to automatically obtain highly optimized routing configurations adequate to support the requirements imposed by their customers. In this way, this novel approach effectively contributes to enhance and automate crucial network planning and man- agement tasks

The use of evolutionary algorithms to solve practical problems in polymer extrusion

This work aims at selecting the operating conditions and designing screws that optimize the performance of single-screw and co-rotating twin-screw extruders, which are machines widely used by the polymer processing industry. A special MOEA, denoted as Reduced Pareto Set Genetic Algorithm, RPSGAe, is presented and used to solve these multiobjective combinatorial problems. Twin screw design is formulated as a Travelling Salesman Problem, TSP, given its discrete nature. Various case studies are analyzed and their validity is discussed, thus demonstrating the potential practical usefulness of this approach

A stopping criterion for multi-objective optimization evolutionary algorithms

This Paper Puts Forward A Comprehensive Study Of The Design Of Global Stopping Criteria For Multi-Objective Optimization. In This Study We Propose A Global Stopping Criterion, Which Is Terms As Mgbm After The Authors Surnames. Mgbm Combines A Novel Progress Indicator, Called Mutual Domination Rate (Mdr) Indicator, With A Simplified Kalman Filter, Which Is Used For Evidence-Gathering Purposes. The Mdr Indicator, Which Is Also Introduced, Is A Special-Purpose Progress Indicator Designed For The Purpose Of Stopping A Multi-Objective Optimization. As Part Of The Paper We Describe The Criterion From A Theoretical Perspective And Examine Its Performance On A Number Of Test Problems. We Also Compare This Method With Similar Approaches To The Issue. The Results Of These Experiments Suggest That Mgbm Is A Valid And Accurate Approach. (C) 2016 Elsevier Inc. All Rights Reserved.This work was funded in part by CNPq BJT Project 407851/2012-7 and CNPq PVE Project 314017/2013-

Development of a multi-objective optimization algorithm based on lichtenberg figures

This doctoral dissertation presents the most important concepts of multi-objective optimization and a systematic review of the most cited articles in the last years of this subject in mechanical engineering. The State of the Art shows a trend towards the use of metaheuristics and the use of a posteriori decision-making techniques to solve engineering problems. This fact increases the demand for algorithms, which compete to deliver the most accurate answers at the lowest possible computational cost. In this context, a new hybrid multi-objective metaheuristic inspired by lightning and Linchtenberg Figures is proposed. The Multi-objective Lichtenberg Algorithm (MOLA) is tested using complex test functions and explicit contrainted engineering problems and compared with other metaheuristics. MOLA outperformed the most used algorithms in the literature: NSGA-II, MOPSO, MOEA/D, MOGWO, and MOGOA. After initial validation, it was applied to two complex and impossible to be analytically evaluated problems. The first was a design case: the multi-objective optimization of CFRP isogrid tubes using the finite element method. The optimizations were made considering two methodologies: i) using a metamodel, and ii) the finite element updating. The last proved to be the best methodology, finding solutions that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the Tsai-Wu failure index and increased by at least 52.57% the natural frequency. In the second application, MOLA was internally modified and associated with feature selection techniques to become the Multi-objective Sensor Selection and Placement Optimization based on the Lichtenberg Algorithm (MOSSPOLA), an unprecedented Sensor Placement Optimization (SPO) algorithm that maximizes the acquired modal response and minimizes the number of sensors for any structure. Although this is a structural health monitoring principle, it has never been done before. MOSSPOLA was applied to a real helicopter’s main rotor blade using the 7 best-known metrics in SPO. Pareto fronts and sensor configurations were unprecedentedly generated and compared. Better sensor distributions were associated with higher hypervolume and the algorithm found a sensor configuration for each sensor number and metric, including one with 100% accuracy in identifying delamination considering triaxial modal displacements, minimum number of sensors, and noise for all blade sections.Esta tese de doutorado traz os conceitos mais importantes de otimização multi-objetivo e uma revisão sistemática dos artigos mais citados nos últimos anos deste tema em engenharia mecânica. O estado da arte mostra uma tendência no uso de meta-heurísticas e de técnicas de tomada de decisão a posteriori para resolver problemas de engenharia. Este fato aumenta a demanda sobre os algoritmos, que competem para entregar respostas mais precisas com o menor custo computacional possível. Nesse contexto, é proposta uma nova meta-heurística híbrida multi-objetivo inspirada em raios e Figuras de Lichtenberg. O Algoritmo de Lichtenberg Multi-objetivo (MOLA) é testado e comparado com outras metaheurísticas usando funções de teste complexas e problemas restritos e explícitos de engenharia. Ele superou os algoritmos mais utilizados na literatura: NSGA-II, MOPSO, MOEA/D, MOGWO e MOGOA. Após validação, foi aplicado em dois problemas complexos e impossíveis de serem analiticamente otimizados. O primeiro foi um caso de projeto: otimização multi-objetivo de tubos isogrid CFRP usando o método dos elementos finitos. As otimizações foram feitas considerando duas metodologias: i) usando um meta-modelo, e ii) atualização por elementos finitos. A última provou ser a melhor metodologia, encontrando soluções que reduziram pelo menos 45,69% da massa, 18,4% do coeficiente de instabilidade, 61,76% do TW e aumentaram em pelo menos 52,57% a frequência natural. Na segunda aplicação, MOLA foi modificado internamente e associado a técnicas de feature selection para se tornar o Seleção e Alocação ótima de Sensores Multi-objetivo baseado no Algoritmo de Lichtenberg (MOSSPOLA), um algoritmo inédito de Otimização de Posicionamento de Sensores (SPO) que maximiza a resposta modal adquirida e minimiza o número de sensores para qualquer estrutura. Embora isto seja um princípio de Monitoramento da Saúde Estrutural, nunca foi feito antes. O MOSSPOLA foi aplicado na pá do rotor principal de um helicóptero real usando as 7 métricas mais conhecidas em SPO. Frentes de Pareto e configurações de sensores foram ineditamente geradas e comparadas. Melhores distribuições de sensores foram associadas a um alto hipervolume e o algoritmo encontrou uma configuração de sensor para cada número de sensores e métrica, incluindo uma com 100% de precisão na identificação de delaminação considerando deslocamentos modais triaxiais, número mínimo de sensores e ruído para todas as seções da lâmina

Evolutionary learning and global search for multi-optimal PID tuning rules

With the advances in microprocessor technology, control systems are widely seen not only in industry but now also in household appliances and consumer electronics. Among all control schemes developed so far, Proportional plus Integral plus Derivative (PID) control is the most widely adopted in practice. Today, more than 90% of industrial controllers have a built-in PID function. Their wide applications have stimulated and sustained the research and development of PID tuning techniques, patents, software packages and hardware modules. Due to parameter interaction and format variation, tuning a PID controller is not as straightforward as one would have anticipated. Therefore, designing speedy tuning rules should greatly reduce the burden on new installation and ‘time-to-market’ and should also enhance the competitive advantages of the PID system under offer. A multi-objective evolutionary algorithm (MOEA) would be an ideal candidate to conduct the learning and search for multi-objective PID tuning rules. A simple to implement MOEA, termed s-MOEA, is devised and compared with MOEAs developed elsewhere. Extensive study and analysis are performed on metrics for evaluating MOEA performance, so as to help with this comparison and development. As a result, a novel visualisation technique, termed “Distance and Distribution” (DD)” chart, is developed to overcome some of the limitations of existing metrics and visualisation techniques. The DD chart allows a user to view the comparison of multiple sets of high order non-dominated solutions in a two-dimensional space. The capability of DD chart is shown in the comparison process and it is shown to be a useful tool for gathering more in-depth information of an MOEA which is not possible in existing empirical studies. Truly multi-objective global PID tuning rules are then evolved as a result of interfacing the s-MOEA with closed-loop simulations under practical constraints. It takes into account multiple, and often conflicting, objectives such as steady-state accuracy and transient responsiveness against stability and overshoots, as well as tracking performance against load disturbance rejection. These evolved rules are compared against other tuning rules both offline on a set of well-recognised PID benchmark test systems and online on three laboratory systems of different dynamics and transport delays. The results show that the rules significantly outperform all existing tuning rules, with multi-criterion optimality. This is made possible as the evolved rules can cover a delay to time constant ratio from zero to infinity based on first-order plus delay plant models. For second-order plus delay plant models, they can also cover all possible dynamics found in practice

Multi-objective ant colony optimization for the twin-screw configuration problem

The Twin-Screw Configuration Problem (TSCP) consists in identifying the best location of a set of available screw elements along a screw shaft. Due to its combinatorial nature, it can be seen as a sequencing problem. In addition, different conflicting objectives may have to be considered when defining a screw configuration and, thus, it is usually tackled as a multi-objective optimization problem. In this research, a multi-objective ant colony optimization (MOACO) algorithm was adapted to deal with the TSCP. The influence of different parameters of the MOACO algorithm was studied and its performance was compared with that of a previously proposed multi-objective evolutionary algorithm and a two-phase local search algorithm. The experimental results showed that MOACO algorithms have a significant potential for solving the TSCP.This work has been supported by the Portuguese Fundacao para a Ciencia e Tecnologia under PhD grant SFRH/BD/21921/2005. Thomas Stutzle acknowledges support of the Belgian F.R.S-FNRS of which he is a research associate, the E-SWARM project, funded by an ERC Advanced Grant, and by the Meta-X project, funded by the Scientific Research Directorate of the French Community of Belgium

Optimization of a Quantum Cascade Laser Operating in the Terahertz Frequency Range Using a Multiobjective Evolutionary Algorithm

A quantum cascade (QC) laser is a specific type of semiconductor laser that operates through principles of quantum mechanics. In less than a decade QC lasers are already able to outperform previously designed double heterostructure semiconductor lasers. Because there is a genuine lack of compact and coherent devices which can operate in the far-infrared region the motivation exists for designing a terahertz QC laser. A device operating at this frequency is expected to be more efficient and cost effective than currently existing devices. It has potential applications in the fields of spectroscopy, astronomy, medicine and free-space communication as well as applications to near-space radar and chemical/biological detection. The overarching goal of this research was to find QC laser parameter combinations which can be used to fabricate viable structures. To ensure operation in the THz region the device must conform to the extremely small energy level spacing range from ~10-15 meV. The time and expense of the design and production process is prohibitive, so an alternative to fabrication was necessary. To accomplish this goal a model of a QC laser, developed at Worchester Polytechnic Institute with sponsorship from the Air Force Research Laboratory Sensors Directorate, and the General Multiobjective Parallel Genetic Algorithm (GenMOP), developed at the Air Force Institute of Technology, were integrated to form a computer simulation which stochastically searches for feasible solutions

DIFFERENTIAL EVOLUTION-BASED METHODS FOR NUMERICAL OPTIMIZATION

Ph.DDOCTOR OF PHILOSOPH