Multi-objective decision-making is critical for everyday tasks and engineering problems. Finding the perfect trade-off to maximize all the solution's criteria requires a considerable amount of experience or the availability of a significant number of resources. This makes these decisions difficult to achieve for expensive problems such as engineering. Most of the time, to solve such expensive problems, we are limited by time, resources, and available expertise. Therefore, it is desirable to simplify or approximate the problem when possible before solving it. The state-of-the-art approach for simplification is model-based or surrogate-based optimization. These approaches use approximation models of the real problem, which are cheaper to evaluate. These models, in essence, are simplified hypotheses of cause-effect relationships, and they replace high estimates with cheap approximations. In this thesis, we investigate surrogate models as wrappers for the real problem and apply \gls{moea} to find Pareto optimal decisions. The core idea of surrogate models is the combination and stacking of several models that each describe an independent objective. When combined, these independent models describe the multi-objective space and optimize this space as a single surrogate hypothesis - the surrogate compositional model. The combination of multiple models gives the potential to approximate more complicated problems and stacking of valid surrogate hypotheses speeds-up convergence. Consequently, a better result is obtained at lower costs. We combine several possible surrogate variants and use those that pass validation. After recombination of valid single objective surrogates to a multi-objective surrogate hypothesis, several instances of \gls{moea}s provide several Pareto front approximations. The modular structure of implementation allows us to avoid a static sampling plan and use self-adaptable models in a customizable portfolio. In numerous case studies, our methodology finds comparable solutions to standard NSGA2 using considerably fewer evaluations. We recommend the present approach for parameter tuning of expensive black-box functions.:1 Introduction 1.1 Motivation 1.2 Objectives 1.3 Research questions 1.4 Results overview 2 Background 2.1 Parameter tuning 2.2 Multi-objective optimization 2.2.1 Metrics for multi-objective solution 2.2.2 Solving methods 2.3 Surrogate optimization 2.3.1 Domain-specific problem 2.3.2 Initial sampling set 2.4 Discussion 3 Related Work 3.1 Comparison criteria 3.2 Platforms and frameworks 3.3 Model-based multi-objective algorithms 3.4 Scope of work 4 Compositional Surrogate 4.1 Combinations of surrogate models 4.1.1 Compositional Surrogate Model [RQ1] 4.1.2 Surrogate model portfolio [RQ2] 4.2 Sampling plan [RQ3] 4.2.1 Surrogate Validation 4.3 Discussion 5 Implementation 5.1 Compositional surrogate 5.2 Optimization orchestrator 6 Evaluation 6.1 Experimental setup 6.1.1 Optimization problems 6.1.2 Optimization search 6.1.3 Surrogate portfolio 6.1.4 Benchmark baseline 6.2 Benchmark 1: Portfolio with compositional surrogates. Dynamic sampling plan 6.3 Benchmark 2: Inner parameters 6.3.1 TutorM parameters 6.3.2 Sampling plan size 6.4 Benchmark 3: Scalability of surrogate models 6.5 Discussion of results 7 Conclusion 8 Future Work A Appendix A.1 Benchmark results on ZDT DTLZ, WFG problems

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-02-14T11:18:13Z No. of bitstreams: 1 TeseAHMP.pdf: 2470407 bytes, checksum: b3f2c2d64bfa00285c28963c74627bea (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-03-20T13:12:18Z (GMT) No. of bitstreams: 1 TeseAHMP.pdf: 2470407 bytes, checksum: b3f2c2d64bfa00285c28963c74627bea (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-03-20T13:12:31Z (GMT) No. of bitstreams: 1 TeseAHMP.pdf: 2470407 bytes, checksum: b3f2c2d64bfa00285c28963c74627bea (MD5) / Made available in DSpace on 2017-03-20T13:23:55Z (GMT). No. of bitstreams: 1 TeseAHMP.pdf: 2470407 bytes, checksum: b3f2c2d64bfa00285c28963c74627bea (MD5) Previous issue date: 2014-12-02 / Não recebi financiamento / The process of building the knowledge base of fuzzy systems has benefited extensively of methods to automatically extract the necessary knowledge from data sets that represent examples of the problem. Among the topics investigated in the most recent research is the matter of balance between accuracy and interpretability, which has been addressed by means of multi-objective genetiv algorithms, NSGA-II being on of the most popular. In this scope, we identified the need to control the diversity of solutions found by these algorithms, so that each solution would balance the Pareto frontier with respect to the goals optimized by the multi-objective genetic algorithm. In this PhD thesis a multi-objective genetic algorithm, named NSGA-DO, is proposed. It is able to find non dominated solutions that balance the Pareto frontier with respect optimization of the objectives. The main characteristicof NSGA-DO is the distance oriented selection of solutions. Once the Pareto frontier is found, the algorithm uses the locations of the solutions in the frontier to find the best distribution of solutions. As for the validation of the proposal, NSGA-DO was applied to a methodology for the generation of fuzzy knowledge bases. Experiments show the superiority of NSGADO when compared to NSGA-II in all three issues analyzed: dispersion, accuracy and interpretability. / A construção da base de conhecimento de sistemas fuzzy tem sido beneficiada intensamente por métodos automáticos que extraem o conhecimento necessário a partir de conjuntos de dados que representam exemplos do problema. Entre os tópicos mais investigados nas pesquisas recentes está a questão do balanceamento entre acuidade e interpretabilidade, que têm sido abordada por meio dos algoritmos genéticos multiobjetivo, sendo o NSGA-II um dos mais populares. Neste escopo, identificou-se a necessidade do controle da distribuição das soluções encontradas por estes algoritmos, a fim de que cada solução possa equilibrar a fronteira de Pareto com relação aos objetivos otimizados pelo algoritmo genético multiobjetivo. Neste sentido, desenvolveu-se neste projeto de doutorado um algoritmo genético multiobjetivo, chamado NSGA-DO, capaz de encontrar soluções não dominadas que equilibram a fronteira de Pareto nos objetivos a serem otimizados. A principal característica do NSGA-DO é a seleção de soluções orientada à distância. Uma vez encontrada a fronteira de Pareto, o algoritmo usa a localização das soluções nesta fronteira para encontrar a melhor distribuição das soluções. Para a validação da proposta, aplicou-se o NSGA-DO em uma metodologia para a geração de bases de conhecimento fuzzy. Experimentos realizados comprovaram a superioridade do NSGA-DO com relação ao NSGA-II nos três quesitos analisados: dispersão, acurácia e interpretabilidade.