Otimização multi-objetivo envolvendo aproximadores de função via processos gaussianos e algoritmos híbridos que empregam otimização direta do hipervolume

Orientador: Fernando José Von ZubenTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: O principal propósito desta tese é reduzir a lacuna entre otimização mono-objetivo e multiobjetivo e mostrar que conectar técnicas de lados opostos pode gerar melhores resultados. Para atingir esta meta, nós fornecemos contribuições em três direções. Primeiro, mostra-se a conexão entre otimalidade da perda média e do hipervolume quando avaliando uma única solução, provando limites de otimalidade quando a solução de um é aplicada ao outro. Ademais, uma avaliação do gradiente do hipervolume mostra que ele pode ser interpretado como um caso particular da perda média ponderada, onde os pesos aumentam conforme as perdas associadas aumentam. Levantou-se a hipótese de que isto pode ajudar a treinar modelos de aprendizado de máquina, uma vez que amostras com erro alto também terão peso alto. Um experimento com uma rede neural valida a hipótese, mostrando melhor desempenho. Segundo, avaliaram-se tentativas anteriores de usar otimização do hipervolume baseada em gradiente para resolver problemas multi-objetivo e por que elas falharam. Baseado na análise, foi proposto um algoritmo híbrido que combina otimização evolutiva e baseada em gradiente. Experimentos nas funções de benchmark ZDT mostram melhor desempenho e convergência mais rápida comparado a algoritmos evolutivos de referência. Finalmente, foram apresentadas condições necessárias e suficientes para que uma função descreva uma fronteira de Pareto válida. Com base nestes resultados, adaptou-se um processo Gaussiano para penalizar violações das condições e mostrou-se que ele fornece melhores estimativas do que outros algoritmos de aproximação. Em particular, ele cria uma curva que não viola as restrições tanto quanto algoritmos que não consideram as condições, sendo mais confiável como um indicador de performance. Foi também demonstrado que uma métrica de otimização comum, quando aproximando funções com processos Gaussianos, é uma boa indicadora das regiões que um algoritmo deveria explorar para encontrar a fronteira de ParetoAbstract: The main purpose of this thesis is to bridge the gap between single-objective and multi- objective optimization and to show that connecting techniques from both ends can lead to improved results. To reach this goal, we provide contributions in three directions. First, we show the connection between optimality of a mean loss and the hypervolume when evaluating a single solution, proving optimality bounds when the solution from one is applied to the other. Furthermore, an evaluation of the gradient of the hypervolume shows that it can be interpreted as a particular case of the weighted mean loss, where the weights increase as their associated losses increases. We hypothesize that this can help to train a machine learning model, since samples with high error will also have high weight. An experiment with a neural network validates the hypothesis, showing improved performance. Second, we evaluate previous attempts at using gradient-based hypervolume optimization to solve multi-objective problems and why they have failed. Based on the analysis, we propose a hybrid algorithm that combines gradient-based and evolutionary optimization. Experiments on the benchmark functions ZDT show improved performance and faster convergence compared with reference evolutionary algorithms. Finally, we prove necessary and sufficient conditions for a function to describe a valid Pareto frontier. Based on this result, we adapt a Gaussian process to penalize violation of the conditions and show that it provides better estimates than other approximation algorithms. In particular, it creates a curve that does not violate the constraints as much as done by algorithms that do not consider the restrictions, being a more reliable performance indicator. We also show that a common optimization metric when approximating functions with Gaussian processes is a good indicator of the regions an algorithm should explore to find the Pareto frontierDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétrica2015/09199-0CAPESFAPES

Multi-Objective Optimization of Mixed-Variable, Stochastic Systems Using Single-Objective Formulations

Many problems exist where one desires to optimize systems with multiple, often competing, objectives. Further, these problems may not have a closed form representation, and may also have stochastic responses. Recently, a method expanded mixed variable generalized pattern search/ranking and selection (MVPS-RS) and Mesh Adaptive Direct Search (MADS) developed for single-objective, stochastic problems to the multi-objective case by using aspiration and reservation levels. However, the success of this method in approximating the true Pareto solution set can be dependent upon several factors. These factors include the experimental design and ranges of the aspiration and reservation levels, and the approximation quality of the nadir point. Additionally, a termination criterion for this method does not yet exist. In this thesis, these aspects are explored. Furthermore, there may be alternatives or additions to this method that can save both computational time and function evaluations. These include the use of surrogates as approximating functions and the expansion of proven singleobjective formulations. In this thesis, two new approaches are developed that make use of all of these previous existing methods in combination

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

A multi-objective evolutionary approach to simulation-based optimisation of real-world problems.

This thesis presents a novel evolutionary optimisation algorithm that can improve the quality of solutions in simulation-based optimisation. Simulation-based optimisation is the process of finding optimal parameter settings without explicitly examining each possible configuration of settings. An optimisation algorithm generates potential configurations and sends these to the simulation, which acts as an evaluation function. The evaluation results are used to refine the optimisation such that it eventually returns a high-quality solution. The algorithm described in this thesis integrates multi-objective optimisation, parallelism, surrogate usage, and noise handling in a unique way for dealing with simulation-based optimisation problems incurred by these characteristics. In order to handle multiple, conflicting optimisation objectives, the algorithm uses a Pareto approach in which the set of best trade-off solutions is searched for and presented to the user. The algorithm supports a high degree of parallelism by adopting an asynchronous master-slave parallelisation model in combination with an incremental population refinement strategy. A surrogate evaluation function is adopted in the algorithm to quickly identify promising candidate solutions and filter out poor ones. A novel technique based on inheritance is used to compensate for the uncertainties associated with the approximative surrogate evaluations. Furthermore, a novel technique for multi-objective problems that effectively reduces noise by adopting a dynamic procedure in resampling solutions is used to tackle the problem of real-world unpredictability (noise). The proposed algorithm is evaluated on benchmark problems and two complex real-world problems of manufacturing optimisation. The first real-world problem concerns the optimisation of a production cell at Volvo Aero, while the second one concerns the optimisation of a camshaft machining line at Volvo Cars Engine. The results from the optimisations show that the algorithm finds better solutions for all the problems considered than existing, similar algorithms. The new techniques for dealing with surrogate imprecision and noise used in the algorithm are identified as key reasons for the good performance.University of Skövde Knowledge Foundation Swede

From Parameter Tuning to Dynamic Heuristic Selection

The importance of balance between exploration and exploitation plays a crucial role while solving combinatorial optimization problems. This balance is reached by two general techniques: by using an appropriate problem solver and by setting its proper parameters. Both problems were widely studied in the past and the research process continues up until now. The latest studies in the field of automated machine learning propose merging both problems, solving them at design time, and later strengthening the results at runtime. To the best of our knowledge, the generalized approach for solving the parameter setting problem in heuristic solvers has not yet been proposed. Therefore, the concept of merging heuristic selection and parameter control have not been introduced. In this thesis, we propose an approach for generic parameter control in meta-heuristics by means of reinforcement learning (RL). Making a step further, we suggest a technique for merging the heuristic selection and parameter control problems and solving them at runtime using RL-based hyper-heuristic. The evaluation of the proposed parameter control technique on a symmetric traveling salesman problem (TSP) revealed its applicability by reaching the performance of tuned in online and used in isolation underlying meta-heuristic. Our approach provides the results on par with the best underlying heuristics with tuned parameters.:1 Introduction 1 1.1 Motivation 1 1.2 Research objective 2 1.3 Solution overview 2 2 Background and RelatedWork Analysis 3 2.1 Optimization Problems and their Solvers 3 2.2 Heuristic Solvers for Optimization Problems 9 2.3 Setting Algorithm Parameters 19 2.4 Combined Algorithm Selection and Hyper-Parameter Tuning Problem 27 2.5 Conclusion on Background and Related Work Analysis 28 3 Online Selection Hyper-Heuristic with Generic Parameter Control 31 3.1 Combined Parameter Control and Algorithm Selection Problem 31 3.2 Search Space Structure 32 3.3 Parameter Prediction Process 34 3.4 Low-Level Heuristics 35 3.5 Conclusion of Concept 36 4 Implementation Details 37 4.2 Search Space 40 4.3 Prediction Process 43 4.4 Low Level Heuristics 48 4.5 Conclusion 52 5 Evaluation 55 5.1 Optimization Problem 55 5.2 Environment Setup 56 5.3 Meta-heuristics Tuning 56 5.4 Concept Evaluation 60 5.5 Analysis of HH-PC Settings 74 5.6 Conclusion 79 6 Conclusion 81 7 FutureWork 83 7.1 Prediction Process 83 7.2 Search Space 84 7.3 Evaluations and Benchmarks 84 Bibliography 87 A Evaluation Results 99 A.1 Results in Figures 99 A.2 Results in numbers 10

Project scheduling under undertainty – survey and research potentials.

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;

Horsetail Matching for Optimization Under Probabilistic, Interval and Mixed Uncertainties

The importance of including uncertainties in the design process of aerospace systems is becoming increasingly recognized, leading to the recent development of many techniques for optimization under uncertainty. Most existing methods represent uncertainties in the problem probabilistically; however, in many real life design applications it is often difficult to assign probability distributions to uncertainties without making strong assumptions. Existing approaches for optimization under different types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Horsetail matching is a flexible approach to optimization under any mix of probabilistic and interval uncertainties that overcomes some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems and the design of a flying wing using a coupled aero-structural analysis code.Engineering and Physical Sciences Research CouncilUnited States. Office of Naval Research. Multidisciplinary University Research Initiative (Award Number FA9550-15-1-0038

Disentangling the drivers of ant community composition: integrating structural, spatial and inter-specific competition at multiple scales.

Plant community-based conservation strategies are used for conserving cryptic diversity such as invertebrates. This approach however assumes plant community composition correlates with patterns of other taxa across the landscape. Composition may instead be influenced by other drivers including competition or stochastic assembly processes resulting in spatial turnover. I evaluated plant community-based conservation strategies using ants as a model system. I first evaluated a regional plant community-based conservation strategy across Sydney. Ants were weakly associated with plant community composition. Overall spatial turnover of ants was low, however within-community patterns were stronger. I then compared the relative importance of plant community, habitat structure and spatial drivers of ant assemblage composition at fine scales within the NSW SW Slopes. Spatial turnover was the best predictor of ant assemblage composition, with some association also with habitat structure. However, plant community composition did not predict ant assemblages. I found competitive exclusion between two abundant dominant ant species, Iridomyrmex purpureus and I. chasei. To investigate the influences of competitive dominance, I sampled ant assemblages along territory boundaries, and measured competitive dominance within territories. I found very strong competitive interactions and rapidly shifting territory boundaries. Food resources were more consistently won by the more abundant I. chasei, with lower species richness and significantly different assemblage composition of affiliate ant species attending baits in their territories. I found that plant community surrogacy provided only weak representation of ant assemblages, and only at course scales between broadly different plant community classes. Spatial turnover in ant assemblages was strong and resulted in high spatial turnover patterns. Competition from dominant species may also structure assemblage patterns

Surrogate-Assisted Unified Optimization Framework for Investigating Marine Structural Design Under Information Uncertainty.

Structural decisions made in the early stages of marine systems design can have a large impact on future acquisition, maintenance and life-cycle costs. However, owing to the unique nature of early stage marine system design, these critical structure decisions are often made on the basis of incomplete information or knowledge about the design. When coupled with design optimization analysis, the complex, uncertain early stage design environment makes it very difficult to deliver a quantified trade-off analysis for decision making. This work presents a novel decision support method that integrates design optimization, high-fidelity analysis, and modeling of information uncertainty for early stage design and analysis. To support this method this dissertation improves the design optimization methods for marine structures by proposing several novel surrogate modeling techniques and strategies. The proposed work treats the uncertainties that are sourced from limited information in a non-statistical interval uncertainty form. This interval uncertainty is treated as an objective function in an optimization framework in order to explore the impact of information uncertainty on structural design performance. In this examination, the potential structural weight penalty regarding information uncertainty can be quickly identified in early stage, avoiding costly redesign later in the design. This dissertation then continues to explore a balanced computational structure between fidelity and efficiency. A proposed novel variable fidelity approach can be applied to wisely allocate expensive high-fidelity computational simulations. In achieving the proposed capabilities for design optimization, several surrogate modeling methods are developed concerning worst-case estimation, clustered multiple meta-modeling, and mixed variable modeling techniques. These surrogate methods have been demonstrated to significantly improve the efficiency of optimizer in dealing with the challenges of early stage marine structure design.PhDNaval Architecture and Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133365/1/yanliuch_1.pd