1,721,081 research outputs found
Model-based evolutionary optimization methods
No full textModel-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests
Metody evoluční optimalizace založené na modelech
No full textStatistické modely se používají pro urychlení optimalizace jak v akademické sféře, tak v průmyslu. Právě v reálných aplikacích, kde je optimalizovaná funkce často finančně nebo časově náročná, mohou statistické modely ušetřit zdroje nebo urychlit optimalizaci. Každá ze tří částí dizertační práce se zabývá jedním takovým modelem: v první části práce nahrazují kopule grafické modely v algoritmech odhadující distribuci, RBF sítě slouží jako náhradní model v genetických algoritmech pro kombinaci spojitých a diskrétních proměnných ve druhé části a třetí část práce používá gaussovské procesy jednak jako model pro vzorkování v bayesovských optimalizačních algoritmech, jednak jako náhradní model v evoluční strategii adaptující kovarianční matici (CMA-ES). Poslední kombinaci, která je popsána klíčové části práce, využívá navržený algoritmus DTS-CMA-ES---dvojitě trénovaný CMA-ES s náhradním modelem. Tento algoritmus využívá nejistotu predikovanou gaussovským procesem, aby vybral část populace CMA-ES k ohodnocení drahou originální funkcí, zatímco zbytek populace je ohodnocen modelem---predikovanou nejpravděpodobnější hodnotou. Výsledky ukázaly, že DTS-CMA-ES konverguje na několika syntetických funkcích rychleji než současné spojité optimalizační algoritmy s náhradním modelem.Model-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests.Matematicko-fyzikální fakultaFaculty of Mathematics and Physic
Comparing Boundary Handling Techniques of CMA-ES on the bbob and sbox-cost Test Suites
No full textInternational audienceBound constraints on the variables are the most basic constraints in an optimization problem formulation and, thus, among the most common. It is therefore essential to understand the impact of different boundary handling techniques on algorithm performance. Equally, it is important to understand the practical impact of using bound constraint handling in an algorithm on principally unbounded problems but where the user has a good indication of the domain of the (sought) optimum. Both questions will be investigated in this paper on the newly introduced box-constrained version sbox-cost of the well-known, unconstrained test suite bbob and for the example of the two boundary handling techniques, implemented in the CMA-ES python module pycma. The numerical experiments performed with the COCO platform show that there is (i) only a minor difference in performance between the two test suites and (ii) a slight performance reduction for the (default) BoundTransform boundary handling compared to the BoundPenalty version of CMA-ES
Optimal μ-Distributions for the Hypervolume Indicator for Problems With Linear Bi-Objective Fronts: Exact and Exhaustive Results
Full text linkcorrected author versionInternational audienceTo simultaneously optimize multiple objective functions, several evolutionary multiobjective optimization (EMO) algorithms have been proposed. Nowadays, often set quality indicators are used when comparing the performance of those algorithms or when selecting ``good'' solutions during the algorithm run. Hence, characterizing the solution sets that maximize a certain indicator is crucial---complying with the optimization goal of many indicator-based EMO algorithms. If these optimal solution sets are upper bounded in size, e.g., by the population size μ, we call them optimal μ-distributions. Recently, optimal μ-distributions for the well-known hypervolume indicator have been theoretically analyzed, in particular, for bi-objective problems with a linear Pareto front. Although the exact optimal μ-distributions have been characterized in this case, not all possible choices of the hypervolume's reference point have been investigated. In this paper, we revisit the previous results and rigorously characterize the optimal μ-distributions also for all other reference point choices. In this sense, our characterization is now exhaustive as the result holds for any linear Pareto front and for any choice of the reference point and the optimal μ-distributions turn out to be always unique in those cases. We also prove a tight lower bound (depending on μ) such that choosing the reference point above this bound ensures the extremes of the Pareto front to be always included in optimal μ-distributions
Theoretical Aspects of Evolutionary Multiobjective Optimization---A Review
Full text linkOptimization problems in practice often involve the simultaneous optimization of 2 or more conflicting objectives. Evolutionary multiobjective optimization (EMO) techniques are well suited for tackling those multiobjective optimization problems because they are able to generate a set of solutions that represent the inherent trade-offs between the objectives. In the beginning, multiobjective evolutionary algorithms have been seen as single-objective algorithms where only the selection scheme needed to be tailored towards multiobjective optimization. In the meantime, EMO has become an independent research field with its specific research questions---and its own theoretical foundations. Several important theoretical studies on EMO have been conducted in recent years which opened up a better understanding of the underlying principles and resulted in the proposition of better algorithms in practice. Besides a brief introduction about the basic principles of EMO, the main goal of this report is to give a general overview of theoretical studies published in the field of EMO and to present some of the theoretical results in more detail. Due to space limitations, we only focus on three main aspects of previous and current research here: (i) performance assessment with quality indicators, (ii) hypervolume-based search, and (iii) rigorous runtime analyses and convergence properties of multiobjective evolutionary algorithms
Theoretical Aspects of Evolutionary Multiobjective Optimization---A Review
No full textOptimization problems in practice often involve the simultaneous optimization of 2 or more conflicting objectives. Evolutionary multiobjective optimization (EMO) techniques are well suited for tackling those multiobjective optimization problems because they are able to generate a set of solutions that represent the inherent trade-offs between the objectives. In the beginning, multiobjective evolutionary algorithms have been seen as single-objective algorithms where only the selection scheme needed to be tailored towards multiobjective optimization. In the meantime, EMO has become an independent research field with its specific research questions---and its own theoretical foundations. Several important theoretical studies on EMO have been conducted in recent years which opened up a better understanding of the underlying principles and resulted in the proposition of better algorithms in practice. Besides a brief introduction about the basic principles of EMO, the main goal of this report is to give a general overview of theoretical studies published in the field of EMO and to present some of the theoretical results in more detail. Due to space limitations, we only focus on three main aspects of previous and current research here: (i) performance assessment with quality indicators, (ii) hypervolume-based search, and (iii) rigorous runtime analyses and convergence properties of multiobjective evolutionary algorithms
Many-Objective Quality Measures
No full textA key concern when undertaking any form of optimisation is how to characterise the quality of the putative solution returned. In many-objective optimisation an added complication is that such measures are on a set of trade-off solutions. We present and discuss the commonly used quality measures for many-objective optimisation, which are a subset of those used in multi-objective optimisation. We discuss the computational aspects and theoretical properties of these measures, highlighting measures for both a posteriori and a priori approaches, where the latter incorporate preference information from a decision maker (DM). We also discuss open areas in this field and forms of many-objective optimisation which are relatively under-explored, and where appropriate quality measures are much less developed including challenges related to developing measures for interactive methods.peerReviewe
Visualisation for Decision Support in Many-Objective Optimisation : State-of-the-art, Guidance and Future Directions
No full textThis chapter describes the state-of-the-art in visualisation for decision support processes in problems with many objectives. Visualisation is an important part of a constructive decision making process for examining real world many-objective problems. The chapter first illustrates how visualisation can be applied to problem framing, guided optimization, trade-off assessment and solution selection. Next, the chapter reviews state-of-the-art visualisation approaches in terms of what is available and what is typically used. Guidance is provided for choosing and applying visualisation techniques including recommendations from the field of visual analytics. These recommendations are illustrated through a complex real-world decision problem with ten objectives. Lastly, the chapter concludes with suggested future research directions for advancing the scope and impact of many-objective optimisation when confronting complex decision making contexts.peerReviewe
Key Issues in Real-World Applications of Many-Objective Optimisation and Decision Analysis
No full textThe insights and benefits to be realised through the optimisation of multiple independent, but conflicting objectives are well recognised by practitioners seeking effective and robust solutions to real-world application problems. Key issues encountered by users of many-objective optimisation (>3 objectives) in a real-world environment are discussed here. These include how to formulate the problem and develop a suitable decision-making framework, together with considering different ways in which decision-makers may be involved. Ways to manage the reduction of computational load and how to reduce the sensitivity of candidate solutions as a result of the inevitable uncertainties that arise in real-world applications are addressed. Other state-of-the-art topics such as the use of machine learning and the management of complex issues arising from multidisciplinary applications are also examined. It is recognised that optimisation in real-world applications is commonly undertaken by users and decision-makers who need not have specialist expertise in many-objective optimisation decision analysis methods. Advice is offered to experts and non-experts alike.peerReviewe
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