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2011 | Buch

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Computational Optimization, Methods and Algorithms

herausgegeben von: Slawomir Koziel, Xin-She Yang

Verlag: Springer Berlin Heidelberg

Buchreihe : Studies in Computational Intelligence

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Computational optimization is an important paradigm with a wide range of applications. In virtually all branches of engineering and industry, we almost always try to optimize something - whether to minimize the cost and energy consumption, or to maximize profits, outputs, performance and efficiency. In many cases, this search for optimality is challenging, either because of the high computational cost of evaluating objectives and constraints, or because of the nonlinearity, multimodality, discontinuity and uncertainty of the problem functions in the real-world systems. Another complication is that most problems are often NP-hard, that is, the solution time for finding the optimum increases exponentially with the problem size. The development of efficient algorithms and specialized techniques that address these difficulties is of primary importance for contemporary engineering, science and industry.

This book consists of 12 self-contained chapters, contributed from worldwide experts who are working in these exciting areas. The book strives to review and discuss the latest developments concerning optimization and modelling with a focus on methods and algorithms for computational optimization. It also covers well-chosen, real-world applications in science, engineering and industry. Main topics include derivative-free optimization, multi-objective evolutionary algorithms, surrogate-based methods, maximum simulated likelihood estimation, support vector machines, and metaheuristic algorithms. Application case studies include aerodynamic shape optimization, microwave engineering, black-box optimization, classification, economics, inventory optimization and structural optimization. This graduate level book can serve as an excellent reference for lecturers, researchers and students in computational science, engineering and industry.

Inhaltsverzeichnis

Frontmatter

Computational Optimization: An Overview

Abstract

Computational optimization is ubiquitous in many applications in engineering and industry. In this chapter, we briefly introduce computational optimization, the optimization algorithms commonly used in practice, and the choice of an algorithm for a given problem. We introduce and analyze the main components of a typical optimization process, and discuss the challenges we may have to overcome in order to obtain optimal solutions correctly and efficiently. We also highlight some of the state-of-the-art developments in optimization and its diverse applications.

Xin-She Yang, Slawomir Koziel

Optimization Algorithms

Abstract

The right choice of an optimization algorithm can be crucially important in finding the right solutions for a given optimization problem. There exist a diverse range of algorithms for optimization, including gradient-based algorithms, derivative-free algorithms and metaheuristics. Modern metaheuristic algorithms are often nature-inspired, and they are suitable for global optimization. In this chapter, we will briefly introduce optimization algorithms such as hill-climbing, trust-region method, simulated annealing, differential evolution, particle swarm optimization, harmony search, firefly algorithm and cuckoo search.

Xin-She Yang

Surrogate-Based Methods

Abstract

Objective functions that appear in engineering practice may come from measurements of physical systems and, more often, from computer simulations. In many cases, optimization of such objectives in a straightforward way, i.e., by applying optimization routines directly to these functions, is impractical. One reason is that simulation-based objective functions are often analytically intractable (discontinuous, non-differentiable, and inherently noisy). Also, sensitivity information is usually unavailable, or too expensive to compute. Another, and in many cases even more important, reason is the high computational cost of measurement/simulations. Simulation times of several hours, days or even weeks per objective function evaluation are not uncommon in contemporary engineering, despite the increase of available computing power. Feasible handling of these unmanageable functions can be accomplished using surrogate models: the optimization of the original objective is replaced by iterative re-optimization and updating of the analytically tractable and computationally cheap surrogate. This chapter briefly describes the basics of surrogate-based optimization, various ways of creating surrogate models, as well as several examples of surrogate-based optimization techniques.

Slawomir Koziel, David Echeverría Ciaurri, Leifur Leifsson

Derivative-Free Optimization

Abstract

In many engineering applications it is common to find optimization problems where the cost function and/or constraints require complex simulations. Though it is often, but not always, theoretically possible in these cases to extract derivative information efficiently, the associated implementation procedures are typically non-trivial and time-consuming (e.g., adjoint-based methodologies). Derivative-free (non-invasive, black-box) optimization has lately received considerable attention within the optimization community, including the establishment of solid mathematical foundations for many of the methods considered in practice. In this chapter we will describe some of the most conspicuous derivative-free optimization techniques. Our depiction will concentrate first on local optimization such as pattern search techniques, and other methods based on interpolation/approximation. Then, we will survey a number of global search methodologies, and finally give guidelines on constraint handling approaches.

Oliver Kramer, David Echeverría Ciaurri, Slawomir Koziel

Maximum Simulated Likelihood Estimation: Techniques and Applications in Economics

Abstract

This chapter discusses maximum simulated likelihood estimation when construction of the likelihood function is carried out by recently proposed Markov chain Monte Carlo (MCMC) methods. The techniques are applicable to parameter estimation and Bayesian and frequentist model choice in a large class of multivariate econometric models for binary, ordinal, count, and censored data.We implement the methodology in a study of the joint behavior of four categories of U.S. technology patents using a copula model for multivariate count data. The results reveal interesting complementarities among several patent categories and support the case for joint modeling and estimation. Additionally, we find that the simulated likelihood algorithm performs well. Even with few MCMC draws, the precision of the likelihood estimate is sufficient for producing reliable parameter estimates and carrying out hypothesis tests.

Ivan Jeliazkov, Alicia Lloro

Optimizing Complex Multi-location Inventory Models Using Particle Swarm Optimization

Abstract

The efficient control of logistics systems is a complicated task. Analytical models allow to estimate the effect of certain policies. However, they necessitate the introduction of simplifying assumptions, and therefore, their scope is limited. To surmount these restrictions, we use Simulation Optimization by coupling a simulator that evaluates the performance of the system with an optimizer. This idea is illustrated for a very general class of multi-location inventory models with lateral transshipments. We discuss the characteristics of such models and introduce Particle Swarm Optimization for their optimization. Experimental studies show the applicability of this approach.

Christian A. Hochmuth, Jörg Lässig, Stefanie Thiem

Traditional and Hybrid Derivative-Free Optimization Approaches for Black Box Functions

Abstract

Picking a suitable optimization solver for any optimization problem is quite challenging and has been the subject of many studies and much debate. This is due in part to each solver having its own inherent strengths and weaknesses. For example, one approach may be global but have slow local convergence properties, while another may have fast local convergence but is unable to globally search the entire feasible region. In order to take advantage of the benefits of more than one solver and to overcome any shortcomings, two or more methods may be combined, forming a hybrid. Hybrid optimization is a popular approach in the combinatorial optimization community, where metaheuristics (such as genetic algorithms, tabu search, ant colony, variable neighborhood search, etc.) are combined to improve robustness and blend the distinct strengths of different approaches. More recently, metaheuristics have been combined with deterministic methods to form hybrids that simultaneously perform global and local searches. In this Chapter, we will examine the hybridization of derivative-free methods to address black box, simulation-based optimization problems. In these applications, the optimization is guided solely by function values (i.e. not by derivative information), and the function values require the output of a computational model. Specifically, we will focus on improving derivative-free sampling methods through hybridization.We will review derivative-free optimization methods, discuss possible hybrids, describe intelligent hybrid approaches that properly utilize both methods, and give an examples of the successful application of hybrid optimization to a problem from the hydrological sciences.

Genetha Anne Gray, Kathleen R. Fowler

Simulation-Driven Design in Microwave Engineering: Methods

Abstract

Today, electromagnetic (EM) simulation is inherent in analysis and design of microwave components. Available simulation packages allow engineers to obtain accurate responses of microwave structures. In the same time the task of microwave component design can be formulated and solved as an optimization problem where the objective function is supplied by an EM solver. Unfortunately, accurate simulations may be computationally expensive; therefore, optimization approaches with the EM solver directly employed in the optimization loop may be very time consuming or even impractical. On the other hand, computationally efficient microwave designs can be realized using surrogate-based optimization. In this chapter, simulation-driven design methods for microwave engineering are described where optimization of the original model is replaced by iterative re-optimization of its surrogate, a computationally cheap low-fidelity model which, in the same time, should have reliable prediction capabilities. These optimization methods include space mapping, simulation-based tuning, variable-fidelity optimization, and various response correction techniques.

Slawomir Koziel, Stanislav Ogurtsov

Variable-Fidelity Aerodynamic Shape Optimization

Abstract

Aerodynamic shape optimization (ASO) plays an important role in the design of aircraft, turbomachinery and other fluid machinery. Simulation-driven ASO involves the coupling of computational fluid dynamics (CFD) solvers with numerical optimization methods. Although being relatively mature and widely used, ASO is still being improved and numerous challenges remain. This chapter provides an overview of simulation-driven ASO methods, with an emphasis on surrogate-based optimization (SBO) techniques. In SBO, a computationally cheap surrogate model is used in lieu of an accurate high-fidelity CFD simulation in the optimization process. Here, a particular focus is given to SBO exploiting surrogate models constructed from corrected physics-based low-fidelity models, often referred to as variable- or multi-fidelity optimization.

Leifur Leifsson, Slawomir Koziel

Evolutionary Algorithms Applied to Multi-Objective Aerodynamic Shape Optimization

Abstract

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

Alfredo Arias-Montaño, Carlos A. Coello Coello, Efrén Mezura-Montes

An Enhanced Support Vector Machines Model for Classification and Rule Generation

Abstract

Based on statistical learning theory, support vector machines (SVM) model is an emerging machine learning technique solving classification problems with small sampling, non-linearity and high dimension. Data preprocessing, parameter selection, and rule generation influence performance of SVM models a lot. Thus, the main purpose of this chapter is to propose an enhanced support vector machines (ESVM) model which can integrate the abilities of data preprocessing, parameter selection and rule generation into a SVM model; and apply the ESVM model to solve real world problems. The structure of this chapter is organized as follows. Section 11.1 presents the purpose of classification and the basic concept of SVM models. Sections 11.2 and 11.3 introduce data preprocessing techniques, metaheuristics for selecting SVM models. Rule extraction of SVM models is addressed in Section 11.4. An enhanced SVM scheme and numerical results are illustrated in Section 11.5 and 11.6. Conclusions are made in Section 11.7.

Ping-Feng Pai, Ming-Fu Hsu

Benchmark Problems in Structural Optimization

Abstract

Structural optimization is an important area related to both optimization and structural engineering. Structural optimization problems are often used as benchmarks to validate new optimization algorithms or to test the suitability of a chosen algorithm. In almost all structural engineering applications, it is very important to find the best possible parameters for given design objectives and constraints which are highly non-linear, involving many different design variables. The field of structural optimization is also an area undergoing rapid changes in terms of methodology and design tools. Thus, it is highly necessary to summarize some benchmark problems for structural optimization. This chapter provides an overview of structural optimization problems of both truss and non-truss cases.

Amir Hossein Gandomi, Xin-She Yang

Backmatter

Titel: Computational Optimization, Methods and Algorithms
herausgegeben von: Slawomir Koziel
Xin-She Yang
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-20859-1
Print ISBN: 978-3-642-20858-4
DOI: https://doi.org/10.1007/978-3-642-20859-1

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Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Computational Optimization: An Overview

Optimization Algorithms

Surrogate-Based Methods

Derivative-Free Optimization

Maximum Simulated Likelihood Estimation: Techniques and Applications in Economics

Optimizing Complex Multi-location Inventory Models Using Particle Swarm Optimization

Traditional and Hybrid Derivative-Free Optimization Approaches for Black Box Functions

Simulation-Driven Design in Microwave Engineering: Methods

Variable-Fidelity Aerodynamic Shape Optimization

Evolutionary Algorithms Applied to Multi-Objective Aerodynamic Shape Optimization

An Enhanced Support Vector Machines Model for Classification and Rule Generation

Benchmark Problems in Structural Optimization

Backmatter

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