Discrete Optimization Algorithms

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. This second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

Cellular Genetic Algorithms defines a new class of optimization algorithms based on the concepts of structured populations and Genetic Algorithms (GAs). The authors explain and demonstrate the validi

Evolutionary algorithms is a class of randomized heuristics inspired by natural evolution. They are applied in many different contexts, in particular in optimization, and analysis of such algorithms h

Network flow theory has been used across a number of disciplines, including theoretical computer science, operations research, and discrete math, to model not only problems in the transportation of goods and information, but also a wide range of applications from image segmentation problems in computer vision to deciding when a baseball team has been eliminated from contention. This graduate text and reference presents a succinct, unified view of a wide variety of efficient combinatorial algorithms for network flow problems, including many results not found in other books. It covers maximum flows, minimum-cost flows, generalized flows, multicommodity flows, and global minimum cuts and also presents recent work on computing electrical flows along with recent applications of these flows to classical problems in network flow theory.

Performance evaluation tools (Petri nets, Markov process, Discrete Event simulation, etc.) and optimization techniques (branch and bound, dynamic programming, genetic algorithm, ant colony optimizati

This book makes available a self-contained collection of modern research addressing the general constrained optimization problems using evolutionary algorithms. Broadly the topics covered include cons

The first book to focus on jumping genes outside bioscience and medicine, Multiobjective Optimization Methodology: A Jumping Gene Approach introduces jumping gene algorithms designed to supply adequat

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. T

This text provides an excellent balance of theory and application that enables you to deploy powerful algorithms, frameworks, and methodologies to solve complex optimization problems in a diverse rang

This is the first book devoted entirely to Particle Swarm Optimization (PSO), which is a non-specific algorithm, similar to evolutionary algorithms, such as taboo search and ant colonies.Since its ori

Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-sem

A more intuitive approach to the mathematical foundations of computer scienceDiscrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and gra

Computing developed as a branch of mathematics, only to drift away from this home as computer science diverged towards more general topics such as the theory of how a computer works. Recently the emphasis has become more mathematical and the new disciplines of software engineering and information technology have emerged. This book is designed to form the basis of a one year course in discrete mathematics for first year computer scientists or software engineers. The material presented covers much of undergraduate algebra with a particular bias towards the computing applications. Topics covered include mathematical logic, set theory, finite and infinite relations and mappings, graphs, graphical algorithms and axiom systems. It concludes with implementations of many of the algorithms in Modula-2 to illustrate how the mathematics may be turned into concrete calculations. Numerous examples and exercises are included with selected solutions to the problems appearing in the appendix. Discrete

Written for a broad audience of students in mathematics, computer science, operations research, statistics, and engineering, this textbook presents a short, lively survey of several fascinating non-calculus topics in modern applied mathematics. Coverage includes probability, mathematical finance, graphs, linear programming, statistics, computer science algorithms, and groups. A key feature is the abundance of interesting examples not normally found in standard finite mathematics courses, such as options pricing and arbitrage, tournaments, and counting formulas. The author assumes a level of mathematical sophistication at the beginning calculus level, that is, students should have had at least a course in pre-calculus, and the added sophistication attained from studying calculus would be useful.

In the last decade, there have been an increasing convergence of interest and methods between theoretical physics and fields as diverse as probability, machine learning, optimization and compressed se

Memetic Algorithms (MAs) are computational intelligence structures combining multiple and various operators in order to address optimization problems. The combination and interaction amongst operator

Memetic Algorithms (MAs) are computational intelligence structures combining multiple and various operators in order to address optimization problems.? The combination and interaction amongst operator

This book offers a basic introduction to genetic algorithms. It provides a detailed explanation of genetic algorithm concepts and examines numerous genetic algorithm optimization problems. In addition

This book is an introduction to relevant aspects of the foraging literature for algorithmic design, and an overview of key families of optimization algorithms that stem from a foraging metaphor. The a

From the reviews of the previous editions ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for stude

What algorithms are tractable depends on the speed of the processor. Given the speed of digital computers, polynomial algorithms are considered tractable. But, a human can take several seconds to make

This book introduces novel methodological approaches to discrete optimization, providing both theoretical insights and algorithmic discoveries which lead to improvements over state-of-the-art technolo

This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors

The major purpose of this book is to introduce the main concepts of discrete optimization problems which have a finite number of feasible solutions. Following common practice, we term this topic combi

Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; found

Optimization techniques have been widely adopted to implement various data mining algorithms. In addition to well-known Support Vector Machines (SVMs) (which are based on quadratic programming), diffe

The wide scope of optimization mandates extensive interaction between various disciplines in the development of the methods and algorithms, and in their fruitful application to real-world problems.Th

This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical o

This book introduces the applications, theory, and algorithms of linear and nonlinear optimization, with an emphasis on the practical aspects of the material. Its unique modular structure provides fle

Optimization is used to determine the most appropriate value of variables under given conditions. The primary focus of using optimisation techniques is to measure the maximum or minimum value of a function depending on the circumstances. This book discusses problem formulation and problem solving with the help of algorithms such as secant method, quasi-Newton method, linear programming and dynamic programming. It also explains important chemical processes such as fluid flow systems, heat exchangers, chemical reactors and distillation systems using solved examples. The book begins by explaining the fundamental concepts followed by an elucidation of various modern techniques including trust-region methods, Levenberg–Marquardt algorithms, stochastic optimization, simulated annealing and statistical optimization. It studies the multi-objective optimization technique and its applications in chemical engineering and also discusses the theory and applications of various optimization software

The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained surv