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Metaheuristics for vehicle routing problems
This book is dedicated to metaheuristics as applied to vehicle routing problems.Several implementations are given as illustrative examples, along with applications to several typical vehicle routing problems.
eBook
One-dimensional empirical measures, order statistics, and Kantorovich transport distances
This work is devoted to the study of rates of convergence of the empirical measures \\mu_{n} = \\frac {1}{n} \\sum_{k=1}^n \\delta_{X_k}, n \\geq 1, over a sample (X_{k})_{k \\geq 1} of independent identically distributed real-valued random variables towards the common distribution \\mu in Kantorovich transport distances W_p. The focus is on finite range bounds on the expected Kantorovich distances \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) or \\big [ \\mathbb{E}(W_{p}^p(\\mu_{n},\\mu )) \\big ]^1/p in terms of moments and analytic conditions on the measure \\mu and its distribution function. The study describes a variety of rates, from the standard one \\frac {1}{\\sqrt n} to slower rates, and both lower and upper-bounds on \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
eBook
Network and discrete location : models, algorithms, and applications
Praise for the First Edition This book is refreshing to read since it takes an important topic... and presents it in a clear and concise manner by using examples that include visual presentations of the problem, solution methods, and results along with an explanation of the mathematical and procedural steps required to model the problem and work through to a solution.\" -Journal of Classification Thoroughly updated and revised, Network and Discrete Location: Models, Algorithms, and Applications, Second Edition remains the go-to guide on facility location modeling. The book offers a unique introduction to methodological tools for solving location models and provides insight into when each approach is useful and what information can be obtained. The Second Edition focuses on real-world extensions of the basic models used in locating facilities, including production and distribution systems, location-inventory models, and defender-interdictor problems. A unique taxonomy of location problems and models is also presented. Featuring examples using the author's own software-SITATION, MOD-DIST, and MENU-OKF-as well as Microsoft Office® Excel®, the book provides: A theoretical and applied perspective on location models and algorithms An intuitive presentation of the uses and limits of modeling techniques An introduction to integrated location-inventory modeling and defender-interdictor models for the design of reliable facility location systems A full range of exercises to equip readers with an understanding of the basic facility location model types Network and Discrete Location: Models, Algorithms, and Applications, Second Edition is an essential resource for practitioners in applied and discrete mathematics, operations research, industrial engineering, and quantitative geography. The book is also a useful textbook for upper-level undergraduate,
graduate, and MBA courses.
eBook
Topological Optimization and Optimal Transport
By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered.
Contents
Part I
* Geometric issues in PDE problems related to the infinity Laplace operator
* Solution of free boundary problems in the presence of geometric uncertainties
* Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
* High-order topological expansions for Helmholtz problems in 2D
* On a new phase field model for the approximation of interfacial energies of multiphase systems
* Optimization of eigenvalues and eigenmodes by using the adjoint method
* Discrete varifolds and surface approximation
Part II
* Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem
* Optimal transportation theory with repulsive costs
* Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations
* On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
* On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows
* Pressureless Euler equations with maximal density constraint: a time-splitting scheme
* Convergence of a fully discrete variational scheme for a thin-film equatio
* Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance
eBook
Metaheuristics for Logistics
This book describes the main classical combinatorial problems that can be encountered when designing a logistics network or driving a supply chain. It shows how these problems can be tackled by metaheuristics, both separately and using an integrated approach. A huge number of techniques, from the simplest to the most advanced ones, are given for helping the reader to implement efficient solutions that meet its needs.
A lot of books have been written about metaheuristics (methods for solving hard optimization problems) and supply chain management (the field in which we find a huge number of combinatorial optimization problems) in the last decades. So, the main reason of this book is to describe how these methods can be implemented for this class of problems.
eBook
Topological Optimization and Optimal Transport
By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored.
eBook
Differential equations methods for the Monge-Kantorevich mass transfer problem
In this volume, the authors demonstrate under some assumptions on $f^+$, $f^-$ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\\mu{^+}=f^+dx$ onto $\\mu^-=f^-dy$ can be constructed by studying the $p$-Laplacian equation $- \\mathrm {div}(\\vert DU_p\\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p\\rightarrow\\infty$. The idea is to show $u_p\\rightarrow u$, where $u$ satisfies $\\vert Du\\vert\\leq 1,-\\mathrm {div}(aDu)=f^+-f^-$ for some density $a\\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f^+$ and $f^-$.
eBook
Dynamic Allocation and Pricing
Dynamic allocation and pricing problems occur in numerous frameworks, including the pricing of seasonal goods in retail, the allocation of a fixed inventory in a given period of time, and the assignment of personnel to incoming tasks. Although most of these problems deal with issues treated in the mechanism design literature, the modern revenue management (RM) literature focuses instead on analyzing properties of restricted classes of allocation and pricing schemes. In this book, Alex Gershkov and Benny Moldovanu propose an approach to optimal allocations and prices based on the theory of mechanism design, adapted to dynamic settings.Drawing on their own recent work on the topic, the authors describe a modern theory of RM that blends the elegant dynamic models from the operations research (OR), management science, and computer science literatures with techniques from the classical mechanism design literature. Illustrating this blending of approaches, they start with well-known complete information, nonstrategic dynamic models that yield elegant explicit solutions. They then add strategic agents that are privately informed and then examine the consequences of these changes on the optimization problem of the designer. Their sequential modeling of both nonstrategic and strategic logic allows a clear picture of the delicate interplay between dynamic trade-offs and strategic incentives. Topics include the sequential assignment of heterogeneous objects, dynamic revenue optimization with heterogeneous objects, revenue maximization in the stochastic and dynamic knapsack model, the interaction between learning about demand and dynamic efficiency, and dynamic models with long-lived, strategic agents.
eBook