Humans interact with and are part of the mysterious processes of nature. Inevitably they have to discover how to manage the environment for their long-term survival and benefit. To do this successfully means learning something about the dynamics of natural processes, and then using the knowledge to work with the forces of nature for some desired outcome. These are intriguing and challenging tasks. This book describes a technique which has much to offer in attempting to achieve the latter task. A knowledge of dynamic programming is useful for anyone interested in the optimal management of agricultural and natural resources for two reasons. First, resource management problems are often problems of dynamic optimization. The dynamic programming approach offers insights into the economics of dynamic optimization which can be explained much more simply than can other approaches. Conditions for the optimal management of a resource can be derived using the logic of dynamic programming, taking as a starting point the usual economic definition of the value of a resource which is optimally managed through time. This is set out in Chapter I for a general resource problem with the minimum of mathematics. The results are related to the discrete maximum principle of control theory. In subsequent chapters dynamic programming arguments are used to derive optimality conditions for particular resources.

An extensively revised edition of a mathematically rigorous yet accessible introduction to algorithms.

Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed.The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.