Dynamic Programming

Dynamic programming has long been applied to numerous areas in mat- matics, science, engineering, business, medicine, information systems, b- mathematics, arti?cial intelligence, among others. Applications of dynamic programming have increased as recent advances have been made in areas such as neural networks, data mining, soft computing, and other areas of com- tational intelligence. The value of dynamic programming formulations and means to obtain their computational solutions has never been greater. This book describes the use of dynamic programming as a computational tool to solve discrete optimization problems. (1) We ?rst formulate large classes of discrete optimization problems in dynamic programming terms, speci?cally by deriving the dynamic progr- ming functional equations (DPFEs) that solve these problems. A text-based language, gDPS, for expressing these DPFEs is introduced. gDPS may be regarded as a high-level speci?cation language, not a conventional procedural computer programming language, but which can be used to obtain numerical solutions. (2)Wethende?neandexaminepropertiesofBellmannets,aclassofPetri nets that serves both as a formal theoretical model of dynamic programming problems, and as an internal computer data structure representation of the DPFEs that solve these problems. (3)Wealsodescribethedesign,implementation,anduseofasoftwaretool, calledDP2PN2Solver, for solving DPFEs. DP2PN2Solver may be regarded as a program generator, whose input is a DPFE, expressed in the input spec- cation language gDPS and internally represented as a Bellman net, and whose output is its numerical solution that is produced indirectly by the generation of solver code, which when executed yields the desired solution.

Reference guide for educational and professional users of the DP software tool Includes supplementary material: sn.pub/extras

Klappentext

This book provides a practical introduction to computationally solving discrete optimization problems using dynamic programming. From the unusually numerous and varied examples presented, readers should more easily be able to formulate dynamic programming solutions to their own problems of interest.

We also provide and describe the design, implementation, and use of a software tool, named DP2PN2Solver, that has been used to numerically solve all of the problems presented earlier in the book. This computational tool can be used by students to solve academic problems if this book is used in coursework, and by practitioners to solve many real-world problems if the state space is not too large.

Finally, this book is also a research monograph that describes a novel application of Petri net theory. DP2PN2Solver takes user input in the form of the DP functional equation for a problem, automatically constructs a Petri net model, called a Bellman net, as an internal computer representation for the DP problem, and then generates from the Bellman net the numerical solution for the DP problem. This solution can be obtained using Java, a spreadsheet, a Petri net tool, and other systems.

Inhalt
Dynamic Programming.- to Dynamic Programming.- Applications of Dynamic Programming.- Modeling of DP Problems.- The DP Specification Language gDPS.- DP Problem Specifications in gDPS.- Bellman Nets: A Class of Petri Nets.- Bellman Net Representations of DP Problems.- Design and Implementation of DP Tool.- DP2PN2Solver Tool.- DP2PN Parser and Builder.- The PN2Solver Modules.- Computational Results.- Java Solver Results of DP Problems.- Other Solver Results.- Conclusions.