Dynamic Programming

1. Front Matter

   Pages i-xviii

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2. Dynamic Programming

   1. Front Matter

      Pages 1-1

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   2. Introduction to Dynamic Programming

      Pages 3-43

   3. Applications of Dynamic Programming

      Pages 45-100

3. Modeling of DP Problems

   1. Front Matter

      Pages 101-101

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   2. The DP Specification Language gDPS

      Pages 103-123

   3. DP Problem Specifications in gDPS

      Pages 125-203

   4. Bellman Nets: A Class of Petri Nets

      Pages 205-220

   5. Bellman Net Representations of DP Problems

      Pages 221-244

4. Design and Implementation of DP Tool

   1. Front Matter

      Pages 245-245

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   2. DP2PN2Solver Tool

      Pages 247-257

   3. DP2PN Parser and Builder

      Pages 259-269

   4. The PN2Solver Modules

      Pages 271-289

5. Computational Results

   1. Front Matter

      Pages 292-292

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   2. Java Solver Results of DP Problems

      Pages 293-320

   3. Other Solver Results

      Pages 321-327

   4. Conclusions

      Pages 329-337

6. Back Matter

   Pages 339-379

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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.

• Bellman Nets
• Computer
• Computer-Aided Design (CAD)
• Dynamics Programming
• Java
• Petri Nets
• model
• modeling
• optimization
• programming

• Department of Information and Computer Sciences, University of Hawaii at Manoa, HI 96822, Honolulu, USA

  Lew Art

• Department of Computer Science Natural Sciences Collegium, Eckerd College, FL 33711, Saint Petersburg, USA

  Holger Mauch

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