By Art Lew

This booklet presents a realistic advent to computationally fixing discrete optimization difficulties utilizing dynamic programming. From the strangely a variety of and sundry examples awarded, readers may still extra simply be capable of formulate dynamic programming suggestions to their very own difficulties of curiosity.

We additionally offer and describe the layout, implementation, and use of a software program software, named DP2PN2Solver, that has been used to numerically resolve the entire difficulties offered prior within the publication. This computational device can be utilized via scholars to unravel educational difficulties if this publication is utilized in coursework, and by means of practitioners to resolve many real-world difficulties if the nation house isn't too huge.

Finally, this publication is usually a examine monograph that describes a unique software of Petri internet idea. DP2PN2Solver takes consumer enter within the type of the DP sensible equation for an issue, instantly constructs a Petri internet version, known as a Bellman web, as an inner desktop illustration for the DP challenge, after which generates from the Bellman internet the numerical answer for the DP challenge. This answer will be got utilizing Java, a spreadsheet, a Petri internet software, and different systems.

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Additional resources for Dynamic Programming: A Computational Tool

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4 Spreadsheet Solutions Above, we showed the basis for a DP program generator that automatically generates a sequence of assignment statements for solving a DPFE using a conventional programming language. We show in this section how a spreadsheet that solves a DPFE can be automatically generated. The assignment statements given Sect. 7 as its computed answer. One advantage of this spreadsheet solution is that “topological” sorting is unnecessary. In this spreadsheet program, only the lengths of the shortest paths are calculated.

To the preceding example, suppose we add a branch (y, x) with distance b(y, x) = 2 (see Fig. 2). The graph is then cyclic, and the equations obtained from the DPFE are as follows: f (s) = min{b(s, x) + f (x), b(s, y) + f (y), b(s, t) + f (t) = min{3 + f (x), 5 + f (y), ∞ + f (t)}, f (x) = min{b(x, y) + f (y), b(x, t) + f (t)} = min{1 + f (y), 8 + f (t)}, f (y) = min{b(y, x) + f (x), b(y, t) + f (t)} = min{2 + f (x), 5 + f (t)}, f (t) = 0. We note that f (x) depends on f (y), and f (y) depends on f (x).

That is the focus of this book. 3 Overview of Book In Chap. 2, we discuss numerous applications of DP. Specifically, we formulate a DPFE for each of these applications. For many applications, we provide alternate formulations as well. This compendium of examples shows the generality and flexibility of dynamic programming as an optimization method and of the DP2PN2Solver software tool described in this book for solving dynamic programming problems. In Chap. 3, we describe gDPS, a text-based specification language for dynamic programming problems.

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