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programming-exercise

# programming-exercise - Programming Exercise CPLEX Tutorial...

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Programming Exercise CPLEX Tutorial Framework/Instances Programming Exercise / ILOG CPLEX Tutorial Andreas M. Chwatal Algorithms and Data Structures Group Institute of Computer Graphics and Algorithms Vienna University of Technology VU Fortgeschrittene Algorithmen und Datenstrukturen Mai 2009 1 Programming Exercise CPLEX Tutorial Framework/Instances Recall the k -node minimum spanning tree ( k -MST) problem from the todays lecture: Given: (undirected) graph G = ( V , E , w ) nonnegative weighting function w ( e ) R Goal: Find a minimum weight tree, spanning exactly k nodes. Programming Exercise: develop a branch-and-bound and a branch-and-cut algorithm for this problem 2 Programming Exercise CPLEX Tutorial Framework/Instances Your Task (1) Carefully read this tutorial Formulate the k -MST problem as integer linear program (ILP), based on a 1 single commodity flow formulation (SCF) 2 cycle elimination formulation (CE), or, alternatively a formulation based on directed connection cuts (DC) Implement the corresponding algorithms, using ILOG CPLEX: 1 a branch-and-bound algorithm for the SCF formulation 2 a branch-and-cut algorithm based on CE/DC using a dynamic cut-separation procedure 3 Programming Exercise CPLEX Tutorial Framework/Instances Your Task (2) For the implementation you should use a C++ framework (which you can find on the webpage of the course) Furthermore you can find test-instances (to described later on), which should be used for the evaluation and analysis of the algorithms Compute the results for each instance for (at least) k = 1 5 | V | and k = 1 2 | V | with both algorithms 4

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Programming Exercise CPLEX Tutorial Framework/Instances Your Task (3) Create a short document (preferably in LaTeX) of no more than three pages containing: 1 Problem description, used variables 2 SCF and CE/DC formulation 3 Short description of implementation, in particular the cut-generation 4 Result table, including 1 objective function value 2 running time 3 number of branch-and-bound nodes 4 node in which optimum has been found 5 For B&C: number of separated cuts 5 Programming Exercise CPLEX Tutorial Framework/Instances Organization You can work on the exercise alone, or in groups of two You have to work on institute-servers (due to CPLEX licence): Servername: behemoth.ads.tuwien.ac.at If you do not have an account yet, you get one after the lecture, or write an email to me. Send the document per email to me/us one day prior to the (oral) exam Make sure, that a correctly working version of your program is available on an institute-server at the time of your exam 6 Programming Exercise CPLEX Tutorial Framework/Instances What is CPLEX? CPLEX: Simplex method and C programming language Commercial optimization software package High performance integer (linear) programming linear programming quadratic programming http://www.ilog.com/products/cplex/ 7 Programming Exercise CPLEX Tutorial Framework/Instances Concert Framework Interface to CPLEX solver (C, C++, C#, Java) Enables to implement: branch-and-bound, branch-and-cut, column generation, ...
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programming-exercise - Programming Exercise CPLEX Tutorial...

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