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Unformatted text preview: 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 knode minimum spanning tree ( kMST) 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 branchandbound and a branchandcut algorithm for this problem 2 Programming Exercise CPLEX Tutorial Framework/Instances Your Task (1) Carefully read this tutorial Formulate the kMST 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 branchandbound algorithm for the SCF formulation 2 a branchandcut algorithm based on CE/DC using a dynamic cutseparation 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 testinstances (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 = d 1 5  V e and k = d 1 2  V e with both algorithms 4 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 cutgeneration 4 Result table, including 1 objective function value 2 running time 3 number of branchandbound 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 instituteservers (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 instituteserver 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)...
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 Spring '97
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