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Published byKristina Wilkerson Modified over 9 years ago
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Solution methodologies for the classical Grant van Dieman Friday 30 th November 2007 Supervisor: Prof. JH van Vuuren Co-supervisor: Mr JN Roux assignment problem
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Slide 2 Overview The classical assignment problem Exact Solution methods A maximum matching algorithm Successive shortest path method Hungarian method Greedy heuristics Comparison Future work
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Slide 3 The classical assignment problem Votaw and Orden (1952) Assumptions x ij is 1 if assignee i is assigned to task j and 0 otherwise The assignment problem is NP complete (Lloyd and Witzenhausen (1986))
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Slide 4 The Weapon Target Assignment Problem Flood (1957) V j : priority of eliminating target j. q ij : is the survival probability of target j if it is engaged by weapon i. x ij =1 if weapon i engage target j and 0 otherwise
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Slide 5 Overview The classical assignment problem Exact Solution methods A maximum matching algorithm Successive shortest path method Hungarian method Greedy heuristics Comparison Future work
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Slide 6 A maximum matching algorithm for weighted bipartite graphs (MWM) q ij V 1 = {assignees} V 2 = {tasks} G :
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Slide 7 A maximum matching algorithm for weighted bipartite graphs (MWM) V 1 = {assignees} V 2 = {tasks} q ij M :
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Slide 8 Overview The classical assignment problem Exact Solution methods A maximum matching algorithm Successive shortest path method Hungarian method Greedy heuristics Comparison Future work
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Slide 9 Successive shortest path algorithm (SSP) Minimum cost flow algorithm Why this algorithm can be used to solve the assignment problem The value of x ij will be binary
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Slide 10 Overview The classical assignment problem Exact Solution methods Successive shortest path method A maximum matching algorithm Hungarian method Greedy heuristics Comparison Future work
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Slide 11 Hungarian Method Kuhn(1955) Special algorithm for the assignment problem Construct reduced cost matrix
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Slide 12 Overview The classical assignment problem Exact Solution methods Successive shortest path method A maximum matching algorithm Hungarian method Greedy heuristics Comparison Future work
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Slide 13 Greedy Heuristics Greedy RTB Greedy RBT Greedy RR Greedy CLR Greedy CRL Greedy CR
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Slide 14 Overview The classical assignment problem Exact Solution methods Successive shortest path method A maximum matching algorithm Hungarian method Greedy heuristics Comparison Future work
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Slide 15 Comparisons Benchmark set 1: JE Beasly (Randomly Generated) 3.4 Ghz, 1024 MB ram, Windows XP
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Slide 16 Comparisons
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Slide 17 Comparisons
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Slide 18 Comparisons Benchmarks set 2: Randomly Generated in Matlab
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Slide 19 Comparisons
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Slide 20 Comparisons
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Slide 21 Future work Advanced Heuristics and Meta-heuristics More exact solution methods Expand algorithms to solve variations of the assignment problem
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Slide 22 References [1] [2] [3] [4] [5]
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