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Maximum Weighted Mixed-Graph Orientation with Transportation Cost

Azadnia, Alireza | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54261 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Eshghi, Koroush
  7. Abstract:
  8. The following research considers the problem of maximum graph orientation aiming to maximize the total weight of satisfied origin-destination pairs for which the capacity of each edge is limited taking into account the distance and cost. the origin of this problem can be traced to biology literature and protein-protein interaction networks. since the problem is a combinatorial optimization one, in addition to deploying exact methods using mathematical programming, heuristic methods are also investigated. addressing the problem, we propose a two-step procedure. in the first stage are detected the paths between origin-destination pairs and in the second one, the solution to the problem is generated using either mathematical programming or heuristic methods including greedy algorithm and minimum regret. a mathematical model is used in the first step to find the paths between origin-destination pairs. a set of random data is used to evaluate the efficiency of the proposed algorithms and a considerable improvement in the speed of the execution was observed as imposing a restriction on the total number of paths between each origin-destination pair which as expected before, resulted in either a reduction or no change in the objective function value. on the other hand, in the second stage, although mathematical programming generates a better solution in comparison to heuristic methods, it also brings about an increase in solving the problem
  9. Keywords:
  10. Mathematical Programming ; Combinatorial Optimization ; Heuristic Algorithm ; Graph Theory ; Mixed Graph

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