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Solving the Network Design Problem by Surrogate Functions and Lower and Upper Bounds on the Objective Function at Different Levels of Budget

Mozafari, Hamid | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51399 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Poorzahedy, Hossein
  7. Abstract:
  8. The purpose of this research is to provide a method for finding a “good” solution to the network design problem with less computational efforts, faster than the existing conventional methods of solving this problem. Network design problem is the problem of selecting a subset of projects from a set of alternative projects so that to optimize the objective function (e.g., the total travel time in the network) subject to the set of existing constraints (e.g., budget). Due to the combinatorial and non-convex nature of the problem, its solution could be very cumbersome and time-consuming. Various methods have been proposed to solve this problem efficiently, providing good solutions at high speeds. Inspired by the specific nature of the design problem, this research attempts to reach a good solution indirectly. This is done by exploring reasons about the presence/absence of specific projects to be/not to be in solution set for a budget level, as well as the use of a function that targets good solutions at that budget level. The traffic assignment problem, which is the sub-problem of network design problem, and the solution of which comprises the main portion of the total cpu-time of the solution, are solved for selected subsets of the projects in order to arrive at good solutions. This selection method is one of the contributions of this study. The experiments in this study (on Sioux Falls and some random networks) show that the proposed selection methods, along with the application of a proposed surrogate function, reduce the number of solutions of the traffic assignment sub-problem significantly. In fact, in an example case with 11 proposed projects, the number of traffic assignment problems solved was 233 for a complete spectrum of the budget levels, which is very low compared to the reported performance in the literature. One favorable feature of the proposed solution method is that it provides the solutions of the problem for all levels of the budget at the same time. Based on the experiments conducted in this study on several networks, the proposed method closely competes, and in many cases outperforms, one of the available efficient meta-heuristic methods in the literature
  9. Keywords:
  10. Budget Constraint ; Network Design ; Random Networks ; Projects Combination ; Surrogate Function ; Computation Speed and Accuracy

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