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Application of Projection Algorithms for Solving Linear Complementarity Problems in Traffic Assignment

Yazdizadeh, Ali | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43062 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Zakaei Aashtiani, Hedayat
  7. Abstract:
  8. In recent decades, widespread application of Linear Complementarity Problems in various branches of science has led to many algorithms which have been proposed to solve these problems in the area of mathematics, economics and computer simulation. Ashtiani used Lemke algorithm for the first time to solve Linear Complementarity Problems in his algorithm for solving Traffic Assignment problem. In this study, Projection Gauss-Seidel algorithm along with two other similar algorithms have been studied for solving Linear Complementarity Problems in Ashtiani Complementarity algorithm and the results are compared with Lemke algorithm. Also an analytical method has been proposed for solving specific batch of Linear Complementarity Problems.
    The results show the inability of Projection Gauss-Seidel algorithm (and two other similar algorithms) to obtain answers of Linear Complementarity Problems in Ashtiani algorithm, but the proposed analytical method can solve Linear Complementarity Problems much faster than Lemke algorithm. In this study also some changes have been done in Ashtiani Complementarity algorithm that ultimately led to improve the time required for solving traffic assignment problem by this algorithm
  9. Keywords:
  10. Traffic Assignment ; Linear Complementarity ; Lemke Algorithm ; Projection Gauss-Seidel Algorithm

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