An Algorithm for the Mixed Transportation Network Design Problem.
This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2016-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC5023175?pdf=render |
| _version_ | 1818899068619849728 |
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| author | Xinyu Liu Qun Chen |
| author_facet | Xinyu Liu Qun Chen |
| author_sort | Xinyu Liu |
| collection | DOAJ |
| description | This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. |
| first_indexed | 2024-12-19T19:42:05Z |
| format | Article |
| id | doaj.art-227f096945244a7da8b471cf2a11563b |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-19T19:42:05Z |
| publishDate | 2016-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-227f096945244a7da8b471cf2a11563b2022-12-21T20:08:14ZengPublic Library of Science (PLoS)PLoS ONE1932-62032016-01-01119e016261810.1371/journal.pone.0162618An Algorithm for the Mixed Transportation Network Design Problem.Xinyu LiuQun ChenThis paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.http://europepmc.org/articles/PMC5023175?pdf=render |
| spellingShingle | Xinyu Liu Qun Chen An Algorithm for the Mixed Transportation Network Design Problem. PLoS ONE |
| title | An Algorithm for the Mixed Transportation Network Design Problem. |
| title_full | An Algorithm for the Mixed Transportation Network Design Problem. |
| title_fullStr | An Algorithm for the Mixed Transportation Network Design Problem. |
| title_full_unstemmed | An Algorithm for the Mixed Transportation Network Design Problem. |
| title_short | An Algorithm for the Mixed Transportation Network Design Problem. |
| title_sort | algorithm for the mixed transportation network design problem |
| url | http://europepmc.org/articles/PMC5023175?pdf=render |
| work_keys_str_mv | AT xinyuliu analgorithmforthemixedtransportationnetworkdesignproblem AT qunchen analgorithmforthemixedtransportationnetworkdesignproblem AT xinyuliu algorithmforthemixedtransportationnetworkdesignproblem AT qunchen algorithmforthemixedtransportationnetworkdesignproblem |