Global optimization method for network design problem with stochastic user equilibrium |
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| Institution: | 1. Osaka Institute of Public Health, 1-3-69 Nakamachi, Higashinari-ku, Osaka 537-0023, Japan;2. R&D Center, NH Foods Ltd., 3-3 Midorigahara, Tukuba, Ibaraki 300-2646, Japan;3. Department of Aquatic Bioscience, Graduate School of Agricultural and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan;4. Aquaculture Research Institute, Kindai University, Shirahama 3153, Nishimuro, Wakayama 649-2211, Japan;5. Laboratory of Parasitology, Joint Faculty of Veterinary Medicine, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8515, Japan;6. Fisheries Research Division, Oita Prefectural Agriculture, Forestry and Fisheries Research Center, 194-6, Kamiura Tsuiura, Saiki, Oita 879-2602, Japan;7. Oita Pharmaceutical Association, 441-1 Hikariya, Bunyo, Oita 870-0855, Japan;8. Research Center of Microorganism Control, Osaka Prefecture University, 1-2 Gakuencho, Naka-ku, Sakai, Osaka 599-8231, Japan;9. Kanagawa Prefectural Institute of Public Health, 1-3-1 Shimomachiya, Chigasaki, Kanagawa, 253-0087, Japan |
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| Abstract: | In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum. |
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| Keywords: | Network design problem Stochastic user equilibrium Mixed-integer linear programming Global optimization Range reduction technique |
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