Equilibrium in Multi-criteria Transportation Networks
We develop a new method to generate the set of equilibrium flows of a multi-criteria transportation network. To this end, we introduce two optimization problems by using a vector version of the Heaviside step function and the distance function to Pareto minimal elements and show that the optimal sol...
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| Veröffentlicht in: | Journal of optimization theory and applications 2016-04, Vol.169 (1), p.116-147 |
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| container_title | Journal of optimization theory and applications |
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| creator | Luc, Dinh The Phuong, Truong Thi Thanh |
| description | We develop a new method to generate the set of equilibrium flows of a multi-criteria transportation network. To this end, we introduce two optimization problems by using a vector version of the Heaviside step function and the distance function to Pareto minimal elements and show that the optimal solutions of these problems are exactly the equilibria of the network. We study the objective functions by establishing their generic differentiability and local calmness at equilibrium solutions. Then we present an algorithm to generate a discrete representation of equilibrium solutions by using a modified Frank–Wolfe reduced gradient method and prove its convergence. We give some numerical examples to illustrate our algorithm and show its advantage over a popular method by using linear scalarization. |
| doi_str_mv | 10.1007/s10957-016-0876-3 |
| format | Article |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algorithms Applications of Mathematics Calculus of Variations and Optimal Control Optimization Convergence Engineering Equilibrium Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Methods Numerical analysis Operations Research/Decision Theory Optimization Representations Studies Theory of Computation Transportation networks Transportation planning Vectors (mathematics) |
| title | Equilibrium in Multi-criteria Transportation Networks |
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