Equilibrium in Multi-criteria Transportation Networks

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• 作者：Dinh The Luc ; Truong Thi Thanh Phuong
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：169
• 期：1
• 页码：116-147
• 全文大小：902 KB
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：169

文摘

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.KeywordsMulti-criteria transportation networkGeneric differentiabilityVector equilibriumVariational inequalitiesFrank–Wolfe reduced gradient method