By handling the travel cost function artfully,the authors formulate the transportation mixed network design problem(MNDP)as a mixed-integer,nonlinear bilevel programming problem,in which the lower-level problem,compar...By handling the travel cost function artfully,the authors formulate the transportation mixed network design problem(MNDP)as a mixed-integer,nonlinear bilevel programming problem,in which the lower-level problem,comparing with that of conventional bilevel DNDP models,is not a side constrained user equilibrium assignment problem,but a standard user equilibrium assignment problem.Then,the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method.By virtue of the optimal-value function,the lower-level assignment problem can be expressed as a nonlinear equality constraint.Therefore,the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem.By exploring the inherent nature of the MNDP,the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently.Thus,a continuously differentiable but still nonconvex optimization formulation of the MNDP is created,and then a locally convergent algorithm is proposed by applying penalty function method.The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment.Finally,a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.展开更多
基金supported by the National Basic Research Program of China under Grant No.2006CB705500the National Natural Science Foundation of China under Grant No.0631001+1 种基金the Program for Changjiang Scholars and Innovative Research Team in UniversityVolvo Research and Educational Foundations
文摘By handling the travel cost function artfully,the authors formulate the transportation mixed network design problem(MNDP)as a mixed-integer,nonlinear bilevel programming problem,in which the lower-level problem,comparing with that of conventional bilevel DNDP models,is not a side constrained user equilibrium assignment problem,but a standard user equilibrium assignment problem.Then,the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method.By virtue of the optimal-value function,the lower-level assignment problem can be expressed as a nonlinear equality constraint.Therefore,the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem.By exploring the inherent nature of the MNDP,the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently.Thus,a continuously differentiable but still nonconvex optimization formulation of the MNDP is created,and then a locally convergent algorithm is proposed by applying penalty function method.The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment.Finally,a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.
