A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as mea...A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.展开更多
In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with ...In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such展开更多
A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior b...A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.展开更多
基金Project(71001079)supported by the National Natural Science Foundation of China
文摘A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.
文摘In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such
基金The Project is supported by the National Natural Science Foundation of China.
文摘A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.
