This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use t...This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundreds and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.展开更多
This paper considers rearrangeable multihop lightwave networks whereby each network node is equipped with a number p of transmitters and receivers, and a spectrum of wavelengths is accessible by, and shared among, all...This paper considers rearrangeable multihop lightwave networks whereby each network node is equipped with a number p of transmitters and receivers, and a spectrum of wavelengths is accessible by, and shared among, all nodes by using the Wavelength Division Multiplexing (WDM). Depending on input traffic flow, nodal transmitters and receivers can be re-tuned to create virtual connectivity best suited with respect to a given optimization criterion. We present an efficient heuristic algorithm that combines two criteria for optimization: throughput maximization, as well as total flow minimization. Throughput maximization criterion is equivalent to congestion minimization, while minimizing total flow under the assumption of having links with equal lengths implies minimization of the average number of hops. Taking into account lengths of the links (i.e. link costs proportional with distances), the total flow minimization becomes equivalent to the total delay minimization. Tabu search is implemented as a two-phase strategy dealing with diversification as well as intensification of search. Computational experiments include consecutive runs with different sets of weights associated with the two criteria. Results for a benchmark set of problems are presented.展开更多
基金Acknowledgments. This work was supported by the National Natural Science Founda- tion of China （11071117, 11274109） and the Natural Science Foundation of Jiangsu Province （BK20141409）.
文摘This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundreds and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.
基金This work was supported partly by the National Science Foundation Grant ANI 9814014 the project 036033-Architectural Elements for Regional Information Infrastructure, funded jointly by the Ministry of Science, Education and Sports of the Republic of Cr
文摘This paper considers rearrangeable multihop lightwave networks whereby each network node is equipped with a number p of transmitters and receivers, and a spectrum of wavelengths is accessible by, and shared among, all nodes by using the Wavelength Division Multiplexing (WDM). Depending on input traffic flow, nodal transmitters and receivers can be re-tuned to create virtual connectivity best suited with respect to a given optimization criterion. We present an efficient heuristic algorithm that combines two criteria for optimization: throughput maximization, as well as total flow minimization. Throughput maximization criterion is equivalent to congestion minimization, while minimizing total flow under the assumption of having links with equal lengths implies minimization of the average number of hops. Taking into account lengths of the links (i.e. link costs proportional with distances), the total flow minimization becomes equivalent to the total delay minimization. Tabu search is implemented as a two-phase strategy dealing with diversification as well as intensification of search. Computational experiments include consecutive runs with different sets of weights associated with the two criteria. Results for a benchmark set of problems are presented.
