Lower-Bound Solution Algorithm for Equilibrium Signal-Setting Problem

2008 ◽  
Vol 2085 (1) ◽  
pp. 104-110 ◽  
Author(s):  
Kaveh F. Sadabadi ◽  
Hedayat Zokaei-Aashtiani ◽  
Ali Haghani
Keyword(s):  
Lower Bound ◽  
Descent Method ◽  
Solution Algorithm ◽  
Network Design Problem ◽  
Steepest Descent Method ◽  
Optimal Flow ◽  
Solution Algorithms ◽  
Global Optima ◽  
Equilibrium Network Design ◽  
Lower Bound Solution

The equilibrium signal-setting problem is stated and subsequently formulated as a continuous equilibrium network design problem. The bilevel formulation is nonconvex and therefore cannot be solved for global optima by using descent solution algorithms. Therefore, a lower bound using a system optimal flow pattern is proposed that will be quite tight in both uncongested and highly congested network traffic situations. A solution algorithm based on the standard steepest-descent method is proposed for the lower-bound problem. Performance of the solution algorithm on a network problem is reported.

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

scholarly journals Improved Immune Algorithm Combined with Steepest Descent Method for Optimal Design of IPMSM for FCEV Traction Motor

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3904
Author(s):  
Ji-Chang Son ◽  
Myung-Ki Baek ◽  
Sang-Hun Park ◽  
Dong-Kuk Lim
Keyword(s):  
Optimal Design ◽  
Permanent Magnet Synchronous Motor ◽  
Torque Ripple ◽  
Descent Method ◽  
Immune Algorithm ◽  
Electric Machines ◽  
Steepest Descent Method ◽  
Superior Performance ◽  
Element Analysis ◽  
Traction Motor

In this paper, an improved immune algorithm (IIA) was proposed for the torque ripple reduction optimal design of an interior permanent magnet synchronous motor (IPMSM) for a fuel cell electric vehicle (FCEV) traction motor. When designing electric machines, both global and local solutions of optimal designs are required as design result should be compared in various aspects, including torque, torque ripple, and cogging torque. To lessen the computational burden of optimization using finite element analysis, the IIA proposes a method to efficiently adjust the generation of additional samples. The superior performance of the IIA was verified through the comparison of optimization results with conventional optimization methods in three mathematical test functions. The optimal design of an IPMSM using the IIA was conducted to verify the applicability in the design of practical electric machines.

Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time

1998 ◽  
Vol 1645 (1) ◽  
pp. 170-175 ◽  
Author(s):  
Ismail Chabini
Keyword(s):  
Large Scale ◽  
Shortest Paths ◽  
Transportation Systems ◽  
Solution Algorithm ◽  
Shortest Path Problems ◽  
Discrete Dynamic ◽  
Solution Algorithms ◽  
Dynamic Network Models ◽  
Early Results ◽  
Run Time

A solution is provided for what appears to be a 30-year-old problem dealing with the discovery of the most efficient algorithms possible to compute all-to-one shortest paths in discrete dynamic networks. This problem lies at the heart of efficient solution approaches to dynamic network models that arise in dynamic transportation systems, such as intelligent transportation systems (ITS) applications. The all-to-one dynamic shortest paths problem and the one-to-all fastest paths problems are studied. Early results are revisited and new properties are established. The complexity of these problems is established, and solution algorithms optimal for run time are developed. A new and simple solution algorithm is proposed for all-to-one, all departure time intervals, shortest paths problems. It is proved, theoretically, that the new solution algorithm has an optimal run time complexity that equals the complexity of the problem. Computer implementations and experimental evaluations of various solution algorithms support the theoretical findings and demonstrate the efficiency of the proposed solution algorithm. The findings should be of major benefit to research and development activities in the field of dynamic management, in particular real-time management, and to control of large-scale ITSs.

Controlling Chaos by Hybrid System Based on FREN and Sliding Mode Control

2005 ◽  
Vol 128 (2) ◽  
pp. 352-358 ◽  
Author(s):  
C. Treesatayapun ◽  
S. Uatrongjit
Keyword(s):  
Sliding Mode ◽  
Adaptive Controller ◽  
Descent Method ◽  
Fuzzy Rules ◽  
System Stability ◽  
Steepest Descent Method ◽  
Upper And Lower Bounds ◽  
Adaptation Algorithm ◽  
Control Effort ◽  
Fine Tune

This paper presents a direct adaptive controller for chaotic systems. The proposed adaptive controller is constructed using the network called fuzzy rules emulated network (FREN). FREN’s structure is based on human knowledge in the form of fuzzy rules. Parameter adaptation algorithm based on the steepest descent method is presented to fine tune the controller’s performance. To improve the system stability, the modified sliding mode algorithm is applied to estimate the upper and lower bounds of the control effort. The suitable control effort is generated by FREN and kept within these bounds. Some computer simulations of using the controller to control the Hénon map have been performed to demonstrate the performance of the proposed controller.

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