Solving the Assignment Problem Using Continuous-Time and Discrete-Time Improved Dual Networks

The assignment problem is an archetypal combinatorial optimization problem. In this brief, we present a continuous-time version and a discrete-time version of the improved dual neural network (IDNN) for solving the assignment problem. Compared with most assignment networks in the literature, the two versions of IDNNs are advantageous in circuit implementation due to their simple structures. Both of them are theoretically guaranteed to be globally convergent to a solution of the assignment problem if only the solution is unique.

[1]  Donald E. Knuth,et al.  The art of computer programming: sorting and searching (volume 3) , 1973 .

[2]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[3]  Timothy X. Brown,et al.  Competitive neural architecture for hardware solution to the assignment problem , 1991, Neural Networks.

[4]  Jun Wang.  Analogue neural network for solving the assignment problem , 1992 .

[5]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[6]  Alan L. Yuille,et al.  The invisible hand algorithm: Solving the assignment problem with statistical physics , 1994, Neural Networks.

[7]  Jun Wang,et al.  Primal and dual assignment networks , 1997, IEEE Trans. Neural Networks.

[8]  J Wang,et al.  Analysis and design of primal-dual assignment networks , 1998, IEEE Trans. Neural Networks.

[9]  Jun Wang,et al.  Digital hardware realization of a recurrent neural network for solving the assignment problem , 2003, Neurocomputing.

[10]  Xiaolin Hu,et al.  An Improved Dual Neural Network for Solving a Class of Quadratic Programming Problems and Its $k$-Winners-Take-All Application , 2008, IEEE Transactions on Neural Networks.

[11]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[12]  W. Haddad,et al.  Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach , 2008 .

[13]  Xiaolin Hu,et al.  An Alternative Recurrent Neural Network for Solving Variational Inequalities and Related Optimization Problems , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Jinde Cao,et al.  A Discrete-Time Recurrent Neural Network with One Neuron for k-Winners-Take-All Operation , 2009, ISNN.

[15]  Long Cheng,et al.  A Delayed Projection Neural Network for Solving Linear Variational Inequalities , 2009, IEEE Transactions on Neural Networks.

[16]  Ting Wang,et al.  Delay-Derivative-Dependent Stability for Delayed Neural Networks With Unbound Distributed Delay , 2010, IEEE Transactions on Neural Networks.

[17]  Jinde Cao,et al.  A Novel Recurrent Neural Network With One Neuron and Finite-Time Convergence for $k$-Winners-Take-All Operation , 2010, IEEE Transactions on Neural Networks.

[18]  Zhigang Zeng,et al.  Multistability of Recurrent Neural Networks With Time-varying Delays and the Piecewise Linear Activation Function , 2010, IEEE Transactions on Neural Networks.

[19]  Jun Wang,et al.  Analysis and Design of a $k$ -Winners-Take-All Model With a Single State Variable and the Heaviside Step Activation Function , 2010, IEEE Transactions on Neural Networks.

[20]  Z. Zeng,et al.  NEW PASSIVITY ANALYSIS OF CONTINUOUS-TIME RECURRENT NEURAL NETWORKS WITH MULTIPLE DISCRETE DELAYS , 2011 .

[21]  Xiaolin Hu,et al.  Solving the Assignment Problem with the Improved Dual Neural Network , 2011, ISNN.

[22]  Qingshan Liu,et al.  A One-Layer Dual Recurrent Neural Network with a Heaviside Step Activation Function for Linear Programming with Its Linear Assignment Application , 2011, ICANN.

[23]  Jun Wang,et al.  Robustness Analysis of Global Exponential Stability of Recurrent Neural Networks in the Presence of Time Delays and Random Disturbances , 2012, IEEE Transactions on Neural Networks and Learning Systems.