Neural Networks Approaches for Combinatorial Optimization Problems

1999 ◽  
pp. 259-293
Author(s):  
Theodore B. Trafalis ◽  
Suat Kasap
Keyword(s):  
Neural Networks ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Combinatorial Optimization Problems

MREM, Discrete Recurrent Network for Optimization

2011 ◽  
pp. 1112-1120
Author(s):  
Enrique Mérida-Casermeiro ◽  
Domingo López-Rodríguez ◽  
Juan M. Ortiz-de-Lazcano-Lobato
Keyword(s):  
Neural Networks ◽  
Combinatorial Optimization ◽  
Image Recognition ◽  
Single Neuron ◽  
Optimization Problems ◽  
Neural Model ◽  
Recurrent Network ◽  
Neural Models ◽  
Seminal Work ◽  
Combinatorial Optimization Problems

Since McCulloch and Pitts’ seminal work (McCulloch & Pitts, 1943), several models of discrete neural networks have been proposed, many of them presenting the ability of assigning a discrete value (other than unipolar or bipolar) to the output of a single neuron. These models have focused on a wide variety of applications. One of the most important models was developed by J. Hopfield in (Hopfield, 1982), which has been successfully applied in fields such as pattern and image recognition and reconstruction (Sun et al., 1995), design of analogdigital circuits (Tank & Hopfield, 1986), and, above all, in combinatorial optimization (Hopfield & Tank, 1985) (Takefuji, 1992) (Takefuji & Wang, 1996), among others. The purpose of this work is to review some applications of multivalued neural models to combinatorial optimization problems, focusing specifically on the neural model MREM, since it includes many of the multivalued models in the specialized literature.

Artificial Higher Order Neural Networks for Modeling Combinatorial Optimization Problems

2013 ◽  
pp. 44-57
Author(s):  
Yuxin Ding
Keyword(s):  
Neural Networks ◽  
Combinatorial Optimization ◽  
Convergence Rates ◽  
Optimization Problems ◽  
High Order ◽  
Hopfield Network ◽  
Hopfield Networks ◽  
Combinatorial Optimization Problems ◽  
Complete Problems ◽  
Higher Order Neural Networks

Traditional Hopfield networking has been widely used to solve combinatorial optimization problems. However, high order Hopfiled networks, as an expansion of traditional Hopfield networks, are seldom used to solve combinatorial optimization problems. In theory, compared with low order networks, high order networks have better properties, such as stronger approximations and faster convergence rates. In this chapter, the authors focus on how to use high order networks to model combinatorial optimization problems. Firstly, the high order discrete Hopfield Network is introduced, then the authors discuss how to find the high order inputs of a neuron. Finally, the construction method of energy function and the neural computing algorithm are presented. In this chapter, the N queens problem and the crossbar switch problem, which are NP-complete problems, are used as examples to illustrate how to model practical problems using high order neural networks. The authors also discuss the performance of high order networks for modeling the two combinatorial optimization problems.

scholarly journals Deep Neural Network Approximated Dynamic Programming for Combinatorial Optimization

2020 ◽  
Vol 34 (02) ◽  
pp. 1684-1691
Author(s):  
Shenghe Xu ◽  
Shivendra S. Panwar ◽  
Murali Kodialam ◽  
T.V. Lakshman
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Dynamic Programming ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Computation Time ◽  
Training Procedure ◽  
Problem Size ◽  
Combinatorial Optimization Problems ◽  
Time Reduction

In this paper, we propose a general framework for combining deep neural networks (DNNs) with dynamic programming to solve combinatorial optimization problems. For problems that can be broken into smaller subproblems and solved by dynamic programming, we train a set of neural networks to replace value or policy functions at each decision step. Two variants of the neural network approximated dynamic programming (NDP) methods are proposed; in the value-based NDP method, the networks learn to estimate the value of each choice at the corresponding step, while in the policy-based NDP method the DNNs only estimate the best decision at each step. The training procedure of the NDP starts from the smallest problem size and a new DNN for the next size is trained to cooperate with previous DNNs. After all the DNNs are trained, the networks are fine-tuned together to further improve overall performance. We test NDP on the linear sum assignment problem, the traveling salesman problem and the talent scheduling problem. Experimental results show that NDP can achieve considerable computation time reduction on hard problems with reasonable performance loss. In general, NDP can be applied to reducible combinatorial optimization problems for the purpose of computation time reduction.

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