Applications to Other Fields

Spin Glasses ◽

Heuristic Algorithms ◽

Optimization Problems ◽

Conformational Dynamics ◽

Prebiotic Evolution ◽

Combinatorial Optimization Problems ◽

Protein Conformational Dynamics ◽

Classic Papers

This chapter explores how spin glass concepts have found use in and, in some cases, further advanced areas such as computational complexity, combinatorial optimization, neural networks, protein conformational dynamics and folding, and computer science (through the introduction of new heuristic algorithms such as simulated annealing and neural-based computation, and through new approaches to analyzing hard combinatorial optimization problems). It also introduces some “short takes” on topics that space constraints prevent covering in detail, but should be at least mentioned: prebiotic evolution, Kauffman's NK model, and the maturation of the immune response. The chapter summarizes the heart of what most people mean when they refer to spin glasses as relevant to complexity. It focuses on the early, classic papers in each subject, giving the reader a flavor of each.

Neural Networks with the Linked State Transition for Constraint Satisfaction and Their Applications to Combinatorial Optimization Problems

Transactions of the Society of Instrument and Control Engineers ◽

10.9746/sicetr1965.31.622 ◽

1995 ◽

Vol 31 (5) ◽

pp. 622-630

Author(s):

Takuya WAKUTSU ◽

Eitaro AIYOSHI

Keyword(s):

Neural Networks ◽

Constraint Satisfaction ◽

State Transition ◽

Optimization Problems ◽

MREM, Discrete Recurrent Network for Optimization

Encyclopedia of Artificial Intelligence ◽

10.4018/978-1-59904-849-9.ch163 ◽

2011 ◽

pp. 1112-1120

Author(s):

Enrique Mérida-Casermeiro ◽

Domingo López-Rodríguez ◽

Juan M. Ortiz-de-Lazcano-Lobato

Keyword(s):

Neural Networks ◽

Image Recognition ◽

Single Neuron ◽

Optimization Problems ◽

Neural Model ◽

Recurrent Network ◽

Neural Models ◽

Seminal Work ◽

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.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

International Journal of Strategic Decision Sciences ◽

10.4018/jsds.2010040104 ◽

2010 ◽

Vol 1 (2) ◽

pp. 82-92 ◽

Cited By ~ 2

Author(s):

Gilbert Laporte

Keyword(s):

Vehicle Routing ◽

Traveling Salesman Problem ◽

Vehicle Routing Problem ◽

Heuristic Algorithms ◽

Optimization Problems ◽

Traveling Salesman ◽

Routing Problem ◽

Combinatorial Optimization Problems ◽

The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196) ◽

Hardware combinatorial optimization problems solver by hysteresis neural networks

10.1109/iscas.2001.921373 ◽

2002 ◽

Author(s):

T. Nakaguchi ◽

K. Jin'no ◽

M. Tanaka

Keyword(s):

Neural Networks ◽

Optimization Problems ◽

A brief introduction to exact, approximation, and heuristic algorithms for solving hard combinatorial optimization problems

2014 16th International Conference on Transparent Optical Networks (ICTON) ◽

10.1109/icton.2014.6876285 ◽

2014 ◽

Cited By ~ 5

Author(s):

P. Festa

Keyword(s):

Heuristic Algorithms ◽

Optimization Problems ◽

Artificial Higher Order Neural Networks for Modeling Combinatorial Optimization Problems

Artificial Higher Order Neural Networks for Modeling and Simulation ◽

10.4018/978-1-4666-2175-6.ch003 ◽

2013 ◽

pp. 44-57

Author(s):

Yuxin Ding

Keyword(s):

Neural Networks ◽

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.