Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Polyhedral combinatorics and neural networks
Neural Computation
The metropolis algorithm for graph bisection
Discrete Applied Mathematics
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Future Generation Computer Systems - Special issue: Bio-inspired solutions to parallel processing problems
Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
Genetic Algorithm and Graph Partitioning
IEEE Transactions on Computers
A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning
Journal of Global Optimization
Neural Networks - 2005 Special issue: IJCNN 2005
Bisecting a 4-connected graph with three resource sets
Discrete Applied Mathematics
A novel optimizing network architecture with applications
Neural Computation
A theoretical investigation into the performance of the Hopfield model
IEEE Transactions on Neural Networks
The mix-matrix method in the problem of binary quadratic optimization
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part I
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The min-bisection problem is an NP-hard combinatorial optimization problem. In this paper an equivalent linearly constrained continuous optimization problem is formulated and an algorithm is proposed for approximating its solution. The algorithm is derived from the introduction of a logarithmic-cosine barrier function, where the barrier parameter behaves as temperature in an annealing procedure and decreases from a sufficiently large positive number to zero. The algorithm searches for a better solution in a feasible descent direction, which has a desired property that lower and upper bounds are always satisfied automatically if the step length is a number between zero and one. We prove that the algorithm converges to at least a local minimum point of the problem if a local minimum point of the barrier problem is generated for a sequence of descending values of the barrier parameter with a limit of zero. Numerical results show that the algorithm is much more efficient than two of the best existing heuristic methods for the min-bisection problem, Kernighan-Lin method with multiple starting points (MSKL) and multilevel graph partitioning scheme (MLGP).