A more efficient deterministic annealing neural network algorithm for the max-bisection problem

•Transform the max-bisection problem to a linearly constrained optimization problem.•Propose a deterministic annealing neural network algorithm by introducing a barrier function in square-root form.•Prove the existence of the integral minimum solution of the max-bisection problem in theory and the p...

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) Vol. 458; pp. 428 - 439
Main Authors: Jiang, Shicong, Dang, Chuangyin
Format: Journal Article
Language:English
Published: Elsevier B.V 11.10.2021
Subjects:
Descent direction
Deterministic annealing
Max-bisection problem
Neural network
Square-root barrier function
Max-bisection problem
Neural network
Deterministic annealing
Square-root barrier function
Descent direction
ISSN:0925-2312, 1872-8286
Online Access:Get full text
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Summary:•Transform the max-bisection problem to a linearly constrained optimization problem.•Propose a deterministic annealing neural network algorithm by introducing a barrier function in square-root form.•Prove the existence of the integral minimum solution of the max-bisection problem in theory and the proof is simpler than other algorithms.•Experimental results show that the proposed method outperforms other methods. The max-bisection problem has extensive applications in network engineering, making it imperative to develop effective methods to solve this problem. However, the efficient computation on this problem remains challenging due to its NP-hard computational complexity. To address this question, in this paper, we transform the max-bisection problem to an artificial linearly constrained optimization problem and develop a modified deterministic annealing neural network algorithm by introducing a barrier function. The barrier parameter of this function acts as the temperature in the annealing process and decreases from a large positive number to zero. The initial value of the barrier parameter promises that the artificial problem is convex and can be easily solved at the beginning of the descending process. The solution to the original max-bisection problem is finally obtained through a descent algorithm, in which the bound limit of the solution is always satisfied as long as the iteration step length is less than one. We have proved the theoretical convergence of the proposed algorithm. Numerical results demonstrate that the proposed algorithm has several advantages over both the approximation algorithms and metaheuristic methods.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2021.06.050