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A deterministic annealing algorithm for approximating a solution of the max-bisection problem.

Chuangyin Dang1, Liping He, Ip Kee Hui

  • 1Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, People's Republic of China. mecdang@cityu.edu.hk

Neural Networks : the Official Journal of the International Neural Network Society
|July 20, 2002
PubMed
Summary

A new deterministic annealing algorithm approximates solutions for the NP-hard max-bisection problem. This method is faster than existing algorithms, offering comparable solution quality for this complex optimization challenge.

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Area of Science:

  • Combinatorial Optimization
  • Computational Complexity
  • Algorithm Design

Background:

  • The max-bisection problem is a known NP-hard problem in combinatorial optimization.
  • Existing approximation algorithms for max-bisection can be computationally intensive.

Purpose of the Study:

  • To formulate an equivalent linearly constrained continuous optimization problem for max-bisection.
  • To propose a novel deterministic annealing algorithm for approximating max-bisection solutions.

Main Methods:

  • Formulation of an equivalent continuous optimization problem.
  • Development of a deterministic annealing algorithm using a square-root barrier function.
  • Analysis of algorithm convergence properties and feasible descent directions.

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Main Results:

  • The proposed algorithm demonstrates convergence to an integral local minimum.
  • Numerical results indicate the algorithm is significantly faster than existing state-of-the-art methods.
  • The algorithm maintains solution quality comparable to established approaches.

Conclusions:

  • The deterministic annealing algorithm provides an efficient and effective method for approximating solutions to the max-bisection problem.
  • The barrier parameter's role as temperature in the annealing process is crucial for convergence.
  • This approach offers a promising alternative for tackling NP-hard optimization problems.