Approximating a solution of the s– t max-cut problem with a deterministic annealing algorithm

Abstract

The s– t max-cut 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 an application of a logarithmic barrier function, where the barrier parameter behaves as temperature in an annealing procedure and decreases to zero from a sufficiently large positive number satisfying that the barrier function is convex. 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 if a local minimum point of the barrier problem is generated for a sequence of descending values of the barrier parameter with zero limit. Numerical results show that the algorithm seems effective and efficient.