Abstract
The maximum clique problem is an NP hard combinatorial optimization problem, which is widely used in industrial and management processes. In order to approach the solution of the maximum clique problem, a deterministic annealing algorithm is proposed. When the barrier parameter is reduced from a large positive number to zero, the algorithm can track the minimum path of the obstacle problem to obtain a high-quality solution, which is a continuous method. The global convergence iteration of the Lagrange multiplier can be performed to obtain the minimum point of the obstacle problem in the feasible descent direction for any given positive value of the barrier parameter and has a desired property that it automatically satisfies the upper and lower bounds of variables if the steplength is a number that is between 0 and 1. Numerical results are provided to illustrate the efficiency of the proposed algorithm.
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