One of the major obstacles in using neural networks to solve combinatorial optimization problems is the convergence toward one of the many local minima instead of the global minima. In this letter, we propose a technique that enables a self-organizing neural network to escape from local minima by virtue of the intermittency phenomenon. It gives rise to novel search dynamics that allow the system to visit multiple global minima as meta-stable states. Numerical experiments performed suggest that the phenomenon is a combined effect of Kohonen-type competitive learning and the iterated softmax function operating near bifurcation. The resultant intermittent search exhibits fractal characteristics when the optimization performance is at its peak in the form of 1/f signals in the time evolution of the cost, as well as power law distributions in the meta-stable solution states. The N-Queens problem is used as an example to illustrate the meta-stable convergence process that sequentially generates, in a single run, 92 solutions to the 8-Queens problem and 4024 solutions to the 17-Queens problem.