Searching characteristics of chaotic neurodynamics for combinatorial optimization

Abstract

An effective algorithm for solving combinatorial optimization problems by using chaotic neurodynamics has already been proposed. Although numerical simulations show that the algorithm is highly efficient, the reason behind its effectiveness has not yet been clarified. In this study, we investigated the searching characteristics of this algorithm for solving combinatorial optimization problems by employing the method of surrogate data, which is frequently used in the field of nonlinear time series analysis. We evaluated how solving abilities depend on bifurcation parameters related to the refractory effects in the chaotic neural networks. Then, we found that the considerable searching ability is decided by refractory effects after neuron firing.

Solving the Steiner tree problem in graphs by chaotic search

“…On the other hand, as one of the effective metaheuristics, an algorithm using chaotic dynamics, or the chaotic search, has already been proposed to escape from undesirable local minima. The chaotic search shows good performance for solving various N P-hard combinatorial optimization problems, such as the traveling salesman problems [13][14][15][16], the quadratic assignment problems [17][18][19], the vehicle routing problems [20,21], the packet routing problems [22][23][24][25][26][27][28][29], and the motif extraction problems [30,31]. However, the Steiner tree problem in graphs has a different feature from the abovementioned combinatorial optimization problems; local searches we introduced in this paper produce not only feasible solutions but also infeasible solutions during the search.…”