Dual-mode dynamics neural network for combinatorial optimization

Abstract

This paper presents a new approach to solving combinatorial optimization problems based on a novel dynamic neural network featuring a dual-mode of network dynamics, the state dynamics and the weight dynamics. The network is referred to here as the dual-mode dynamics neural network (D2NN). Recently, neural network approaches have been studied for solutions to combinatorial optimization problems. There are two major difficulties in the neural network approaches. First, the objective function for a given problem must have the form that can be mapped onto the network, and secondly, due to the local minima problem, the quality of the solution is quite sensitive to various factors, such as the initial state and the parameters in the objective function. The proposed scheme overcomes these difficulties (1) by maintaining the objective function separately from the network energy function, rather than mapping it onto the network, and (2) by introducing a weight dynamics utilizing the objective function to overcome the local minima problem. The state dynamics defines state trajectories in a direction to minimize the network energy specified by the current weights and states, whereas the weight dynamics generates weight trajectories in a direction to minimize a preassigned external objective function at a current state. D2NN is operated in such a way that the two modes of network dynamics alternately govern the network until an equilibrium is reached. The simulation results on the N-Queen problem and the knapsack problem indicate a superior performance of the D2NN.