A Quantum Inspired Learning Cellular Automaton for Solving the Travelling Salesman Problem

Cellular automata (CA) have been shown to be suitable for modelling and simulating complex adaptive systems. To achieve adaptation to the exterior environment, Learning Cellular Automata (LCA) have been proposed as an extension of traditional CA, which exhibit only local adaptation, in order to allow a global adaptation of the automaton to its environment. In this paper, a new variant of LCA is described. It relies on two main ideas: The first one is to enhance the learning capabilities of the cellular automaton by using new operations inspired from the Reynolds´s Boids model and the second one is to foster diversity of cells´ states within the cellular automaton by adopting a quantum representation of the CA cells. Through solving the Travelling Salesman Problem, we show the effectiveness of the proposed model in implementing a LCA. Therefore a better simulation of complex adaptive systems can be envisaged.