A New Local Rule for Convergence of ICLA to a Compatible Point

Many problems in the modern world have a decentralized and distributed nature. Irregular cellular learning automata (ICLA) is a powerful mathematical model for decentralized problems and applications. Convergence of ICLA to a compatible point is very important because this convergence can provide efficient solutions for the problems. The local rule of ICLA can play a key role in this convergence. A local rule that simply rewards or punishes learning automata just based on the response of environment and actions of neighbors does not guarantee convergence of ICLA to a compatible point. In this paper, we present a new local rule that guarantees convergence to a compatible point. Formal proofs for the convergence are provided and results of the conducted experiments support our theoretical findings.