Multistage extremal optimization for hard travelling salesman problem

The adjustable parameters of probability distributions adopted by extremal optimization (EO) and its modified versions play a critical role in controlling their performances. Unlike the traditional static probability distribution based strategy, this paper presents a novel method called multistage EO to explore the configuration space of hard travelling salesman problem (TSP) by using different values of the parameters in different stages. This method is to optimize with multi-start techniques starting from random states in the first stage. In all later stages, it always selects the best configuration obtained from the last stage as the initial one for optimization in the current stage. The superior performance of the proposed method is proved by the experimental tests with the well-known hard TSP instances.