Multiple local neighbourhood search for extremal optimisation

Abstract

Extremal optimisation (EO) uses a somewhat unusual mechanism to transform one solution into another. This consists of computing a probabilistic worst solution component value, and changing it to a random value. While simple and avoiding problems with premature convergence, it is mostly incompatible with combinatorial problems, particularly those requiring permutations as solution structures. This paper demonstrates that standard local search operators (e.g., 1-opt, 2-optand 3-opt ?used singly or from a neighborhood) can be readily integrated into the canonical EOframework, without compromising the integrity of the original algorithm. The idea, in some senses may be viewed as a quasi-memetic algorithm. In particular, the primary purpose of this paper is the application and analysis of multiple local search operator neighborhoods. Issues of solution component ranking techniques and methods for generating local transition operator endpoints are also examined. The difficult and under used asymmetric travelling salesman problem is employed to test these concepts. Results indicate that the simultaneous use of local search operators provides for improved performance over operators used individually