Arbitrary elementary landscapes & AR(1) processes

Neighborhood specification is a dominant consideration in assuring the success of a direct search approach to a difficult combinatorial optimization problem. Previous research has shown the efficacy of imposing an elementary landscape upon the search topology. Barnes et al. [J.W. Barnes, S. Dokov, B. Dimova, A. Solomon, A theory of elementary landscapes, Applied Mathematics Letters 16 (2003)] generalize the notion of elementary landscapes to embrace arbitrary neighborhood digraphs. Stadler [P.F. Stadler, Landscapes and their correlation functions, Journal of Mathematical Chemistry 20 (1996)] shows, for the special case of symmetric-regular neighborhood digraphs, that the autocorrelation function associated with a smooth elementary landscape is consistent with an AR(1) time series. In this paper, we extend this idea to arbitrary neighborhood digraphs. © 2004 Elsevier Ltd. All rights reserved.