Towards the landscape rotation as a perturbation strategy on the quadratic assignment problem

Joan Alza, Mark Bartlett, Josu Ceberio, John A. W. McCall

Abstract: Recent work in combinatorial optimisation have demonstrated that neighbouring solutions of a local optima may belong to more favourable attraction basins. In this sense, the perturbation strategy plays a critical role on local search based algorithms to kick the search of the algorithm into more prominent areas of the space. In this paper, we investigate the landscape rotation as a perturbation strategy to redirect the search of an stuck algorithm. This technique rearranges the mapping of solutions to different objective values without altering important properties of the problem's landscape such as the number and quality of optima, among others. Particularly, we investigate two rotation based perturbation strategies: (i) a profoundness rotation method and (ii) a broadness rotation method. These methods are applied into the stochastic hill-climbing heuristic and tested and compared on different instances of the quadratic assignment problem against other algorithm versions. Performed experiments reveal that the landscape rotation is an efficient perturbation strategy to shift the search in a controlled way. Nevertheless, an empirical investigation of the landscape rotation demonstrates that it needs to be cautiously manipulated in the permutation space since a small rotation does not necessarily mean a small disturbance in the fitness landscape.