A Hybrid Evolutionary Approach to the Nurse Rostering Problem

Nurse rostering is a difficult search problem with many constraints. In the literature, a number of approaches have been investigated including penalty function methods to tackle these constraints within genetic algorithm frameworks. In this paper, we investigate an extension of a previously proposed stochastic ranking method, which has demonstrated superior performance to other constraint handling techniques when tested against a set of constrained optimisation benchmark problems. An initial experiment on nurse rostering problems demonstrates that the stochastic ranking method is better in finding feasible solutions but fails to obtain good results with regard to the objective function. To improve the performance of the algorithm, we hybridise it with a recently proposed simulated annealing hyper-heuristic within a local search and genetic algorithm framework. The hybrid algorithm shows significant improvement over both the genetic algorithm with stochastic ranking and the simulated annealing hyper-heuristic alone. The hybrid algorithm also considerably outperforms the methods in the literature which have the previously best known results.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

Unconditional constants and polynomial inequalities

If P is a polynomial on Rm of degree at most n then we define the polynomial |P|. Now if B is a convex compact set in Rm, we define the norm ||P||B of P as the maximum of P on B, and then we investigate the inequality || |P| ||B