Estimating attraction basin sizes

The performance of local search algorithms is influenced by the properties that the neighborhood imposes on the search space. Among these properties, the number of local optima has been traditionally considered as a complexity measure of the instance, and different methods for its estimation have been developed. The accuracy of these estimators depends on properties such as the relative attraction basin sizes. As calculating the exact attraction basin sizes becomes unaffordable for moderate problem sizes, their estimations are required. The lack of techniques achieving this purpose encourages us to propose two methods that estimate the attraction basin size of a given local optimum. The first method takes uniformly at random solutions from the whole search space, while the second one takes into account the structure defined by the neighborhood. They are tested on different instances of problems in the permutation space, considering the swap and the adjacent swap neighborhoods

A sequencing approach for creating new train timetables

Train scheduling is a complex and time consuming task of vital importance. To schedule trains more accurately and efficiently than permitted by current techniques a novel hybrid job shop approach has been proposed and implemented. Unique characteristics of train scheduling are first incorporated into a disjunctive graph model of train operations. A constructive algorithm that utilises this model is then developed. The constructive algorithm is a general procedure that constructs a schedule using insertion, backtracking and dynamic route selection mechanisms. It provides a significant search capability and is valid for any objective criteria. Simulated Annealing and Local Search meta-heuristic improvement algorithms are also adapted and extended. An important feature of these approaches is a new compound perturbation operator that consists of many unitary moves that allows trains to be shifted feasibly and more easily within the solution. A numerical investigation and case study is provided and demonstrates that high quality solutions are obtainable on real sized applications