Kathryn A. Dowsland

Nurse scheduling with tabu search and strategic oscillation

The problem of producing rosters for nursing staff in a large general hospital is tackled using tabu search with strategic oscillation. The objective is to ensure that enough nurses are on duty at all times while taking account of individual preferences and requests for days off in a way that is seen to treat all employees fairly. This is achieved using a variant of tabu search which repeatedly oscillates between finding a feasible cover, and improving it in terms of preference costs. Within each phase the search is controlled by a combination of different neighbourhoods and candidate lists designed to aggressively seek out local optima and then to react to the problems encountered on arrival. The result is a robust and effective method which is able to match the quality of solutions produced by a human expert.

An indirect genetic algorithm for a nurse-scheduling problem

This paper describes a Genetic Algorithms (GAs) approach to a manpower-scheduling problem arising at a major UK hospital. Although GAs have been successfully used for similar problems in the past, they always had to overcome the limitations of the classical GAs paradigm in handling the conflict between objectives and constraints. The approach taken here is to use an indirect coding based on permutations of the nurses, and a heuristic decoder that builds schedules from these permutations. Computational experiments based on 52 weeks of live data are used to evaluate three different decoders with varying levels of intelligence, and four well-known crossover operators. Results are further enhanced by introducing a hybrid crossover operator and by making use of simple bounds to reduce the size of the solution space. The results reveal that the proposed algorithm is able to find high quality solutions and is both faster and more flexible than a recently published Tabu Search approach.

Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem

There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. In order to overcome this, successful implementations frequently make use of problem specific knowledge. This paper is concerned with the development of a GA for a nurse rostering problem at a major UK hospital. The structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating sub-populations. Problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. Empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical GA to the point where it is able to provide a practical solution to the problem.

A robust simulated annealing based examination timetabling system

Abstract This paper is concerned with the development of an examination scheduling system that is sufficiently flexible to deal with the many different objectives and constraints found across a broad spectrum of universities and colleges. The problem is solved in two phases using simulated annealing. The first phase seeks out a feasible solution and the second finds an improvement in terms of meeting the secondary objectives and soft constraints. As the quality of a simulated annealing solution is known to depend on the parameters used to control the algorithm and the way in which the problem is modelled within the simulated annealing framework a successful implemetation relies on judicious choices in both areas. A number of different choices are suggested and compared using a test-bed of problems derived from data from a variety of institutions. The final result is a robust system that is capable of dealing with a wide range of problem specifications and data characteristics. The examination scheduling problem varies in detail from institution to institution. Thus any generic approach must be robust enough to work well over the full spectrum of problem characteristics. It is well-known that the quality of solutions produced by any simulated annealing implementation depends on the correct choice of solution space and neighbourhood, as well as the parameters that govern the cooling schedule. As these choices are sensitive to the precise problem details the design of a generic simulated annealing based approach to examination scheduling needs to address this issue carefully. This paper examines this problem with respect to an implementation that has already been shown to work well at a single institution. The basic framework is used to test different neighbourhoods and cooling schedules over a variety of problems and to examine whether or not biases in sampling have a significant effect on solution quality. The results indicate that the choice of neighbourhood is the most important decision and that neighbourhoods based on the graph-theoretic concept of Kempe chains are the most effective regardless of the objectives or size of the problem.

Some experiments with simulated annealing techniques for packing problems

Abstract Experiments with a variety of combinatorial optimisation problems have shown that the simulated annealing algorithm is an effective local search heuristic method. The basic requirements of the algorithm are a neighbourhood structure on the set of feasible solutions and a number of parameters which govern the acceptance or rejection of new solutions generated during the search. The quality of the solution is very sensitive to both these factors. This paper is concerned with the application of the simulated annealing approach to packing problems and describes a series of experiments carried out to ascertain the effectiveness of the method for such problems and the most appropriate neighbourhood structure to use and the best parameters to apply.

Solving a Nurse Scheduling Problem with Knapsacks, Networks and Tabu Search

This paper illustrates how a modern heuristic and two classical integer programming models have been combined to provide a solution to a nurse rostering problem at a major UK hospital. Neither a heuristic nor an exact approach based on a standard IP package was able to meet all the practical requirements. This was overcome by using a variant of tabu search as the core method, but applying knapsack and network flow models in pre- and post-processing phases. The result is a successful software tool that frees senior nursing staff from a time consuming administrative task.

Solution approaches to irregular nesting problems

This paper reviews some of the approaches which have been adopted in the solution of problems involving the nesting of irregularly shaped pieces. Such problems arise in a wide variety of application areas and the purpose of this paper is to bring together problems and solution approaches from a number of diverse domains.

Variants of simulated annealing for the examination timetabling problem

This paper is concerned with the use of simulated annealing in the solution of the multi-objective examination timetabling problem. The solution method proposed optimizes groups of objectives in different phases. Some decisions from earlier phases may be altered later as long as the solution quality with respect to earlier phases does not deteriorate. However, such limitations may disconnect the solution space, thereby causing optimal or near-optimal solutions to be missed. Three variants of our basic simulated annealing implementation which are designed to overcome this problem are proposed and compared using real university data as well as artificial data sets. The underlying principles and conclusions stemming from the use of this method are generally applicable to many other multi-objective type problems.

An algorithm for polygon placement using a bottom-left strategy

Abstract This paper describes a fast and efficient implementation of a bottom-left (BL) placement algorithm for polygon packing. The algorithm allows pieces to be nested within the partial layout produced by previously placed pieces, and produces an optimal BL layout in the sense that the positions considered are guaranteed to contain the bottom-left position of the infinite set of possibilities. Full details of the way in which these positions are calculated are given. Computational experiments comparing the results of different orderings on a variety of datasets from the literature are reported, and these illustrate that problems having in excess of 100 pieces of several piece types can be solved within one minute on a modern desktop PC. The procedure can easily be incorporated into algorithms that apply more sophisticated piece selection procedures.

An exact algorithm for the pallet loading problem

Abstract The two-dimensional packing problem of finding optimal layouts for identical rectangular boxes on a rectangular pallet has interested OR practitioners for many years. The problem is NP-complete and solution methods to date tend to be heuristic. This paper discusses the development of an exact tree search algorithm based on a graph-theoretic model of the problem.