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Most, but not all, ion channels appear to obey the law of microscopic reversibility (or detailed balance). During the fitting of reaction mechanisms it is therefore often required that cycles in the mechanism should obey microscopic reversibility at all times. In complex reaction mechanisms, especially those that contain cubic arrangements of states, it may not be obvious how to achieve this. Three general methods for imposing microscopic reversibility are described. The first method works by setting the 'obvious' four-state cycles in the correct order. The second method, based on the idea of a spanning tree, works by finding independent cycles (which will often have more than four states) such that the order in which they are set does not matter. The third method uses linear algebra to solve for constrained rates.

Aickelin, Uwe and Dowsland, Kathryn (2000) 'Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem'. Journal of Scheduling,3 (3 A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.ukExploiting problem structure in a genetic algorithm approach to a nurse rostering problem. Summary.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 cooperating 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.