A Component Based Heuristic Search Method with Evolutionary Eliminations

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with evolutionary eliminations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then to implement two evolutionary elimination strategies mimicking natural selection and natural mutation process on these components respectively to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs an evaluation function which evaluates how well each component contributes towards the final objective. Two elimination steps are then applied: the first elimination eliminates a number of components that are deemed not worthy to stay in the current schedule; the second elimination may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems.Comment: 27 pages, 4 figure

Partnering Strategies for Fitness Evaluation in a Pyramidal Evolutionary Algorithm

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes for (sub-)fitness evaluation purposes are examined for two multiple-choice optimisation problems. It is shown that random partnering strategies perform best by providing better sampling and more diversity

'On the Application of Hierarchical Coevolutionary Genetic Algorithms: Recombination and Evaluation Partners'

This paper examines the use of a hierarchical coevolutionary genetic algorithm under different partnering strategies. Cascading clusters of sub-populations are built from the bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations potentially search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the sub-populations on solution quality are examined for two constrained optimisation problems. We examine a number of recombination partnering strategies in the construction of higher-level individuals and a number of related schemes for evaluating sub-solutions. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements

An Estimation of Distribution Algorithm for Nurse Scheduling

Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems

'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126

Building Better Nurse Scheduling Algorithms

The aim of this research is twofold: Firstly, to model and solve a complex nurse scheduling problem with an integer programming formulation and evolutionary algorithms. Secondly, to detail a novel statistical method of comparing and hence building better scheduling algorithms by identifying successful algorithm modifications. The comparison method captures the results of algorithms in a single figure that can then be compared using traditional statistical techniques. Thus, the proposed method of comparing algorithms is an objective procedure designed to assist in the process of improving an algorithm. This is achieved even when some results are non-numeric or missing due to infeasibility. The final algorithm outperforms all previous evolutionary algorithms, which relied on human expertise for modification

A Component Based Heuristic Search Method with AdaptivePerturbations for Hospital Personnel Scheduling

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with adaptive perturbations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then mimic a natural evolutionary process on these components to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs a dynamic evaluation function which evaluates how well each component contributes towards the final objective. Two perturbation steps are then applied: the first perturbation eliminates a number of components that are deemed not worthy to stay in the current schedule; the second perturbation may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems