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.

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.

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.

Multiple-Retrieval Case-Based Reasoning for Course Timetabling Problems

The structured representation of cases by attribute graphs in a Case-Based Reasoning (CBR) system for course timetabling has been the subject of previous research by the authors. In that system, the case base is organised as a decision tree and the retrieval process chooses those cases which are sub attribute graph isomorphic to the new case. The drawback of that approach is that it is not suitable for solving large problems. This paper presents a multiple-retrieval approach that partitions a large problem into small solvable sub-problems by recursively inputting the unsolved part of the graph into the decision tree for retrieval. The adaptation combines the retrieved partial solutions of all the partitioned sub-problems and employs a graph heuristic method to construct the whole solution for the new case. We present a methodology which is not dependant upon problem specific information and which, as such, represents an approach which underpins the goal of building more general timetabling systems. We also explore the question of whether this multiple-retrieval CBR could be an effective initialisation method for local search methods such as Hill Climbing, Tabu Search and Simulated Annealing. Significant results are obtained from a wide range of experiments. An evaluation of the CBR system is presented and the impact of the approach on timetabling research is discussed. We see that the approach does indeed represent an effective initialisation method for these approaches.

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.

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.