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

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

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

A genetic algorithm with composite chromosome for shift assignment of part-time employees

Personnel scheduling problems involve multiple tasks, including assigning shifts to workers. The purpose is usually to satisfy objectives and constraints arising from management, labour unions and employee preferences. The shift assignment problem is usually highly constrained and difficult to solve. The problem can be further complicated (i) if workers have mixed skills; (ii) if the start/end times of shifts are flexible; and (iii) if multiple criteria are considered when evaluating the quality of the assignment. This paper proposes a genetic algorithm using composite chromosome encoding to tackle the shift assignment problem that typically arises in retail stores, where most employees work part-time, have mixed-skills and require flexible shifts. Experiments on a number of problem instances extracted from a real-world retail store, show the effectiveness of the proposed approach in finding good-quality solutions. The computational results presented here also include a comparison with results obtained by formulating the problem as a mixed-integer linear programming model and then solving it with a commercial solver. Results show that the proposed genetic algorithm exhibits an effective and efficient performance in solving this difficult optimisation problem

A harmony search algorithm for nurse rostering problems

Harmony search algorithm (HSA) is a relatively new nature-inspired algorithm. It evolves solutions in the problem search space by mimicking the musical improvisation process in seeking agreeable harmony measured by aesthetic standards. The nurse rostering problem (NRP) is a well-known NP-hard scheduling problem that aims at allocating the required workload to the available staff nurses at healthcare organizations to meet the operational requirements and a range of preferences. This work investigates research issues of the parameter settings in HSA and application of HSA to effectively solve complex NRPs. Due to the well-known fact that most NRPs algorithms are highly problem (or even instance) dependent, the performance of our proposed HSA is evaluated on two sets of very different nurse rostering problems. The first set represents a real world dataset obtained from a large hospital in Malaysia. Experimental results show that our proposed HSA produces better quality rosters for all considered instances than a genetic algorithm (implemented herein). The second is a set of well-known benchmark NRPs which are widely used by researchers in the literature. The proposed HSA obtains good results (and new lower bound for a few instances) when compared to the current state of the art of meta-heuristic algorithms in recent literature

Fuzzy multi-criteria simulated evolution for nurse re-rostering

Abstract: In a fuzzy environment where the decision making involves multiple criteria, fuzzy multi-criteria decision making approaches are a viable option. The nurse re-rostering problem is a typical complex problem situation, where scheduling decisions should consider fuzzy human preferences, such as nurse preferences, decision maker’s choices, and patient expectations. For effective nurse schedules, fuzzy theoretic evaluation approaches have to be used to incorporate the fuzzy human preferences and choices. The present study seeks to develop a fuzzy multi-criteria simulated evolution approach for the nurse re-rostering problem. Experimental results show that the fuzzy multi-criteria approach has a potential to solve large scale problems within reasonable computation times

An Optimization Technique to Prepare Nurse Schedule for a Monthly TIME Horizon

Nurse scheduling problem is one of the most difficult scheduling problems to solve since its solution space is large and it expects to comply many constraints. There is no standard model or a method of solution for nurse scheduling. The main objective of this study is to search for a scientific method to prepare a monthly working schedule for a group of nursing officers employed in a hospital. We propose an optimization method to prepare an optimal schedule. Initially, we develop an optimization model by formulating the objective and the constraints of the problem. The optimization model that we are interestedin is a 0-1 Integer Linear Programming problem. We apply the Branch-and-Bound technique to solve the problem using the optimization software package LINGO. Finally, the solution to the optimization problem is formulated to a regular nurse schedule. The methodology is illustrated by preparing a monthly schedule for a private hospital in Sri Lanka