'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization 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, 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 Indirect Genetic Algorithm for a Nurse Scheduling Problem

This paper describes a Genetic Algorithms approach to a manpower-scheduling problem arising at a major UK hospital. Although Genetic Algorithms have been successfully used for similar problems in the past, they always had to overcome the limitations of the classical Genetic Algorithms 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.

A Bayesian optimization algorithm for the nurse scheduling problem

A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse’s assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization 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, 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 Constructive Genetic Algorithm for permutation flowshop scheduling

The general flowshop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on in machines. In permutation flowshops the sequence of jobs is the same on all machines. A significant research effort has been devoted for sequencing jobs in a flowshop minimizing the makespan. This paper describes the application of a Constructive Genetic Algorithm (CGA) to makespan minimization on flowshop scheduling. The CGA was proposed recently as an alternative to traditional GA approaches, particularly, for evaluating schemata directly. The population initially formed only by schemata, evolves controlled by recombination to a population of well-adapted structures (schemata instantiation). The CGA implemented is based on the NEH classic heuristic and a local search heuristic used to define the fitness functions. The parameters of the CGA are calibrated using a Design of Experiments (DOE) approach. The computational results are compared against some other successful algorithms from the literature on Taillard`s well-known standard benchmark. The computational experience shows that this innovative CGA approach provides competitive results for flowshop scheduling; problems. (C) 2007 Elsevier Ltd. All rights reserved.

Scheduling in a two-machine flowshop for the minimization of the mean absolute deviation from a common due date

This paper addresses the minimization of the mean absolute deviation from a common due date in a two-machine flowshop scheduling problem. We present heuristics that use an algorithm, based on proposed properties, which obtains an optimal schedule fora given job sequence. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. Computational experiments show that the developed heuristics outperform results found in the literature for problems up to 500 jobs. (C) 2007 Elsevier Ltd. All rights reserved.

Short-term wind forecasting for energy resources scheduling

This paper proposes a wind power forecasting methodology based on two methods: direct wind power forecasting and wind speed forecasting in the first phase followed by wind power forecasting using turbines characteristics and the aforementioned wind speed forecast. The proposed forecasting methodology aims to support the operation in the scope of the intraday resources scheduling model, namely with a time horizon of 5 minutes. This intraday model supports distribution network operators in the short-term scheduling problem, in the smart grid context. A case study using a real database of 12 months recorded from a Portuguese wind power farm was used. The results show that the straightforward methodology can be applied in the intraday model with high wind speed and wind power accuracy. The wind power forecast direct method shows better performance than wind power forecast using turbine characteristics and wind speed forecast obtained in first phase.

Scheduling maintenance activities of electric power transmission networks using an hybrid constraint method

In this paper we present a Constraint Logic Programming (CLP) based model, and hybrid solving method for the Scheduling of Maintenance Activities in the Power Transmission Network. The model distinguishes from others not only because of its completeness but also by the way it models and solves the Electric Constraints. Specifically we present a efficient filtering algorithm for the Electrical Constraints. Furthermore, the solving method improves the pure CLP methods efficiency by integrating a type of Local Search technique with CLP. To test the approach we compare the method results with another method using a 24 bus network, which considerers 42 tasks and 24 maintenance periods.

Distribution network short term scheduling in Smart Grid context

The large increase of Distributed Generation (DG) in Power Systems (PS) and specially in distribution networks makes the management of distribution generation resources an increasingly important issue. Beyond DG, other resources such as storage systems and demand response must be managed in order to obtain more efficient and “green” operation of PS. More players, such as aggregators or Virtual Power Players (VPP), that operate these kinds of resources will be appearing. This paper proposes a new methodology to solve the distribution network short term scheduling problem in the Smart Grid context. This methodology is based on a Genetic Algorithms (GA) approach for energy resource scheduling optimization and on PSCAD software to obtain realistic results for power system simulation. The paper includes a case study with 99 distributed generators, 208 loads and 27 storage units. The GA results for the determination of the economic dispatch considering the generation forecast, storage management and load curtailment in each period (one hour) are compared with the ones obtained with a Mixed Integer Non-Linear Programming (MINLP) approach.

Multi-apprentice learning for meta-heuristics parameter tuning in a multi agent scheduling system

The scheduling problem is considered in complexity theory as a NP-hard combinatorial optimization problem. Meta-heuristics proved to be very useful in the resolution of this class of problems. However, these techniques require parameter tuning which is a very hard task to perform. A Case-based Reasoning module is proposed in order to solve the parameter tuning problem in a Multi-Agent Scheduling System. A computational study is performed in order to evaluate the proposed CBR module performance.

Application-specific modified particle swarm optimization for energy resource scheduling considering vehicle-to-grid

This paper presents a modified Particle Swarm Optimization (PSO) methodology to solve the problem of energy resources management with high penetration of distributed generation and Electric Vehicles (EVs) with gridable capability (V2G). The objective of the day-ahead scheduling problem in this work is to minimize operation costs, namely energy costs, regarding he management of these resources in the smart grid context. The modifications applied to the PSO aimed to improve its adequacy to solve the mentioned problem. The proposed Application Specific Modified Particle Swarm Optimization (ASMPSO) includes an intelligent mechanism to adjust velocity limits during the search process, as well as self-parameterization of PSO parameters making it more user-independent. It presents better robustness and convergence characteristics compared with the tested PSO variants as well as better constraint handling. This enables its use for addressing real world large-scale problems in much shorter times than the deterministic methods, providing system operators with adequate decision support and achieving efficient resource scheduling, even when a significant number of alternative scenarios should be considered. The paper includes two realistic case studies with different penetration of gridable vehicles (1000 and 2000). The proposed methodology is about 2600 times faster than Mixed-Integer Non-Linear Programming (MINLP) reference technique, reducing the time required from 25 h to 36 s for the scenario with 2000 vehicles, with about one percent of difference in the objective function cost value.

Two-type heterogeneous multiprocessor scheduling: Is there a phase transition? (Extended Abstract)

Consider the problem of non-migratively scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform. We ask the following question: Does there exist a phase transition behavior for the two-type heterogeneous multiprocessor scheduling problem? We also provide some initial observations via simulations performed on randomly generated task sets.

A synchronous transition protocol with periodicity for global scheduling of multimode real-time systems on multiprocessors

We consider the global scheduling problem of multimode real-time systems upon identical multiprocessor platforms. During the execution of a multimode system, the system can change from one mode to another such that the current task set is replaced with a new task set. Thereby, ensuring that deadlines are met requires not only that a schedulability test is performed on tasks in each mode but also that (i) a protocol for transitioning from one mode to another is specified and (ii) a schedulability test for each transition is performed. In this paper, we extend the synchronous transition protocol SM-MSO in order to take into account mode-independent tasks [1], i.e., tasks of which the execution pattern must not be jeopardized by the mode changes.

A hybrid genetic algorithm for the multi-mode resource-constrained project scheduling

A construction project is a group of discernible tasks or activities that are conduct-ed in a coordinated effort to accomplish one or more objectives. Construction projects re-quire varying levels of cost, time and other resources. To plan and schedule a construction project, activities must be defined sufficiently. The level of detail determines the number of activities contained within the project plan and schedule. So, finding feasible schedules which efficiently use scarce resources is a challenging task within project management. In this context, the well-known Resource Constrained Project Scheduling Problem (RCPSP) has been studied during the last decades. In the RCPSP the activities of a project have to be scheduled such that the makespan of the project is minimized. So, the technological precedence constraints have to be observed as well as limitations of the renewable resources required to accomplish the activities. Once started, an activity may not be interrupted. This problem has been extended to a more realistic model, the multi-mode resource con-strained project scheduling problem (MRCPSP), where each activity can be performed in one out of several modes. Each mode of an activity represents an alternative way of combining different levels of resource requirements with a related duration. Each renewable resource has a limited availability for the entire project such as manpower and machines. This paper presents a hybrid genetic algorithm for the multi-mode resource-constrained pro-ject scheduling problem, in which multiple execution modes are available for each of the ac-tivities of the project. The objective function is the minimization of the construction project completion time. To solve the problem, is applied a two-level genetic algorithm, which makes use of two separate levels and extend the parameterized schedule generation scheme. It is evaluated the quality of the schedules and presents detailed comparative computational re-sults for the MRCPSP, which reveal that this approach is a competitive algorithm.

Project scheduling under multiple resources constraints using a genetic algorithm

The resource constrained project scheduling problem (RCPSP) is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. During the last couple of years many heuristic procedures have been developed for this problem, but still these procedures often fail in finding near-optimal solutions. This paper proposes a genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities and delay times of the activities are defined by the genetic algorithm. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Project scheduling using a competitive genetic algorithm

- The resource constrained project scheduling problem (RCPSP) is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. During the last couple of years many heuristic procedures have been developed for this problem, but still these procedures often fail in finding near-optimal solutions. This paper proposes a genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities and delay times of the activities are defined by the genetic algorithm. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm