'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,

'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 Set Covering Problems'

This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder function. The genetic algorithm itself provides this decoder with permutations of the solution variables and other parameters. Second, it will be shown that results can be further improved by adding another indirect optimisation layer. The decoder will not directly seek out low cost solutions but instead aims for good exploitable solutions. These are then post optimised by another hill-climbing algorithm. Although seemingly more complicated, we will show that this three-stage approach has advantages in terms of solution quality, speed and adaptability to new types of problems over more direct approaches. Extensive computational results are presented and compared to the latest evolutionary and other heuristic approaches to the same data instances.

An evolutionary squeaky wheel optimisation approach to personnel scheduling

The quest for robust heuristics that are able to solve more than one problem is ongoing. In this paper, we present, discuss and analyse a technique called Evolutionary Squeaky Wheel Optimisation and apply it to two different personnel scheduling problems. Evolutionary Squeaky Wheel Optimisation improves the original Squeaky Wheel Optimisation’s effectiveness and execution speed by incorporating two additional steps (Selection and Mutation) for added evolution. In the Evolutionary Squeaky Wheel Optimisation, a cycle of Analysis-Selection-Mutation-Prioritization-Construction continues until stopping conditions are reached. The aim of the Analysis step is to identify below average solution components by calculating a fitness value for all components. The Selection step then chooses amongst these underperformers and discards some probabilistically based on fitness. The Mutation step further discards a few components at random. Solutions can become incomplete and thus repairs may be required. The repair is carried out by using the Prioritization step to first produce priorities that determine an order by which the following Construction step then schedules the remaining components. Therefore, improvements in the Evolutionary Squeaky Wheel Optimisation is achieved by selective solution disruption mixed with iterative improvement and constructive repair. Strong experimental results are reported on two different domains of personnel scheduling: bus and rail driver scheduling and hospital nurse scheduling.

Polyphenol Extraction Optimisation From Ceylon Gooseberry (dovyalis Hebecarpa) Pulp.

Originally from Asia, Dovyalis hebecarpa is a dark purple/red exotic berry now also produced in Brazil. However, no reports were found in the literature about phenolic extraction or characterisation of this berry. In this study we evaluate the extraction optimisation of anthocyanins and total phenolics in D. hebecarpa berries aiming at the development of a simple and mild analytical technique. Multivariate analysis was used to optimise the extraction variables (ethanol:water:acetone solvent proportions, times, and acid concentrations) at different levels. Acetone/water (20/80 v/v) gave the highest anthocyanin extraction yield, but pure water and different proportions of acetone/water or acetone/ethanol/water (with >50% of water) were also effective. Neither acid concentration nor time had a significant effect on extraction efficiency allowing to fix the recommended parameters at the lowest values tested (0.35% formic acid v/v, and 17.6 min). Under optimised conditions, extraction efficiencies were increased by 31.5% and 11% for anthocyanin and total phenolics, respectively as compared to traditional methods that use more solvent and time. Thus, the optimised methodology increased yields being less hazardous and time consuming than traditional methods. Finally, freeze-dried D. hebecarpa showed high content of target phytochemicals (319 mg/100g and 1,421 mg/100g of total anthocyanin and total phenolic content, respectively).

Impact Of Pharmacist Interventions On Drug-related Problems And Laboratory Markers In Outpatients With Human Immunodeficiency Virus Infection.

Substantial complexity has been introduced into treatment regimens for patients with human immunodeficiency virus (HIV) infection. Many drug-related problems (DRPs) are detected in these patients, such as low adherence, therapeutic inefficacy, and safety issues. We evaluated the impact of pharmacist interventions on CD4+ T-lymphocyte count, HIV viral load, and DRPs in patients with HIV infection. In this 18-month prospective controlled study, 90 outpatients were selected by convenience sampling from the Hospital Dia-University of Campinas Teaching Hospital (Brazil). Forty-five patients comprised the pharmacist intervention group and 45 the control group; all patients had HIV infection with or without acquired immunodeficiency syndrome. Pharmaceutical appointments were conducted based on the Pharmacotherapy Workup method, although DRPs and pharmacist intervention classifications were modified for applicability to institutional service limitations and research requirements. Pharmacist interventions were performed immediately after detection of DRPs. The main outcome measures were DRPs, CD4+ T-lymphocyte count, and HIV viral load. After pharmacist intervention, DRPs decreased from 5.2 (95% confidence interval [CI] =4.1-6.2) to 4.2 (95% CI =3.3-5.1) per patient (P=0.043). A total of 122 pharmacist interventions were proposed, with an average of 2.7 interventions per patient. All the pharmacist interventions were accepted by physicians, and among patients, the interventions were well accepted during the appointments, but compliance with the interventions was not measured. A statistically significant increase in CD4+ T-lymphocyte count in the intervention group was found (260.7 cells/mm(3) [95% CI =175.8-345.6] to 312.0 cells/mm(3) [95% CI =23.5-40.6], P=0.015), which was not observed in the control group. There was no statistical difference between the groups regarding HIV viral load. This study suggests that pharmacist interventions in patients with HIV infection can cause an increase in CD4+ T-lymphocyte counts and a decrease in DRPs, demonstrating the importance of an optimal pharmaceutical care plan.

Graded Meshes In Bio-thermal Problems With Transmission-line Modeling Method.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.

[access To Information About How To Prevent Oral Problems Among School Children In The Public School Network].

The scope of this study is to identify the prevalence of access to information about how to prevent oral problems among schoolchildren in the public school network, as well as the factors associated with such access. This is a cross-sectional and analytical study conducted among 12-year-old schoolchildren in a Brazilian municipality with a large population. The examinations were performed by 24 trained dentists and calibrated with the aid of 24 recorders. Data collection occurred in 36 public schools selected from the 89 public schools of the city. Descriptive, univariate and multiple analyses were conducted. Of the 2510 schoolchildren included in the study, 2211 reported having received information about how to prevent oral problems. Access to such information was greater among those who used private dental services; and lower among those who used the service for treatment, who evaluated the service as regular or bad/awful. The latter use toothbrush only or toothbrush and tongue scrubbing as a means of oral hygiene and who reported not being satisfied with the appearance of their teeth. The conclusion drawn is that the majority of schoolchildren had access to information about how to prevent oral problems, though access was associated with the characteristics of health services, health behavior and outcomes.

Trends and strategies of ozone application in environmental problems

Efforts presented by the scientific community in recent years towards the development of numerous green chemical processes and wastewater treatment technologies are presented and discussed. In the light of these approaches, environmentally friendly technologies, as well as the key role played by the well-known advanced oxidation processes, are discussed, giving special attention to the ones comprising ozone applications. Fundamentals and applied aspects dealing with ozone technology and its application are also presented.

Changes in parents' and self-reports of behavioral problems in Brazilian adolescents after behavioral treatment with urine alarm for nocturnal enuresis

PURPOSE: Compare parents' reports of youth problems (PRYP) with adolescent problems self-reports (APSR) pre/post behavioral treatment of nocturnal enuresis (NE) based on the use of a urine alarm. MATERIALS AND METHODS: Adolescents (N = 19) with mono-symptomatic (primary or secondary) nocturnal enuresis group treatment for 40 weeks. Discharge criterion was established as 8 weeks with consecutive dry nights. PRYP and APSR were scored by the Child Behavior Checklist (CBCL) and Youth Self-Report (YSR). RESULTS: Pre-treatment data: 1) Higher number of clinical cases based on parent report than on self-report for Internalizing Problems (IP) (13/19 vs. 4/19), Externalizing Problems (EP) (7/19 vs. 5/19) and Total Problem (TP) (11/19 vs. 5/19); 2) Mean PRYP scores for IP (60.8) and TP (61) were within the deviant range (T score ≥ 60); while mean PRYP scores for EP (57.4) and mean APSR scores (IP = 52.4, EP = 49.5, TP = 52.4) were within the normal range. Difference between PRYP' and APSR' scores was significant. Post treatment data: 1) Discharge for majority of the participants (16/19); 2) Reduction in the number of clinical cases on parental evaluation: 9/19 adolescents remained within clinical range for IP, 2/19 for EP, and 7/19 for TP. 3) All post-treatment mean scores were within the normal range; the difference between pre and post evaluation scores was significant for PRYP. CONCLUSIONS: The behavioral treatment based on the use of urine alarm is effective for adolescents with mono-symptomatic (primary and secondary) nocturnal enuresis. The study favors the hypothesis that enuresis is a cause, not a consequence, of other behavioral problems.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture-the Adaptive Culture Heuristic (ACH)-on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(1/4) so that the number of agents must increase with the fourth power of the problem size, N proportional to F(4), to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F(6) which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Continuous opinions and discrete actions in opinion dynamics problems

A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors, and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.

Clinical relationships and ethical problems in primary care, Sao Paulo, SP, Brazil

Objectives: Main Objective: to identify ethical problems in primary care according to nurses` and doctors` perceptions. Secondary Objective: to know ethical issues of patient-professional relationships in primary care. Design: Synthesis to integrate and reinterpret primary results of qualitative studies. Setting: Primary healthcare centers, Sao Paulo, SP, Brazil. Participants and/or context: Incidental sample of 34 nurses and 36 medical doctors working in primary healthcare centers selected by convenience. Methods: Individual, semi-structured interviews to identity situations considered as sources of ethical problems. The sample is socially representative of primary care health centers and professionals. Data collection assured discourse saturation. Hermeneutic-dialectical discourse analysis was used to study the results. Results: Patient-professional relationships and team work were the main sources of ethical problems. The most important problems were patient information, privacy, confidentiality, interpersonal relationship, linkage and patient autonomy. These issues reflect the recent changes in clinical relation ships and show the peculiarities of primary care with its continuous care which lasts a long time. Healthcare involves multiprofessional team work in the midst of the patient claims for autonomy. Good care of patients needs requires a relationship based on communication and cooperation, and includes feelings and values, with communication skills. Conclusions: Ethical problems in primary care are common situations. For quality and humane primary care the relationship should consist of dialogue, trust and cooperation. (C) 2009 Elsevier Espana, S.L. All rights reserved.