'The application of Bayesian Optimization and Classifier Systems in Nurse Scheduling'

Abstract. Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each person's assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems.

'Explicit Learning: an Effort towards Human Scheduling Algorithms'

Abstract Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of a general scheduling algorithm is still in its infancy. Mimicking the natural evolutionary process of the survival of the fittest, Genetic Algorithms (GAs) have attracted much attention in solving difficult scheduling problems in recent years. Some obstacles exist when using GAs: there is no canonical mechanism to deal with constraints, which are commonly met in most real-world scheduling problems, and small changes to a solution are difficult. To overcome both difficulties, indirect approaches have been presented (in [1] and [2]) for nurse scheduling and driver scheduling, where GAs are used by mapping the solution space, and separate decoding routines then build solutions to the original problem. In our previous indirect GAs, learning is implicit and is restricted to the efficient adjustment of weights for a set of rules that are used to construct schedules. The major limitation of those approaches is that they learn in a non-human way: like most existing construction algorithms, once the best weight combination is found, the rules used in the construction process are fixed at each iteration. However, normally a long sequence of moves is needed to construct a schedule and using fixed rules at each move is thus unreasonable and not coherent with human learning processes. When a human scheduler is working, he normally builds a schedule step by step 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 completed yet, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this research we intend to design more human-like scheduling algorithms, by using ideas derived from Bayesian Optimization Algorithms (BOA) and Learning Classifier Systems (LCS) to implement explicit learning from past solutions. BOA can be applied to learn to identify good partial solutions and to complete them by building a Bayesian network of the joint distribution of solutions [3]. A Bayesian network is a directed acyclic graph with each node corresponding to one variable, and each variable corresponding to individual rule by which a schedule will be constructed step by step. The conditional probabilities are computed according to an initial set of promising solutions. Subsequently, each new instance for each node is generated by using the corresponding conditional probabilities, until values for all nodes have been generated. 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 Bayesian network is updated again using the current set of good rule strings. The algorithm thereby tries to explicitly identify and mix promising building blocks. It should be noted that for most scheduling problems the structure of the network model is known and all the 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. In the LCS approach, each rule has its strength showing its current usefulness in the system, and this strength is constantly assessed [4]. To implement sophisticated learning based on previous solutions, an improved LCS-based algorithm is designed, which consists of the following three steps. The initialization step is to assign each rule at each stage a constant initial strength. Then rules are selected by using the Roulette Wheel strategy. The next step is to reinforce the strengths of the rules used in the previous solution, keeping the strength of unused rules unchanged. The selection step is to select fitter rules for the next generation. It is envisaged that the LCS part of the algorithm will be used as a hill climber to the BOA algorithm. This is exciting and ambitious research, which might provide the stepping-stone for a new class of scheduling algorithms. Data sets from nurse scheduling and mall problems will be used as test-beds. It is envisaged that once the concept has been proven successful, it will be implemented into general scheduling algorithms. It is also hoped that this research will give some preliminary answers about how to include human-like learning into scheduling algorithms and may therefore be of interest to researchers and practitioners in areas of scheduling and evolutionary computation. References 1. Aickelin, U. and Dowsland, K. (2003) 'Indirect Genetic Algorithm for a Nurse Scheduling Problem', Computer & Operational Research (in print). 2. Li, J. and Kwan, R.S.K. (2003), 'Fuzzy Genetic Algorithm for Driver Scheduling', European Journal of Operational Research 147(2): 334-344. 3. Pelikan, M., Goldberg, D. and Cantu-Paz, E. (1999) 'BOA: The Bayesian Optimization Algorithm', IlliGAL Report No 99003, University of Illinois. 4. Wilson, S. (1994) 'ZCS: A Zeroth-level Classifier System', Evolutionary Computation 2(1), pp 1-18.

Models and algorithms for real-world optimization problems

This thesis deals with efficient solution of optimization problems of practical interest. The first part of the thesis deals with bin packing problems. The bin packing problem (BPP) is one of the oldest and most fundamental combinatorial optimiza- tion problems. The bin packing problem and its generalizations arise often in real-world ap- plications, from manufacturing industry, logistics and transportation of goods, and scheduling. After an introductory chapter, I will present two applications of two of the most natural extensions of the bin packing: Chapter 2 will be dedicated to an application of bin packing in two dimension to a problem of scheduling a set of computational tasks on a computer cluster, while Chapter 3 deals with the generalization of BPP in three dimensions that arise frequently in logistic and transportation, often com- plemented with additional constraints on the placement of items and characteristics of the solution, like, for example, guarantees on the stability of the items, to avoid potential damage to the transported goods, on the distribution of the total weight of the bins, and on compatibility with loading and unloading operations. The second part of the thesis, and in particular Chapter 4 considers the Trans- mission Expansion Problem (TEP), where an electrical transmission grid must be expanded so as to satisfy future energy demand at the minimum cost, while main- taining some guarantees of robustness to potential line failures. These problems are gaining importance in a world where a shift towards renewable energy can impose a significant geographical reallocation of generation capacities, resulting in the ne- cessity of expanding current power transmission grids.

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.

Prevalence and comorbidity of behavioral problems of children aged three to six: Results of the Braunschweiger Kindergartenstudie

Prevalence and comorbidity of behavioral problems of children aged three to six: Results of the Braunschweiger Kindergartenstudie Objectives: To analyze the frequency of behavioral and emotional problems and comorbidity of kindergarten children in Braunschweig as rated by their parents. Method: The analysis is part of the Braunschweiger Kindergartenstudie. In a sample of N = 809 children aged three to six the parents rated their children using a modified version of the Child Behavior Checklist/CBCL 4-18. Results: The prevalence rates range from 0.5% to 5.0%. The most frequent behavioral problems in kindergarten children were aggressive behavior and attention problems, followed by social problems. The study also provides bidirectional comorbidity rates. Conclusion: Finally the prevalence rates and the implications of the findings for prevention of behavioral problems in children are discussed.

The impact of perinatal and socioeconomic factors on mental health problems of children from a poor Brazilian city: a longitudinal study

Low birth weight and preterm birth, and social disadvantage may negatively affect mental health of children, but findings have been inconsistent. To assess the influence of perinatal and social factors on mental health problems in children aged 7-9 years. A random sample of 805 births in So Luis, Brazil was studied in 1997/1998 and again in 2005/2006. Perinatal, socioeconomic and demographic variables were assessed within 24 h after delivery. The Strengths and Difficulties Questionnaire (SDQ) was used to assess mental health problems in the children. Simple and multiple Poisson regressions were used for statistical analysis. The overall prevalence of mental health problems in the total sample was 47.7%. The prevalences of emotional and conduct problems were 58.2 and 48.8%, respectively. Only paternal age (< 20 years) was associated with mental health problems as measured by the full SDQ scale (prevalence ratio PR = 1.27). Children born to single mothers (PR = 1.31) and those with birth weight from 1,500 to 2,499 g (PR = 1.18) and from 2,500 to 2,999 g (PR = 1.17) had a higher risk of emotional problems, but those from low income families had a lower risk (PR = 0.80). Children with a father of less than 20 years had a higher risk of having problems with their peers (PR = 1.75). A maternal education of 9 years or over was inversely associated with peer (PR = 0.70) and conduct problems (PR = 0.73). Girls had a lower risk of conduct (PR = 0.77) and hyperactivity problems (PR = 0.68). A maternal education of 4 years or less increased the risk of hyperactivity (PR = 1.48). Socioeconomic and demographic conditions were better predictors of mental health problems in children than birth weight or preterm birth. However, since most effect sizes were small most mental health problems were, unexplained by the variables in the study.

Mortality problems in Brazil and in Germany: past-present-future. Learning from each other?

This article was written by a Swiss-German historical demographer after having visited different Brazilian Universities in 1984 as a guest-professor. It aims at promoting a real dialog between developed and developing countries, commencing the discussion with the question: Can we learn from each other? An affirmative answer is given, but not in the superficial manner in which the discussion partners simply want to give each other some "good advice" or in which the one declares his country's own development to be the solely valid standard. Three points are emphasized: 1. Using infant mortality in S. Paulo from 1908 to 1983 as an example, it is shown that Brazil has at its disposal excellent, highly varied research literature that is unjustifiably unknown to us (in Europe) for the most part. Brazil by no means needs our tutoring lessons as regards the causal relationships; rather, we could learn two things from Brazil about this. For one, it becomes clear that our almost exclusively medical-biological view is inappropriate for passing a judgment on the present-day problems in Brazil and that any conclusions so derived are thus only transferable to a limited extent. For another, we need to reinterpret the history of infant mortality in our own countries up to the past few decades in a much more encompassing "Brazilian" sense. 2. A fruitful dialog can only take place if both partners frankly present their problems. For this reason, the article refers with much emprasis to our present problems in dealing with death and dying - problems arising near the end of the demographic and epidemiologic transitions: the superanuation of the population, chronic-incurable illnesses as the main causes of death, the manifold dependencies of more and more elderly and really old people at the end of a long life. Brazil seems to be catching up to us in this and will be confronted with these problems sooner or later. A far-sighted discussion already at this time seems thus to be useful. 3. The article, however, does not want to conclude with the rather depressing state of affairs of problems alternatingly superseding each other. Despite the caution which definitely has a place when prognoses are being made on the basis of extrapolations from historical findings, the foreseeable development especially of the epidemiologic transition in the direction of a rectangular survival curve does nevertheless provide good reason for being rather optimistic towards the future: first in regards to the development in our own countries, but then - assuming that the present similar tendencies of development are stuck to - also in regard to Brazil.

Self-optimization module for scheduling using case-based reasoning

Metaheuristics performance is highly dependent of the respective parameters which need to be tuned. Parameter tuning may allow a larger flexibility and robustness but requires a careful initialization. The process of defining which parameters setting should be used is not obvious. The values for parameters depend mainly on the problem, the instance to be solved, the search time available to spend in solving the problem, and the required quality of solution. This paper presents a learning module proposal for an autonomous parameterization of Metaheuristics, integrated on a Multi-Agent System for the resolution of Dynamic Scheduling problems. The proposed learning module is inspired on Autonomic Computing Self-Optimization concept, defining that systems must continuously and proactively improve their performance. For the learning implementation it is used Case-based Reasoning, which uses previous similar data to solve new cases. In the use of Case-based Reasoning it is assumed that similar cases have similar solutions. After a literature review on topics used, both AutoDynAgents system and Self-Optimization module are described. Finally, a computational study is presented where the proposed module is evaluated, obtained results are compared with previous ones, some conclusions are reached, and some future work is referred. It is expected that this proposal can be a great contribution for the self-parameterization of Metaheuristics and for the resolution of scheduling problems on dynamic environments.

Meta-heuristics self-configuration for scheduling

Scheduling resolution requires the intervention of highly skilled human problemsolvers. This is a very hard and challenging domain because current systems are becoming more and more complex, distributed, interconnected and subject to rapidly changing. A natural Autonomic Computing evolution in relation to Current Computing is to provide systems with Self-Managing ability with a minimum human interference. This paper addresses the resolution of complex scheduling problems using cooperative negotiation. A Multi-Agent Autonomic and Meta-heuristics based framework with self-configuring capabilities is proposed.

Self-optimization for dynamic scheduling in manufacturing systems

Scheduling is a critical function that is present throughout many industries and applications. A great need exists for developing scheduling approaches that can be applied to a number of different scheduling problems with significant impact on performance of business organizations. A challenge is emerging in the design of scheduling support systems for manufacturing environments where dynamic adaptation and optimization become increasingly important. In this paper, we describe a Self-Optimizing Mechanism for Scheduling System through Nature Inspired Optimization Techniques (NIT).

MASDScheGATS: a prototype system for dynamic scheduling

A manufacturing system has a natural dynamic nature observed through several kinds of random occurrences and perturbations on working conditions and requirements over time. For this kind of environment it is important the ability to efficient and effectively adapt, on a continuous basis, existing schedules according to the referred disturbances, keeping performance levels. The application of Meta-Heuristics and Multi-Agent Systems to the resolution of this class of real world scheduling problems seems really promising. This paper presents a prototype for MASDScheGATS (Multi-Agent System for Distributed Manufacturing Scheduling with Genetic Algorithms and Tabu Search).

BASS 4: a software system for ergonomic design and evaluation of working hours

OBJECTIVE: To extend an existing computer programme for the evaluation and design of shift schedules (BASS 3) by integrating workload as well as economic aspects. METHODS: The redesigned prototype BASS 4 includes a new module with a suitable and easily applicable screening method (EBA) for the assessment of the intensity of physical, emotional and cognitive workload components and their temporal patterns. Specified criterion functions based on these ratings allow for an adjustment of shift and rest duration according to the intensity of physical and mental workload. Furthermore, with regard to interactive effects both workload and temporal conditions, e.g. time of day, are taken into account. In a second new module, important economic aspects and criteria have been implemented. Different ergonomic solutions for scheduling problems can now also be evaluated with regard to their economic costs. RESULTS: The new version of the computer programme (BASS 4) can now simultaneously take into account numerous ergonomic, legal, agreed and economic criteria for the design and evaluation of working hours. CONCLUSIONS: BASS 4 can now be used as an instrument for the design and the evaluation of working hours with regard to legal, ergonomic and economic aspects at the shop floor as well as in administrative (e.g. health and safety inspection) and research problems.

Case-based reasoning for meta-heuristics self-parameterization in a multi-agent scheduling system

A novel agent-based approach to Meta-Heuristics self-configuration is proposed in this work. Meta-heuristics are examples of algorithms where parameters need to be set up as efficient as possible in order to unsure its performance. This paper presents a learning module for self-parameterization of Meta-heuristics (MHs) in a Multi-Agent System (MAS) for resolution of scheduling problems. The learning is based on Case-based Reasoning (CBR) and two different integration approaches are proposed. A computational study is made for comparing the two CBR integration perspectives. In the end, some conclusions are reached and future work outlined.

Self-optimization aspects for dynamic scheduling

Scheduling is a critical function that is present throughout many industries and applications. A great need exists for developing scheduling approaches that can be applied to a number of different scheduling problems with significant impact on performance of business organizations. A challenge is emerging in the design of scheduling support systems for manufacturing environments where dynamic adaptation and optimization become increasingly important. At this scenario, self-optimizing arise as the ability of the agent to monitor its state and performance and proactively tune itself to respond to environmental stimuli.

Self-managing agents for dynamic scheduling in manufacturing

The main purpose of this paper is to propose a Multi-Agent Autonomic and Bio-Inspired based framework with selfmanaging capabilities to solve complex scheduling problems using cooperative negotiation. Scheduling resolution requires the intervention of highly skilled human problem-solvers. This is a very hard and challenging domain because current systems are becoming more and more complex, distributed, interconnected and subject to rapidly changing. A natural Autonomic Computing (AC) evolution in relation to Current Computing is to provide systems with Self-Managing ability with a minimum human interference.