Is Our Students Learning - QuestionMark: Extending E-Assessment Systems for Adapative Marking and Feedback

Our key contribution is a flexible, automated marking system that adds desirable functionality to existing E-Assessment systems. In our approach, any given E-Assessment system is relegated to a data-collection mechanism, whereas marking and the generation and distribution of personalised per-student feedback is handled separately by our own system. This allows content-rich Microsoft Word feedback documents to be generated and distributed to every student simultaneously according to a per-assessment schedule.

The feedback is adaptive in that it corresponds to the answers given by the student and provides guidance on where they may have gone wrong. It is not limited to simple multiple choice which are the most prescriptive question type offered by most E-Assessment Systems and as such most straightforward to mark consistently and provide individual per-alternative feedback strings. It is also better equipped to handle the use of mathematical symbols and images within the feedback documents which is more flexible than existing E-Assessment systems, which can only handle simple text strings.

As well as MCQs the system reliably and robustly handles Multiple Response, Text Matching and Numeric style questions in a more flexible manner than Questionmark: Perception and other E-Assessment Systems. It can also reliably handle multi-part questions where the response to an earlier question influences the answer to a later one and can adjust both scoring and feedback appropriately.

New question formats can be added at any time provided a corresponding marking method conforming to certain templates can also be programmed. Indeed, any question type for which a programmatic method of marking can be devised may be supported by our system. Furthermore, since the student’s response to each is question is marked programmatically, our system can be set to allow for minor deviations from the correct answer, and if appropriate award partial marks.

Remoção de instrumentos fraturados em Endodontia

A área da Endodontia está em constante progresso. Os materiais utilizados nos instrumentos Endodônticos, primordialmente, eram construídos com base em cordas de piano. Seguiu-se uma fase em que estes eram de aço de carbono, mas sofriam corrosão significativa devido ao cloro presente no hipoclorito de sódio, bem como aos processos de esterilização a vapor. Foi necessário evoluir novamente e foram introduzidos os instrumentos de aço inoxidável. Estes apresentavam alta resistência e dureza, mas algumas desvantagens devido à falta de flexibilidade. Atualmente, os instrumentos de NiTi proporcionam uma melhor flexibilidade e efeito de memória de forma. A fratura de instrumentos em Endodontia pode ocorrer por dois grandes fatores: a torção e a flexão por fadiga cíclica, podendo também ser a conjugação de ambos. Fatores anatômicos, como a curvatura e a largura do canal ou outros fatores como ciclos de esterilização, número de usos, etc., podem influenciar uma fratura mais precoce dos instrumentos. A incidência da fratura de instrumentos, embora seja pouco frequente, pode ser reduzida a um mínimo absoluto se os clínicos usarem as características de torque e de stress adequadas. Um bom conhecimento dos procedimentos clínicos, da anatomia, dos materiais e a utilização de instrumentos como o microscópio podem ajudar a prevenir ou a resolver a fratura dos instrumentos. No entanto, a melhor forma de prevenir a fratura é a sua prevenção. A desinfeção é o procedimento mais importante para o sucesso de um tratamento Endodôntico, portanto para que isto seja possível, é necessária uma boa conformação canalar. A presença de um instrumento no interior do canal pode comprometer a desinfecção, especialmente caso tenha ocorrido numa fase precoce da preparação canalar. Aquando da fratura de um instrumento, deve-se refletir sobre os procedimentos a seguir, podendo-se optar por várias abordagens, nomeadamente pela manutenção do instrumento no canal e obturação incorporando o fragmento, pela remoção do segmento através de diversas técnicas (ultrassons ou técnicas de microtubos, etc.), e ainda pela realização do bypass ou pela cirurgia Endodôntica. Em última instância pode ser realizada a extração do elemento dentário.

'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.

'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.

'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,

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.

New Directions in Commercial Secrecy and Encryption Protocols

Secure transmission of bulk data is of interest to many content providers. A commercially-viable distribution of content requires technology to prevent unauthorised access. Encryption tools are powerful, but have a performance cost. Without encryption, intercepted data may be illicitly duplicated and re-sold, or its commercial value diminished because its secrecy is lost. Two technical solutions make it possible to perform bulk transmissions while retaining security without too high a performance overhead. These are: 1. a) hierarchical encryption - the stronger the encryption, the harder it is to break but also the more computationally expensive it is. A hierarchical approach to key exchange means that simple and relatively weak encryption and keys are used to encrypt small chunks of data, for example 10 seconds of video. Each chunk has its own key. New keys for this bottom-level encryption are exchanged using a slightly stronger encryption, for example a whole-video key could govern the exchange of the 10-second chunk keys. At a higher level again, there could be daily or weekly keys, securing the exchange of whole-video keys, and at a yet higher level, a subscriber key could govern the exchange of weekly keys. At higher levels, the encryption becomes stronger but is used less frequently, so that the overall computational cost is minimal. The main observation is that the value of each encrypted item determines the strength of the key used to secure it. 2. b) non-symbolic fragmentation with signal diversity - communications are usually assumed to be sent over a single communications medium, and the data to have been encrypted and/or partitioned in whole-symbol packets. Network and path diversity break up a file or data stream into fragments which are then sent over many different channels, either in the same network or different networks. For example, a message could be transmitted partly over the phone network and partly via satellite. While TCP/IP does a similar thing in sending different packets over different paths, this is done for load-balancing purposes and is invisible to the end application. Network and path diversity deliberately introduce the same principle as a secure communications mechanism - an eavesdropper would need to intercept not just one transmission path but all paths used. Non-symbolic fragmentation of data is also introduced to further confuse any intercepted stream of data. This involves breaking up data into bit strings which are subsequently disordered prior to transmission. Even if all transmissions were intercepted, the cryptanalyst still needs to determine fragment boundaries and correctly order them. These two solutions depart from the usual idea of data encryption. Hierarchical encryption is an extension of the combined encryption of systems such as PGP but with the distinction that the strength of encryption at each level is determined by the "value" of the data being transmitted. Non- symbolic fragmentation suppresses or destroys bit patterns in the transmitted data in what is essentially a bit-level transposition cipher but with unpredictable irregularly-sized fragments. Both technologies have applications outside the commercial and can be used in conjunction with other forms of encryption, being functionally orthogonal.

Applied web traffic analysis for numerical encoding of SQL Injection attack features.

SQL Injection Attack (SQLIA) remains a technique used by a computer network intruder to pilfer an organisation’s confidential data. This is done by an intruder re-crafting web form’s input and query strings used in web requests with malicious intent to compromise the security of an organisation’s confidential data stored at the back-end database. The database is the most valuable data source, and thus, intruders are unrelenting in constantly evolving new techniques to bypass the signature’s solutions currently provided in Web Application Firewalls (WAF) to mitigate SQLIA. There is therefore a need for an automated scalable methodology in the pre-processing of SQLIA features fit for a supervised learning model. However, obtaining a ready-made scalable dataset that is feature engineered with numerical attributes dataset items to train Artificial Neural Network (ANN) and Machine Leaning (ML) models is a known issue in applying artificial intelligence to effectively address ever evolving novel SQLIA signatures. This proposed approach applies numerical attributes encoding ontology to encode features (both legitimate web requests and SQLIA) to numerical data items as to extract scalable dataset for input to a supervised learning model in moving towards a ML SQLIA detection and prevention model. In numerical attributes encoding of features, the proposed model explores a hybrid of static and dynamic pattern matching by implementing a Non-Deterministic Finite Automaton (NFA). This combined with proxy and SQL parser Application Programming Interface (API) to intercept and parse web requests in transition to the back-end database. In developing a solution to address SQLIA, this model allows processed web requests at the proxy deemed to contain injected query string to be excluded from reaching the target back-end database. This paper is intended for evaluating the performance metrics of a dataset obtained by numerical encoding of features ontology in Microsoft Azure Machine Learning (MAML) studio using Two-Class Support Vector Machines (TCSVM) binary classifier. This methodology then forms the subject of the empirical evaluation.

TROMBONE MUSIC OF SCANDINAVIA: A STUDY OF TROMBONE SOLO AND CHAMBER WORKS FROM SWEDEN, NORWAY, AND DENMARK

This dissertation project aims to establish Scandinavian trombone solo and chamber works as a major contribution to the trombone repertoire. From the late 19th century to modern day, Scandinavian composers have produced a steady output of trombone works of substantial musical quality. Deep-rooted in the traditions of strong military wind bands, Scandinavia has also produced an unusual number of trombone virtuosos, ranging from those holding positions in leading orchestras, and internationally renowned pedagogues, to trombonists enjoying careers as soloists. In this study I propose that it is the symbiotic relationship between strong performers and traditionally nationalist composers that created the fertile environment for the large number of popular trombone solo and chamber repertoire not seen in any other region besides the Paris Conservatory and its infamous test pieces. I also interpret the selected repertoire through the prism of nationalism and influence of folk music, and convey that the allure of the mystic Nordic folk influences enhances the appeal of the Scandinavian trombone repertoire to world-wide audiences and performers. The dissertation project was realized over three solo recitals, each showcasing the music of Sweden, Norway, and Denmark respectively. For each program, I looked to choose a standard work from the trombone solo repertoire, a work written for or by a native virtuoso, and a lesser-known work that warrants the attention of other performers for its musical qualities. The recital of Swedish music presented Mandrake in the Corner by Christian Lindberg, Subadobe by Frederik Högberg, A Christian Song by Jan Sandström, and Concertino for trombone and strings by Lars-Erik Larsson. The recital of Norwegian music presented Concerto for Trombone op. 76 by Egil Hovland, Ordner Seg by Øystein Baadsvik, Elegi by Magne Amdahl, and Concerto in F major by Ole Olsen. The recital of Danish music presented Rapsodia Borealis by Søren Hyldgaard, Madrigal by Bo Gunge, Romance for trombone and piano by Axel Jørgensen, Concerto for trombone by Launy Grøndahl, and Three Swedish Tunes by Mogens Andresen. Through the performance of works from these three countries, the dissertation establishes Scandinavia as a rich source of solo trombone repertoire perpetuated by nationalist composers and virtuosos, as well as providing a brief survey of Scandinavian trombone works of various instrumentation and difficulty levels to be enjoyed by student, professional, and amateur performers and their audience.

PROPOSTA DE MODELO DE MEDIÇÕES PARA CONTRATAÇÃO DO GERENCIAMENTO DE PROCESSO DE NEGÓCIO (BUSINESS PROCESS MANAGEMENT- BPM)

O Gerenciamento de Processo de Negócio (Business Process Management- BPM) tem sido uma prática adotada pelas organizações públicas e privadas. O BPM possibilita a identificação eficaz das necessidades e das informações necessárias para suportar a operacionalização ou a automatização do processo de negócio. Considerando que as organizações têm necessitado terceirizar esse serviço, o objetivo desse trabalho foi propor um modelo de medição para contratação dos serviços de BPM. Para atender a esse objetivo, o modelo conceitual construído partiu da premissa que a gestão da contratação de um BPM deve fornecer critérios para mensurar a demanda, ou serviço, avaliar a qualidade dos serviços prestados e a qualidade do produto recebido. O estudo adotou como instrumentos de coleta de dados a pesquisa documental e a revisão sistemática. Com base nos objetivos e questões de pesquisa foram identificados os strings para busca, definidas as fontes de busca, critérios de inclusão e exclusão dos resultados. Todos os trabalhos selecionados foram lidos e analisados e foi utilizado um mapa mental para consolidação dos resultados. Foi utilizado o GQM (Goal, Questions, Metrics) para a elaboração das medições e adotado o estudo de caso. Parte das medições propostas foram aplicadas em 13 modelos de processo de negócio do mundo real com o objetivo de verificar sua coerência e comparar os resultados. Foi realizada entrevista com especialista em modelagem de processos de negócios para avaliar os resultados obtidos e, na percepção deste especialista a maior parte das métricas propostas pela pesquisa é adequada à realidade de mercado, considerando o contexto de terceirização desse serviço.

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.

Experiências formativas de jovens instrumentistas : um estudo a partir de entrevistas narrativas

Dissertação (mestrado)—Universidade de Brasília, Instituto de Artes, Departamento de Música, Programa de Pós-graduação em Música, 2015.

'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.

'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.