Dynamic Optimization of SLA-Based Services Scaling Rules

Current advanced cloud infrastructure management solutions allow scheduling actions for dynamically changing the number of running virtual machines (VMs). This approach, however, does not guarantee that the scheduled number of VMs will properly handle the actual user generated workload, especially if the user utilization patterns will change. We propose using a dynamically generated scaling model for the VMs containing the services of the distributed applications, which is able to react to the variations in the number of application users. We answer the following question: How to dynamically decide how many services of each type are needed in order to handle a larger workload within the same time constraints? We describe a mechanism for dynamically composing the SLAs for controlling the scaling of distributed services by combining data analysis mechanisms with application benchmarking using multiple VM configurations. Based on processing of multiple application benchmarks generated data sets we discover a set of service monitoring metrics able to predict critical Service Level Agreement (SLA) parameters. By combining this set of predictor metrics with a heuristic for selecting the appropriate scaling-out paths for the services of distributed applications, we show how SLA scaling rules can be inferred and then used for controlling the runtime scale-in and scale-out of distributed services. We validate our architecture and models by performing scaling experiments with a distributed application representative for the enterprise class of information systems. We show how dynamically generated SLAs can be successfully used for controlling the management of distributed services scaling.

Optimización de la programación(scheduling) en Talleres de Mecanizado

Los problemas de programación de tareas son muy importantes en el mundo actual. Se puede decir que se presentan en todos los fundamentos de la industria moderna, de ahí la importancia de que estos sean óptimos, de forma que se puedan ahorrar recursos que estén asociados al problema. La programación adecuada de trabajos en procesos de manufactura, constituye un importante problema que se plantea dentro de la producción en muchas empresas. El orden en que estos son procesados, no resulta indiferente, sino que determinará algún parámetro de interés, cuyos valores convendrá optimizar en la medida de lo posible. Así podrá verse afectado el coste total de ejecución de los trabajos, el tiempo necesario para concluirlos o el stock de productos en curso que será generado. Esto conduce de forma directa al problema de determinar cuál será el orden más adecuado para llevar a cabo los trabajos con vista a optimizar algunos de los anteriores parámetros u otros similares. Debido a las limitaciones de las técnicas de optimización convencionales, en la presente tesis se presenta una metaheurística basada en un Algoritmo Genético Simple (Simple Genetic Algorithm, SGA), para resolver problemas de programación de tipo flujo general (Job Shop Scheduling, JSS) y flujo regular (Flow Shop Scheduling, FSS), que están presentes en un taller con tecnología de mecanizado con el objetivo de optimizar varias medidas de desempeño en un plan de trabajo. La aportación principal de esta tesis, es un modelo matemático para medir el consumo de energía, como criterio para la optimización, de las máquinas que intervienen en la ejecución de un plan de trabajo. Se propone además, un método para mejorar el rendimiento en la búsqueda de las soluciones encontradas, por parte del Algoritmo Genético Simple, basado en el aprovechamiento del tiempo ocioso. ABSTRACT The scheduling problems are very important in today's world. It can be said to be present in all the basics of modern industry, hence the importance that these are optimal, so that they can save resources that are associated with the problem. The appropriate programming jobs in manufacturing processes is an important problem that arises in production in many companies. The order in which they are processed, it is immaterial, but shall determine a parameter of interest, whose values agree optimize the possible. This may be affected the total cost of execution of work, the time needed to complete them or the stock of work in progress that will be generated. This leads directly to the problem of determining what the most appropriate order to carry out the work in order to maximize some of the above parameters or other similar. Due to the limitations of conventional optimization techniques, in this work present a metaheuristic based on a Simple Genetic Algorithm (Simple Genetic Algorithm, SGA) to solve programming problems overall flow rate (Job Shop Scheduling, JSS) and regular flow (Flow Shop Scheduling, FSS), which are present in a workshop with machining technology in order to optimize various performance measures in a plan. The main contribution of this thesis is a mathematical model to measure the energy consumption as a criterion for the optimization of the machines involved in the implementation of a work plan. It also proposes a method to improve performance in finding the solutions, by the simple genetic algorithm, based on the use of idle time.

OSIA: Out-of-order scheduling for in-order arriving in concurrent multi-path transfer.

One major problem of concurrent multi-path transfer (CMT) scheme in multi-homed mobile networks is that the utilization of different paths with diverse delays may cause packet reordering among packets of the same ?ow. In the case of TCP-like, the reordering exacerbates the problem by bringing more timeouts and unnecessary retransmissions, which eventually degrades the throughput of connections considerably. To address this issue, we ?rst propose an Out-of-order Scheduling for In-order Arriving (OSIA), which exploits the sending time discrepancy to preserve the in-order packet arrival. Then, we formulate the optimal traf?c scheduling as a constrained optimization problem and derive its closedform solution by our proposed progressive water-?lling solution. We also present an implementation to enforce the optimal scheduling scheme using cascaded leaky buckets with multiple faucets, which provides simple guidelines on maximizing the utilization of aggregate bandwidth while decreasing the probability of triggering 3 dupACKs. Compared with previous work, the proposed scheme has lower computation complexity and can also provide the possibility for dynamic network adaptability and ?ner-grain load balancing. Simulation results show that our scheme signi?cantly alleviates reordering and enhances transmission performance.

Transformation�based implementation and optimization of programs exploiting the basic Andorra model.

The characteristics of CC and CLP systems are in principle very dierent However a recent trend towards convergence in the implementation techniques for these systems can be observed While CLP and Prolog systems have been incorporating capabilities to deal with userdened suspension and coroutining CC compilers have been trying to coalesce negrained tasks into coarsergrained sequential threads This convergence of techniques opens up the possibility of having a general purpose kernel language and abstract machine to serve as a compilation target for a variety of userlevel languages We propose a transformation technique directed towards such an objective In particular we report on techniques to support the Andorra computational model essentially emulating the AndorraI system via program transformation into a sequential language with delay primitives The system is automatic comprising an optional program analyzer and a basic transformer to the kernel language It turns out that a simple parallel CLP or Prolog system with dynamic scheduling is sucient as a kernel language for this purpose The preliminary results are quite encouraging performance of the resulting system is comparable to the current AndorraI implementation.

Energy-based Fair Queuing: Energy-centric Processor Scheduling Algorithm for Battery-limited Mobile Systems

Los dispositivos móviles modernos disponen cada vez de más funcionalidad debido al rápido avance de las tecnologías de las comunicaciones y computaciones móviles. Sin embargo, la capacidad de la batería no ha experimentado un aumento equivalente. Por ello, la experiencia de usuario en los sistemas móviles modernos se ve muy afectada por la vida de la batería, que es un factor inestable de difícil de control. Para abordar este problema, investigaciones anteriores han propuesto un esquema de gestion del consumo (PM) centrada en la energía y que proporciona una garantía sobre la vida operativa de la batería mediante la gestión de la energía como un recurso de primera clase en el sistema. Como el planificador juega un papel fundamental en la administración del consumo de energía y en la garantía del rendimiento de las aplicaciones, esta tesis explora la optimización de la experiencia de usuario para sistemas móviles con energía limitada desde la perspectiva de un planificador que tiene en cuenta el consumo de energía en un contexto en el que ésta es un recurso de primera clase. En esta tesis se analiza en primer lugar los factores que contribuyen de forma general a la experiencia de usuario en un sistema móvil. Después se determinan los requisitos esenciales que afectan a la experiencia de usuario en la planificación centrada en el consumo de energía, que son el reparto proporcional de la potencia, el cumplimiento de las restricciones temporales, y cuando sea necesario, el compromiso entre la cuota de potencia y las restricciones temporales. Para cumplir con los requisitos, el algoritmo clásico de fair queueing y su modelo de referencia se extienden desde los dominios de las comunicaciones y ancho de banda de CPU hacia el dominio de la energía, y en base a ésto, se propone el algoritmo energy-based fair queueing (EFQ) para proporcionar una planificación basada en la energía. El algoritmo EFQ está diseñado para compartir la potencia consumida entre las tareas mediante su planificación en función de la energía consumida y de la cuota reservada. La cuota de consumo de cada tarea con restricciones temporales está protegida frente a diversos cambios que puedan ocurrir en el sistema. Además, para dar mejor soporte a las tareas en tiempo real y multimedia, se propone un mecanismo para combinar con el algoritmo EFQ para dar preferencia en la planificación durante breves intervalos de tiempo a las tareas más urgentes con restricciones temporales.Las propiedades del algoritmo EFQ se evaluan a través del modelado de alto nivel y la simulación. Los resultados de las simulaciones indican que los requisitos esenciales de la planificación centrada en la energía pueden lograrse. El algoritmo EFQ se implementa más tarde en el kernel de Linux. Para evaluar las propiedades del planificador EFQ basado en Linux, se desarrolló un banco de pruebas experimental basado en una sitema empotrado, un programa de banco de pruebas multihilo, y un conjunto de pruebas de código abierto. A través de experimentos específicamente diseñados, esta tesis verifica primero las propiedades de EFQ en la gestión de la cuota de consumo de potencia y la planificación en tiempo real y, a continuación, explora los beneficios potenciales de emplear la planificación EFQ en la optimización de la experiencia de usuario para sistemas móviles con energía limitada. Los resultados experimentales sobre la gestión de la cuota de energía muestran que EFQ es más eficaz que el planificador de Linux-CFS en la gestión de energía, logrando un reparto proporcional de la energía del sistema independientemente de en qué dispositivo se consume la energía. Los resultados experimentales en la planificación en tiempo real demuestran que EFQ puede lograr de forma eficaz, flexible y robusta el cumplimiento de las restricciones temporales aunque se dé el caso de aumento del el número de tareas o del error en la estimación de energía. Por último, un análisis comparativo de los resultados experimentales sobre la optimización de la experiencia del usuario demuestra que, primero, EFQ es más eficaz y flexible que los algoritmos tradicionales de planificación del procesador, como el que se encuentra por defecto en el planificador de Linux y, segundo, que proporciona la posibilidad de optimizar y preservar la experiencia de usuario para los sistemas móviles con energía limitada. Abstract Modern mobiledevices have been becoming increasingly powerful in functionality and entertainment as the next-generation mobile computing and communication technologies are rapidly advanced. However, the battery capacity has not experienced anequivalent increase. The user experience of modern mobile systems is therefore greatly affected by the battery lifetime,which is an unstable factor that is hard to control. To address this problem, previous works proposed energy-centric power management (PM) schemes to provide strong guarantee on the battery lifetime by globally managing energy as the first-class resource in the system. As the processor scheduler plays a pivotal role in power management and application performance guarantee, this thesis explores the user experience optimization of energy-limited mobile systemsfrom the perspective of energy-centric processor scheduling in an energy-centric context. This thesis first analyzes the general contributing factors of the mobile system user experience.Then itdetermines the essential requirements on the energy-centric processor scheduling for user experience optimization, which are proportional power sharing, time-constraint compliance, and when necessary, a tradeoff between the power share and the time-constraint compliance. To meet the requirements, the classical fair queuing algorithm and its reference model are extended from the network and CPU bandwidth sharing domain to the energy sharing domain, and based on that, the energy-based fair queuing (EFQ) algorithm is proposed for performing energy-centric processor scheduling. The EFQ algorithm is designed to provide proportional power shares to tasks by scheduling the tasks based on their energy consumption and weights. The power share of each time-sensitive task is protected upon the change of the scheduling environment to guarantee a stable performance, and any instantaneous power share that is overly allocated to one time-sensitive task can be fairly re-allocated to the other tasks. In addition, to better support real-time and multimedia scheduling, certain real-time friendly mechanism is combined into the EFQ algorithm to give time-limited scheduling preference to the time-sensitive tasks. Through high-level modelling and simulation, the properties of the EFQ algorithm are evaluated. The simulation results indicate that the essential requirements of energy-centric processor scheduling can be achieved. The EFQ algorithm is later implemented in the Linux kernel. To assess the properties of the Linux-based EFQ scheduler, an experimental test-bench based on an embedded platform, a multithreading test-bench program, and an open-source benchmark suite is developed. Through specifically-designed experiments, this thesis first verifies the properties of EFQ in power share management and real-time scheduling, and then, explores the potential benefits of employing EFQ scheduling in the user experience optimization for energy-limited mobile systems. Experimental results on power share management show that EFQ is more effective than the Linux-CFS scheduler in managing power shares and it can achieve a proportional sharing of the system power regardless of on which device the energy is spent. Experimental results on real-time scheduling demonstrate that EFQ can achieve effective, flexible and robust time-constraint compliance upon the increase of energy estimation error and task number. Finally, a comparative analysis of the experimental results on user experience optimization demonstrates that EFQ is more effective and flexible than traditional processor scheduling algorithms, such as those of the default Linux scheduler, in optimizing and preserving the user experience of energy-limited mobile systems.

Optimization methods for the operating room management under uncertainty: stochastic programming vs. decomposition approach

The operating theatres are the engine of the hospitals; proper management of the operating rooms and its staff represents a great challenge for managers and its results impact directly in the budget of the hospital. This work presents a MILP model for the efficient schedule of multiple surgeries in Operating Rooms (ORs) during a working day. This model considers multiple surgeons and ORs and different types of surgeries. Stochastic strategies are also implemented for taking into account the uncertain in surgery durations (pre-incision, incision, post-incision times). In addition, a heuristic-based methods and a MILP decomposition approach is proposed for solving large-scale ORs scheduling problems in computational efficient way. All these computer-aided strategies has been implemented in AIMMS, as an advanced modeling and optimization software, developing a user friendly solution tool for the operating room management under uncertainty.

Managing daily surgery schedules in a teaching hospital: a mixed-integer optimization approach

Background: This study examined the daily surgical scheduling problem in a teaching hospital. This problem relates to the use of multiple operating rooms and different types of surgeons in a typical surgical day with deterministic operation durations (preincision, incision, and postincision times). Teaching hospitals play a key role in the health-care system; however, existing models assume that the duration of surgery is independent of the surgeon's skills. This problem has not been properly addressed in other studies. We analyze the case of a Spanish public hospital, in which continuous pressures and budgeting reductions entail the more efficient use of resources. Methods: To obtain an optimal solution for this problem, we developed a mixed-integer programming model and user-friendly interface that facilitate the scheduling of planned operations for the following surgical day. We also implemented a simulation model to assist the evaluation of different dispatching policies for surgeries and surgeons. The typical aspects we took into account were the type of surgeon, potential overtime, idling time of surgeons, and the use of operating rooms. Results: It is necessary to consider the expertise of a given surgeon when formulating a schedule: such skill can decrease the probability of delays that could affect subsequent surgeries or cause cancellation of the final surgery. We obtained optimal solutions for a set of given instances, which we obtained through surgical information related to acceptable times collected from a Spanish public hospital. Conclusions: We developed a computer-aided framework with a user-friendly interface for use by a surgical manager that presents a 3-D simulation of the problem. Additionally, we obtained an efficient formulation for this complex problem. However, the spread of this kind of operation research in Spanish public health hospitals will take a long time since there is a lack of knowledge of the beneficial techniques and possibilities that operational research can offer for the health-care system.

Integrated component scheduling models for chip shooter machines

This paper focuses on minimizing printed circuit board (PCB) assembly time for a chipshootermachine, which has a movable feeder carrier holding components, a movable X–Y table carrying a PCB, and a rotary turret with multiple assembly heads. The assembly time of the machine depends on two inter-related optimization problems: the component sequencing problem and the feeder arrangement problem. Nevertheless, they were often regarded as two individual problems and solved separately. This paper proposes two complete mathematical models for the integrated problem of the machine. The models are verified by two commercial packages. Finally, a hybrid genetic algorithm previously developed by the authors is presented to solve the model. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total assembly time.

Mathematical Optimization for the Train Timetabling Problem

AMS Subj. Classification: 90C57; 90C10;

Variable Neighborhood Search for the File Transfer Scheduling Problem

ACM Computing Classification System (1998): I.2.8, G.1.6.

Optimization of transit transfer times: A system-wide approach

This dissertation presents a system-wide approach, based on genetic algorithms, for the optimization of transfer times for an entire bus transit system. Optimization of transfer times in a transit system is a complicated problem because of the large set of binary and discrete values involved. The combinatorial nature of the problem imposes a computational burden and makes it difficult to solve by classical mathematical programming methods. ^ The genetic algorithm proposed in this research attempts to find an optimal solution for the transfer time optimization problem by searching for a combination of adjustments to the timetable for all the routes in the system. It makes use of existing scheduled timetables, ridership demand at all transfer locations, and takes into consideration the randomness of bus arrivals. ^ Data from Broward County Transit are used to compute total transfer times. The proposed genetic algorithm-based approach proves to be capable of producing substantial time savings compared to the existing transfer times in a reasonable amount of time. ^ The dissertation also addresses the issues related to spatial and temporal modeling, variability in bus arrival and departure times, walking time, as well as the integration of scheduling and ridership data. ^

Resource management and optimization in wireless mesh networks

A wireless mesh network is a mesh network implemented over a wireless network system such as wireless LANs. Wireless Mesh Networks(WMNs) are promising for numerous applications such as broadband home networking, enterprise networking, transportation systems, health and medical systems, security surveillance systems, etc. Therefore, it has received considerable attention from both industrial and academic researchers. This dissertation explores schemes for resource management and optimization in WMNs by means of network routing and network coding.^ In this dissertation, we propose three optimization schemes. (1) First, a triple-tier optimization scheme is proposed for load balancing objective. The first tier mechanism achieves long-term routing optimization, and the second tier mechanism, using the optimization results obtained from the first tier mechanism, performs the short-term adaptation to deal with the impact of dynamic channel conditions. A greedy sub-channel allocation algorithm is developed as the third tier optimization scheme to further reduce the congestion level in the network. We conduct thorough theoretical analysis to show the correctness of our design and give the properties of our scheme. (2) Then, a Relay-Aided Network Coding scheme called RANC is proposed to improve the performance gain of network coding by exploiting the physical layer multi-rate capability in WMNs. We conduct rigorous analysis to find the design principles and study the tradeoff in the performance gain of RANC. Based on the analytical results, we provide a practical solution by decomposing the original design problem into two sub-problems, flow partition problem and scheduling problem. (3) Lastly, a joint optimization scheme of the routing in the network layer and network coding-aware scheduling in the MAC layer is introduced. We formulate the network optimization problem and exploit the structure of the problem via dual decomposition. We find that the original problem is composed of two problems, routing problem in the network layer and scheduling problem in the MAC layer. These two sub-problems are coupled through the link capacities. We solve the routing problem by two different adaptive routing algorithms. We then provide a distributed coding-aware scheduling algorithm. According to corresponding experiment results, the proposed schemes can significantly improve network performance.^

Power and thermal aware scheduling for real-time computing systems

Over the past few decades, we have been enjoying tremendous benefits thanks to the revolutionary advancement of computing systems, driven mainly by the remarkable semiconductor technology scaling and the increasingly complicated processor architecture. However, the exponentially increased transistor density has directly led to exponentially increased power consumption and dramatically elevated system temperature, which not only adversely impacts the system's cost, performance and reliability, but also increases the leakage and thus the overall power consumption. Today, the power and thermal issues have posed enormous challenges and threaten to slow down the continuous evolvement of computer technology. Effective power/thermal-aware design techniques are urgently demanded, at all design abstraction levels, from the circuit-level, the logic-level, to the architectural-level and the system-level. ^ In this dissertation, we present our research efforts to employ real-time scheduling techniques to solve the resource-constrained power/thermal-aware, design-optimization problems. In our research, we developed a set of simple yet accurate system-level models to capture the processor's thermal dynamic as well as the interdependency of leakage power consumption, temperature, and supply voltage. Based on these models, we investigated the fundamental principles in power/thermal-aware scheduling, and developed real-time scheduling techniques targeting at a variety of design objectives, including peak temperature minimization, overall energy reduction, and performance maximization. ^ The novelty of this work is that we integrate the cutting-edge research on power and thermal at the circuit and architectural-level into a set of accurate yet simplified system-level models, and are able to conduct system-level analysis and design based on these models. The theoretical study in this work serves as a solid foundation for the guidance of the power/thermal-aware scheduling algorithms development in practical computing systems.^

Optimal day-ahead scheduling of integrated urban energy systems

An optimal day-ahead scheduling method (ODSM) for the integrated urban energy system (IUES) is introduced, which considers the reconfigurable capability of an electric distribution network. The hourly topology of a distribution network, a natural gas network, the energy centers including the combined heat and power (CHP) units, different energy conversion devices and demand responsive loads (DRLs), are optimized to minimize the day-ahead operation cost of the IUES. The hourly reconfigurable capability of the electric distribution network utilizing remotely controlled switches (RCSs) is explored and discussed. The operational constraints from the unbalanced three-phase electric distribution network, the natural gas network, and the energy centers are considered. The interactions between the electric distribution network and the natural gas network take place through conversion of energy among different energy vectors in the energy centers. An energy conversion analysis model for the energy center was developed based on the energy hub model. A hybrid optimization method based on genetic algorithm (GA) and a nonlinear interior point method (IPM) is utilized to solve the ODSM model. Numerical studies demonstrate that the proposed ODSM is able to provide the IUES with an effective and economical day-ahead scheduling scheme and reduce the operational cost of the IUES.

'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.