Optimal virtual cluster-based multiprocessor scheduling

Scheduling of constrained deadline sporadic task systems on multiprocessor platforms is an area which has received much attention in the recent past. It is widely believed that finding an optimal scheduler is hard, and therefore most studies have focused on developing algorithms with good processor utilization bounds. These algorithms can be broadly classified into two categories: partitioned scheduling in which tasks are statically assigned to individual processors, and global scheduling in which each task is allowed to execute on any processor in the platform. In this paper we consider a third, more general, approach called cluster-based scheduling. In this approach each task is statically assigned to a processor cluster, tasks in each cluster are globally scheduled among themselves, and clusters in turn are scheduled on the multiprocessor platform. We develop techniques to support such cluster-based scheduling algorithms, and also consider properties that minimize total processor utilization of individual clusters. In the last part of this paper, we develop new virtual cluster-based scheduling algorithms. For implicit deadline sporadic task systems, we develop an optimal scheduling algorithm that is neither Pfair nor ERfair. We also show that the processor utilization bound of us-edf{m/(2m−1)} can be improved by using virtual clustering. Since neither partitioned nor global strategies dominate over the other, cluster-based scheduling is a natural direction for research towards achieving improved processor utilization bounds.

Optimal tuning of fractional controllers using genetic algorithms

This study addresses the optimization of fractional algorithms for the discrete-time control of linear and non-linear systems. The paper starts by analyzing the fundamentals of fractional control systems and genetic algorithms. In a second phase the paper evaluates the problem in an optimization perspective. The results demonstrate the feasibility of the evolutionary strategy and the adaptability to distinct types of systems.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

An optimal boundary fair scheduling

Nowadays, many real-time operating systems discretize the time relying on a system time unit. To take this behavior into account, real-time scheduling algorithms must adopt a discrete-time model in which both timing requirements of tasks and their time allocations have to be integer multiples of the system time unit. That is, tasks cannot be executed for less than one time unit, which implies that they always have to achieve a minimum amount of work before they can be preempted. Assuming such a discrete-time model, the authors of Zhu et al. (Proceedings of the 24th IEEE international real-time systems symposium (RTSS 2003), 2003, J Parallel Distrib Comput 71(10):1411–1425, 2011) proposed an efficient “boundary fair” algorithm (named BF) and proved its optimality for the scheduling of periodic tasks while achieving full system utilization. However, BF cannot handle sporadic tasks due to their inherent irregular and unpredictable job release patterns. In this paper, we propose an optimal boundary-fair scheduling algorithm for sporadic tasks (named BF TeX ), which follows the same principle as BF by making scheduling decisions only at the job arrival times and (expected) task deadlines. This new algorithm was implemented in Linux and we show through experiments conducted upon a multicore machine that BF TeX outperforms the state-of-the-art discrete-time optimal scheduler (PD TeX ), benefiting from much less scheduling overheads. Furthermore, it appears from these experimental results that BF TeX is barely dependent on the length of the system time unit while PD TeX —the only other existing solution for the scheduling of sporadic tasks in discrete-time systems—sees its number of preemptions, migrations and the time spent to take scheduling decisions increasing linearly when improving the time resolution of the system.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Optimal choice between even- and uneven-aged forestry: the case of non-industrial private forest owners

An infinite-horizon discrete time model with multiple size-class structures using a transition matrix is built to assess optimal harvesting schedules in the context of Non-Industrial Private Forest (NIPF) owners. Three model specifications accounting for forest income, financial return on an asset and amenity valuations are considered. Numerical simulations suggest uneven-aged forest management where a rational forest owner adapts her or his forest policy by influencing the regeneration of trees or adjusting consumption dynamics depending on subjective time preference and market return rate dynamics on the financial asset. Moreover she or he does not value significantly non-market benefits captured by amenity valuations relatively to forest income.

Harvest control rule vs optimal harvesting of an age-structured population: The case of the Ibero-Atlantic Sardine Fishery

Research Masters

The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

Blood pressure and LDL-cholesterol targets for prevention of recurrent strokes and cognitive decline in the hypertensive patient: design of the European Society of Hypertension-Chinese Hypertension League Stroke in Hypertension Optimal Treatment randomized trial.

BACKGROUND AND OBJECTIVES: The SBP values to be achieved by antihypertensive therapy in order to maximize reduction of cardiovascular outcomes are unknown; neither is it clear whether in patients with a previous cardiovascular event, the optimal values are lower than in the low-to-moderate risk hypertensive patients, or a more cautious blood pressure (BP) reduction should be obtained. Because of the uncertainty whether 'the lower the better' or the 'J-curve' hypothesis is correct, the European Society of Hypertension and the Chinese Hypertension League have promoted a randomized trial comparing antihypertensive treatment strategies aiming at three different SBP targets in hypertensive patients with a recent stroke or transient ischaemic attack. As the optimal level of low-density lipoprotein cholesterol (LDL-C) level is also unknown in these patients, LDL-C-lowering has been included in the design. PROTOCOL DESIGN: The European Society of Hypertension-Chinese Hypertension League Stroke in Hypertension Optimal Treatment trial is a prospective multinational, randomized trial with a 3 × 2 factorial design comparing: three different SBP targets (1, <145-135; 2, <135-125; 3, <125 mmHg); two different LDL-C targets (target A, 2.8-1.8; target B, <1.8 mmol/l). The trial is to be conducted on 7500 patients aged at least 65 years (2500 in Europe, 5000 in China) with hypertension and a stroke or transient ischaemic attack 1-6 months before randomization. Antihypertensive and statin treatments will be initiated or modified using suitable registered agents chosen by the investigators, in order to maintain patients within the randomized SBP and LDL-C windows. All patients will be followed up every 3 months for BP and every 6 months for LDL-C. Ambulatory BP will be measured yearly. OUTCOMES: Primary outcome is time to stroke (fatal and non-fatal). Important secondary outcomes are: time to first major cardiovascular event; cognitive decline (Montreal Cognitive Assessment) and dementia. All major outcomes will be adjudicated by committees blind to randomized allocation. A Data and Safety Monitoring Board has open access to data and can recommend trial interruption for safety. SAMPLE SIZE CALCULATION: It has been calculated that 925 patients would reach the primary outcome after a mean 4-year follow-up, and this should provide at least 80% power to detect a 25% stroke difference between SBP targets and a 20% difference between LDL-C targets.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

Optimal slopes and speeds in uphill ski mountaineering: a laboratory study.

The purpose of this study was to estimate the energy cost of linear (EC) and vertical displacement (ECvert), mechanical efficiency and main stride parameters during simulated ski mountaineering at different speeds and gradients, to identify an optimal speed and gradient that maximizes performance. 12 subjects roller skied on a treadmill at three different inclines (10, 17 and 24 %) at three different speeds (approximately 70, 80 and 85 % of estimated peak heart rate). Energy expenditure was calculated by indirect calorimetry, while biomechanical parameters were measured with an inertial sensor-based system. At 10 % there was no significant change with speed in EC, ECvert and mechanical efficiency. At 17 and 24 % the fastest speed was significantly more economical. There was a significant effect of gradient on EC, ECvert and mechanical efficiency. The most economical gradient was the steepest one. There was a significant increase of stride frequency with speed. At steep gradients only, relative thrust phase duration decreased significantly, while stride length increased significantly with speed. There was a significant effect of gradient on stride length (decrease with steepness) and relative thrust phase duration (increase with steepness). A combination of a decreased relative thrust phase duration with increased stride length and frequency decreases ECvert. To minimize the energy expenditure to reach the top of a mountain and to optimize performance, ski-mountaineers should choose a steep gradient (~24 %) and, provided they possess sufficient metabolic scope, combine it with a fast speed (~6 km h(-1)).

Implementing the OPTIMAL model : the impact on students' motivation in an elementary school games environment

Optimal challenge occurs when an individual perceives the challenge of the task to be equaled or matched by his or her own skill level (Csikszentmihalyi, 1990). The purpose of this study was to test the impact of the OPTIMAL model on physical education students' motivation and perceptions of optimal challenge across four games categories (i. e. target, batting/fielding, net/wall, invasion). Enjoyment, competence, student goal orientation and activity level were examined in relation to the OPTIMAL model. A total of 22 (17 M; 5 F) students and their parents provided informed consent to take part in the study and were taught four OPTIMAL lessons and four non-OPTIMAL lessons ranging across the four different games categories by their own teacher. All students completed the Task and Ego in Sport Questionnaire (TEOSQ; Duda & Whitehead, 1998), the Intrinsic Motivation Inventory (IMI; McAuley, Duncan, & Tanmien, 1987) and the Children's Perception of Optimal Challenge Instrument (CPOCI; Mandigo, 2001). Sixteen students (two each lesson) were observed by using the System for Observing Fitness Instruction Time tool (SOFTT; McKenzie, 2002). As well, they participated in a structured interview which took place after each lesson was completed. Quantitative results concluded that no overall significant difference was found in motivational outcomes when comparing OPTIMAL and non-OPTIMAL lessons. However, when the lessons were broken down into games categories, significant differences emerged. Levels of perceived competence were found to be higher in non-OPTIMAL batting/fielding lessons compared to OPTIMAL lessons, whereas levels of enjoyment and perceived competence were found to be higher in OPTIMAL invasion lessons in comparison to non-OPTIMAL invasion lessons. Qualitative results revealed significance in feehngs of skill/challenge balance, enjoyment and competence in the OPTIMAL lessons. Moreover, a significance of practically twice the active movement time percentage was found in OPTIMAL lessons in comparison to non-OPTIMAL lessons.