Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Exact solutions for the agricultural and the two-dimensional packing problems

Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions.

Response programming in dementia of the Alzheimer type: A kinematic analysis

Although planning is important for the functioning of patients with dementia of the Alzheimer Type (DAT), little is known about response programming in DAT. This study used a cueing paradigm coupled with quantitative kinematic analysis to document the preparation and execution of movements made by a group of 12 DAT patients and their age and sex matched controls. Participants connected a series of targets placed upon a WACOM SD420 graphics tablet, in response to the pattern of illumination of a set of light emitting diodes (LEDs). In one condition, participants could programme the upcoming movement, whilst in another they were forced to reprogramme this movement on-line (i.e. they were not provided with advance information about the location of the upcoming target). DAT patients were found to have programming deficits, taking longer to initiate movements; particularly in the absence of cues. While problems spontaneously programming a movement might cause a greater reliance upon on-line guidance, when both groups were required to guide the movement on-line, DAT patients continued to show slower and less efficient movements implying declining sensori-motor function; these differences were not simply due to strategy or medication status. (C) 1997 Elsevier Science Ltd.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.

Risk Aversion in a Mixed-Integer Nonlinear Approach to Support Decision-Making for a Hydro Power Producer

In this paper, a mixed-integer nonlinear approach is proposed to support decision-making for a hydro power producer, considering a head-dependent hydro chain. The aim is to maximize the profit of the hydro power producer from selling energy into the electric market. As a new contribution to earlier studies, a risk aversion criterion is taken into account, as well as head-dependency. The volatility of the expected profit is limited through the conditional value-at-risk (CVaR). The proposed approach has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems.

Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to eat her studies, we model the on-off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement.

Hydro energy systems management in Portugal: Profit-based evaluation of a mixed-integer nonlinear approach

In this paper, a novel mixed-integer nonlinear approach is proposed to solve the short-term hydro scheduling problem in the day-ahead electricity market, considering not only head-dependency, but also start/stop of units, discontinuous operating regions and discharge ramping constraints. Results from a case study based on one of the main Portuguese cascaded hydro energy systems are presented, showing that the proposedmixed-integer nonlinear approach is proficient. Conclusions are duly drawn. (C) 2010 Elsevier Ltd. All rights reserved.

Distributed energy resource short-term scheduling using signaled particle swarm optimization

Distributed Energy Resources (DER) scheduling in smart grids presents a new challenge to system operators. The increase of new resources, such as storage systems and demand response programs, results in additional computational efforts for optimization problems. On the other hand, since natural resources, such as wind and sun, can only be precisely forecasted with small anticipation, short-term scheduling is especially relevant requiring a very good performance on large dimension problems. Traditional techniques such as Mixed-Integer Non-Linear Programming (MINLP) do not cope well with large scale problems. This type of problems can be appropriately addressed by metaheuristics approaches. This paper proposes a new methodology called Signaled Particle Swarm Optimization (SiPSO) to address the energy resources management problem in the scope of smart grids, with intensive use of DER. The proposed methodology’s performance is illustrated by a case study with 99 distributed generators, 208 loads, and 27 storage units. The results are compared with those obtained in other methodologies, namely MINLP, Genetic Algorithm, original Particle Swarm Optimization (PSO), Evolutionary PSO, and New PSO. SiPSO performance is superior to the other tested PSO variants, demonstrating its adequacy to solve large dimension problems which require a decision in a short period of time.

Addressing the facilities layout design problem through constraint logic programming

One of the most difficult problems that face researchers experimenting with complex systems in real world applications is the Facility Layout Design Problem. It relies with the design and location of production lines, machinery and equipment, inventory storage and shipping facilities. In this work it is intended to address this problem through the use of Constraint Logic Programming (CLP) technology. The use of Genetic Algorithms (GA) as optimisation technique in CLP environment is also an issue addressed. The approach aims the implementation of genetic algorithm operators following the CLP paradigm.

An efficient method for optimal location and sizing of fixed and switched shunt capacitors in large distribution systems

This paper proposes a computationally efficient methodology for the optimal location and sizing of static and switched shunt capacitors in large distribution systems. The problem is formulated as the maximization of the savings produced by the reduction in energy losses and the avoided costs due to investment deferral in the expansion of the network. The proposed method selects the nodes to be compensated, as well as the optimal capacitor ratings and their operational characteristics, i.e. fixed or switched. After an appropriate linearization, the optimization problem was formulated as a large-scale mixed-integer linear problem, suitable for being solved by means of a widespread commercial package. Results of the proposed optimizing method are compared with another recent methodology reported in the literature using two test cases: a 15-bus and a 33-bus distribution network. For the both cases tested, the proposed methodology delivers better solutions indicated by higher loss savings, which are achieved with lower amounts of capacitive compensation. The proposed method has also been applied for compensating to an actual large distribution network served by AES-Venezuela in the metropolitan area of Caracas. A convergence time of about 4 seconds after 22298 iterations demonstrates the ability of the proposed methodology for efficiently handling large-scale compensation problems.

Optimal methodology for distribution systems reconfiguration based on OPF and solved by decomposition technique

This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, balancing load among feeders and subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. The Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the Master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS. The effectiveness of the proposal is demonstrated through two examples extracted from the literature.

A distributed system for learning programming on-line

Several Web-based on-line judges or on-line programming trainers have been developed in order to allow students to train their programming skills. However, their pedagogical functionalities in the learning of programming have not been clearly defined. EduJudge is a project which aims to integrate the “UVA On-line Judge”, an existing on-line programming trainer with an important number of problems and users, into an effective educational environment consisting of the e-learning platform Moodle and the competitive learning tool QUESTOURnament. The result is the EduJudge system which allows teachers to apply different pedagogical approaches using a proven e-learning platform, makes problems easy to search through an effective search engine, and provides an automated evaluation of the solutions submitted to these problems. The final objective is to provide new learning strategies to motivate students and present programming as an easy and attractive challenge. EduJudge has been tried and tested in three algorithms and programming courses in three different Engineering degrees. The students’ motivation and satisfaction levels were analysed alongside the effects of the EduJudge system on students’ academic outcomes. Results indicate that both students and teachers found that among other multiple benefits the EduJudge system facilitates the learning process. Furthermore, the experi- ment also showed an improvement in students’ academic outcomes. It must be noted that the students’ level of satisfaction did not depend on their computer skills or their gender.

Application-specific modified particle swarm optimization for energy resource scheduling considering vehicle-to-grid

This paper presents a modified Particle Swarm Optimization (PSO) methodology to solve the problem of energy resources management with high penetration of distributed generation and Electric Vehicles (EVs) with gridable capability (V2G). The objective of the day-ahead scheduling problem in this work is to minimize operation costs, namely energy costs, regarding he management of these resources in the smart grid context. The modifications applied to the PSO aimed to improve its adequacy to solve the mentioned problem. The proposed Application Specific Modified Particle Swarm Optimization (ASMPSO) includes an intelligent mechanism to adjust velocity limits during the search process, as well as self-parameterization of PSO parameters making it more user-independent. It presents better robustness and convergence characteristics compared with the tested PSO variants as well as better constraint handling. This enables its use for addressing real world large-scale problems in much shorter times than the deterministic methods, providing system operators with adequate decision support and achieving efficient resource scheduling, even when a significant number of alternative scenarios should be considered. The paper includes two realistic case studies with different penetration of gridable vehicles (1000 and 2000). The proposed methodology is about 2600 times faster than Mixed-Integer Non-Linear Programming (MINLP) reference technique, reducing the time required from 25 h to 36 s for the scenario with 2000 vehicles, with about one percent of difference in the objective function cost value.

Programming atomic multicasts in CAN

In Distributed Computer-Controlled Systems (DCCS), a special emphasis must be given to the communication infrastructure, which must provide timely and reliable communication services. CAN networks are usually suitable to support small-scale DCCS. However, they are known to present some reliability problems, which can lead to an unreliable behaviour of the supported applications. In this paper, an atomic multicast protocol for CAN networks is proposed. This protocol explores the CAN synchronous properties, providing a timely and reliable service to the supported applications. The implementation of such protocol in Ada, on top of the Ada version of Real-Time Linux is presented, which is used to demonstrate the advantages and disadvantages of the platform to support reliable communications in DCCS.

Application of integer and fractional models in electrochemical systems

This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.