Search results for: multiple objective linear programming

Authors: Omid Borazjani, Mahmoud Roosta, Khodakhast Isapour, Ali Reza Rajabi

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This paper presents an application of Artificial Neural Network (ANN) algorithm for improving power system voltage stability. The training data is obtained by solving several normal and abnormal conditions using the Linear Programming technique. The selected objective function gives minimum deviation of the reactive power control variables, which leads to the maximization of minimum Eigen value of load flow Jacobian. The considered reactive power control variables are switchable VAR compensators, OLTC transformers and excitation of generators. The method has been implemented on a modified IEEE 30-bus test system. The results obtain from the test clearly show that the trained neural network is capable of improving the voltage stability in power system with a high level of precision and speed.

Keywords: Artificial Neural Network (ANN), Load Flow, Voltage Stability, Power Systems.

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Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

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In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.

Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection

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Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

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The Markov decision process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, Dynamic Programming, Monte Carlo simulation, Periodic replacement, Weibull distribution.

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Authors: K. Jaroensutasinee

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The general global behavior of particle S a non-linear (Q - xy)2 potential cannot be revealed a Poincare surface of section method (PSS) because inost trajectories take practically infinitely long time to integrate numerically before they come back to the surface. In this study as an alternative to PSS, a multiple scale perturbation is applied to analyze global adiabatic, non-adiabatic and chaotic behavior of particles in this potential. It was found that the results can be summarized as a form of a Fermi-like map. Additionally, this method gives a variation of global stochasticity criteria with Q.

Keywords: Multiple Scak Perturbation The Poincare Surface or Section, Fermi Map

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Authors: Michael Todinov, Eberechi Weli

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The paper suggests for the first time the use of dynamic programming techniques for optimal risk reduction in the railway industry. It is shown that by using the concept ‘amount of removed risk by a risk reduction option’, the problem related to optimal allocation of a fixed budget to achieve a maximum risk reduction in the railway industry can be reduced to an optimisation problem from dynamic programming. For n risk reduction options and size of the available risk reduction budget B (expressed as integer number), the worst-case running time of the proposed algorithm is O (n x (B+1)), which makes the proposed method a very efficient tool for solving the optimal risk reduction problem in the railway industry. 

Keywords: Optimisation, railway risk reduction, budget constraints, dynamic programming.

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Authors: Vichai Rungreunganaun, Chirawat Woarawichai

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The objective of this research is to calculate the optimal inventory lot-sizing for each supplier and minimize the total inventory cost which includes joint purchase cost of the products, transaction cost for the suppliers, and holding cost for remaining inventory. Genetic algorithms (GAs) are applied to the multi-product and multi-period inventory lot-sizing problems with supplier selection under storage space. Also a maximum storage space for the decision maker in each period is considered. The decision maker needs to determine what products to order in what quantities with which suppliers in which periods. It is assumed that demand of multiple products is known over a planning horizon. The problem is formulated as a mixed integer programming and is solved with the GAs. The detailed computation results are presented.

Keywords: Genetic Algorithms, Inventory lot-sizing, Supplier selection, Storage space.

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Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He

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This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.

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Authors: Jean Berger, Nassirou Lo, Martin Noel

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Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: Search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization.

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Authors: Yun Jong Choi, Nam Woong, PooGyeon Park

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Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.

Keywords: Input saturation, linear-growth bounded disturbances, linear matrix inequality (LMI), variable structure control

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Authors: Abbas Al-Refaie

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This study optimized the performance of plastic extrusion process of drip irrigation pipes using fuzzy goal programming. Two main responses were of main interest; roll thickness and hardness. Four main process factors were studied. The L₁₈ array was then used for experimental design. The individual-moving range control charts were used to assess the stability of the process, while the process capability index was used to assess process performance. Confirmation experiments were conducted at the obtained combination of optimal factor setting by fuzzy goal programming. The results revealed that process capability was improved significantly from -1.129 to 0.8148 for roll thickness and from 0.0965 to 0.714 and hardness. Such improvement results in considerable savings in production and quality costs.

Keywords: Fuzzy goal programming, extrusion process, process capability, irrigation plastic pipes.

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Authors: Oscar Vega Camacho, Andrea Vargas Guevara, Ellery Rowina Ariza

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This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its wastewater treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: Decision making, Markov chain, optimization, wastewater.

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Authors: Monica Hoedltke Pietruchinski, Andrey Ricardo Pimentel

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The teaching of computer programming for beginners has been generally considered as a difficult and challenging task. Several methodologies and research tools have been developed, however, the difficulty of teaching still remains. Our work integrates the state of the art in teaching programming with game software and further provides metrics for the evaluation of student performance in a collaborative activity of playing games. This paper aims to present a multi-agent system architecture to be incorporated to the educational collaborative game software for teaching programming that monitors, evaluates and encourages collaboration by the participants. A literature review has been made on the concepts of Collaborative Learning, Multi-agents systems, collaborative games and techniques to teach programming using these concepts simultaneously.

Keywords: Architecture of multi-agent systems, collaborative evaluation, collaboration assessment, gamifying educational software.

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Authors: I. Mahdavi, A. Jazayeri, M. Jahromi, R. Jafari, H. Iranmanesh

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One of the most important problems in production planning of flexible manufacturing system (FMS) is machine tool selection and operation allocation problem that directly influences the production costs and times .In this paper minimizing machining cost, set-up cost and material handling cost as a multi-objective problem in flexible manufacturing systems environment are considered. We present a 0-1 integer linear programming model for the multiobjective machine tool selection and operation allocation problem and due to the large scale nature of the problem, solving the problem to obtain optimal solution in a reasonable time is infeasible, Paretoant colony optimization (P-ACO) approach for solving the multiobjective problem in reasonable time is developed. Experimental results indicate effectiveness of the proposed algorithm for solving the problem.

Keywords: Flexible manufacturing system, Production planning, Machine tool selection, Operation allocation, Multiobjective optimization, Metaheuristic.

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Authors: Fouad Salha , X. Guillaud

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Directional over current relays (DOCR) are commonly used in power system protection as a primary protection in distribution and sub-transmission electrical systems and as a secondary protection in transmission systems. Coordination of protective relays is necessary to obtain selective tripping. In this paper, an approach for efficiency reduction of DOCRs nonlinear optimum coordination (OC) is proposed. This was achieved by modifying the objective function and relaxing several constraints depending on the four constraints classification, non-valid, redundant, pre-obtained and valid constraints. According to this classification, the far end fault effect on the objective function and constraints, and in consequently on relay operating time, was studied. The study was carried out, firstly by taking into account the near-end and far-end faults in DOCRs coordination problem formulation; and then faults very close to the primary relays (nearend faults). The optimal coordination (OC) was achieved by simultaneously optimizing all variables (TDS and Ip) in nonlinear environment by using of Genetic algorithm nonlinear programming techniques. The results application of the above two approaches on 6-bus and 26-bus system verify that the far-end faults consideration on OC problem formulation don-t lose the optimality.

Keywords: Backup/Primary relay, Coordination time interval (CTI), directional over current relays, Genetic algorithm, time dial setting (TDS), pickup current setting (Ip), nonlinear programming.

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Authors: C. Ardil

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Unmanned combat aircraft (UCA) are expanding significantly in several defense industries, along with artificial intelligence improvements in highly precise technology. UCA is crucial in military settings for targeting enemy elements, and objects. UCA is also utilized for highly precise reconnaissance and surveillance tasks. To select the best alternative for critical missions, a methodical and effective strategy for UCA selection is required. Multiple criteria decision-making (MCDM) methodologies are ideally equipped to handle the complexity of alternative aircraft selection. To analyze UCA alternatives for the selection process, an integrated methodology built on the objective criteria weights and preference analysis for reference ideal solution (PARIS). First, the weights of essential elements are determined using the average weight (AW), standard deviation (SW) and entropy weight (EW) approach. The weights of the evaluation criteria affect the decision-making process. The aircraft choices in the decision problem are then ranked using objective criteria weights along with the PARIS technique. The validation and sensitivity analysis of the proposed MCDM approach are discussed.

Keywords: unmanned combat aircraft (UCA), multiple criteria decision making, MCDM, PARIS

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Authors: M. Zareiee, A. Dideban

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This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Wei Sun, Yan Dong

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There is an increasing interest in introducing computational thinking at an early age. Computational thinking, like mathematical thinking, engineering thinking, and scientific thinking, is a kind of analytical thinking. Learning computational thinking skills is not only to improve technological literacy, but also allows learners to equip with practicable skills such as problem-solving skills. As people realize the importance of computational thinking, the field of educational technology faces a problem: how to choose appropriate tools and activities to help students develop computational thinking skills. Robots are gradually becoming a popular teaching tool, as robots provide a tangible way for young children to access to technology, and controlling a robot through programming offers them opportunities to engage in developing computational thinking. This study explores whether the introduction of flowcharts into the robotics programming courses can help children convert natural language into a programming language more easily, and then to better cultivate their computational thinking skills. An experimental study was adopted with a sample of children ages six to seven (N = 16) participated, and a one-meter-tall humanoid robot was used as the teaching tool. Results show that children can master basic programming concepts through robotic courses. Children's computational thinking has been significantly improved. Besides, results suggest that flowcharts do have an impact on young children’s computational thinking skills development, but it only has a significant effect on the "sequencing" and "correspondence" skills. Overall, the study demonstrates that the humanoid robot and flowcharts have qualities that foster young children to learn programming and develop computational thinking skills.

Keywords: Robotics, computational thinking, programming, young children, flowcharts.

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Authors: Nobuhiko Hishinuma, Jun Igari, Rentaro Yoshioka

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When programming in languages such as C, Java, etc., it is difficult to reconstruct the programmer's ideas only from the program code. This occurs mainly because, much of the programmer's ideas behind the implementation are not recorded in the code during implementation. For example, physical aspects of computation such as spatial structures, activities, and meaning of variables are not required as instructions to the computer and are often excluded. This makes the future reconstruction of the original ideas difficult. AIDA, which is a multimedia programming language based on the cyberFilm model, can solve these problems allowing to describe ideas behind programs using advanced annotation methods as a natural extension to programming. In this paper, a development environment that implements the AIDA language is presented with a focus on the annotation methods. In particular, an actual scientific numerical computation code is created and the effects of the annotation methods are analyzed.

Keywords: cyberFilm, development environment, knowledge engineering, multimedia programming language

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

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This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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Authors: Manpreet Singh, V. P. Agrawal, Gurmanjot Singh Bhatti

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From the last decades, there is a significant technological advancement in the field of robotics, and a number of modular self-reconfigurable robots were introduced that can help in space exploration, bucket to stuff, search, and rescue operation during earthquake, etc. As there are numbers of self-reconfigurable robots, choosing the optimum one is always a concern for robot user since there is an increase in available features, facilities, complexity, etc. The objective of this research work is to present a multiple attribute decision making based methodology for coding, evaluation, comparison ranking and selection of modular self-reconfigurable robots using a technique for order preferences by similarity to ideal solution approach. However, 86 attributes that affect the structure and performance are identified. A database for modular self-reconfigurable robot on the basis of different pertinent attribute is generated. This database is very useful for the user, for selecting a robot that suits their operational needs. Two visual methods namely linear graph and spider chart are proposed for ranking of modular self-reconfigurable robots. Using five robots (Atron, Smores, Polybot, M-Tran 3, Superbot), an example is illustrated, and raking of the robots is successfully done, which shows that Smores is the best robot for the operational need illustrated, and this methodology is found to be very effective and simple to use.

Keywords: Self-reconfigurable robots, MADM, TOPSIS, morphogenesis, scalability.

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

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Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: Non-Linear Wilcoxon, robust estimation, Variogram estimation.

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Authors: Bala Dhandayuthapani Veerasamy

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Parallel programming models exist as an abstraction of hardware and memory architectures. There are several parallel programming models in commonly use; they are shared memory model, thread model, message passing model, data parallel model, hybrid model, Flynn-s models, embarrassingly parallel computations model, pipelined computations model. These models are not specific to a particular type of machine or memory architecture. This paper expresses the model program for concurrent approach to data parallel model through java programming.

Keywords: Concurrent, Data Parallel, JDK, Parallel, Thread

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Authors: Tomoaki Hashimoto

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Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the effectiveness of the obtained stability condition.

Keywords: Computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems.

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: Dynamic response, Nonlinear impact response, Finite Element analysis, Numerical analysis.

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Authors: Mahshid Hatamzad, Geanette Polanco

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Improving the performance of Winter Road Maintenance (WRM) can increase the traffic safety and reduce the cost as well as environmental impacts. This study evaluates the efficiency of WRM technique, named salting, in the Arctic area by using Data Envelopment Analysis (DEA), which is a non-parametric linear method to measure the efficiencies of decision-making units (DMUs) based on handling multiple inputs and multiple outputs at the same time that their associated weights are not known. Here, roads are considered as DMUs for which the efficiency must be determined. The three input variables considered are traffic flow, road area and WRM cost. In addition, the two output variables included are level of safety in the roads and environment impacts resulted from WRM, which is also considered as an uncontrollable factor in the second scenario. The results show the performance of DMUs from the most efficient WRM to the inefficient/least efficient one and this information provides decision makers with technical support and the required suggested improvements for inefficient WRM, in order to achieve a cost-effective WRM and a safe road transportation during wintertime in the Arctic areas.

Keywords: DEA, environmental impacts, risk and safety, WRM.

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Authors: Hamed Rafiei, Masoud Rabbani

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This paper deals with the project selection problem. Project selection problem is one of the problems arose firstly in the field of operations research following some production concepts from primary product mix problem. Afterward, introduction of managerial considerations into the project selection problem have emerged qualitative factors and criteria to be regarded as well as quantitative ones. To overcome both kinds of criteria, an analytic network process is developed in this paper enhanced with fuzzy sets theory to tackle the vagueness of experts- comments to evaluate the alternatives. Additionally, a modified version of Least-Square method through a non-linear programming model is augmented to the developed group decision making structure in order to elicit the final weights from comparison matrices. Finally, a case study is considered by which developed structure in this paper is validated. Moreover, a sensitivity analysis is performed to validate the response of the model with respect to the condition alteration.

Keywords: Analytic network process, Fuzzy sets theory, Nonlinear programming, Project selection.

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Authors: Sadaf Khalid, Fahim Arif

Abstract:

Wide applicability of concurrent programming practices in developing various software applications leads to different concurrency errors amongst which data race is the most important. Java provides greatest support for concurrent programming by introducing various concurrency packages. Aspect oriented programming (AOP) is modern programming paradigm facilitating the runtime interception of events of interest and can be effectively used to handle the concurrency problems. AspectJ being an aspect oriented extension to java facilitates the application of concepts of AOP for data race detection. Volatile variables are usually considered thread safe, but they can become the possible candidates of data races if non-atomic operations are performed concurrently upon them. Various data race detection algorithms have been proposed in the past but this issue of volatility and atomicity is still unaddressed. The aim of this research is to propose some suggestions for incorporating certain conditions for data race detection in java programs at the volatile fields by taking into account support for atomicity in java concurrency packages and making use of pointcuts. Two simple test programs will demonstrate the results of research. The results are verified on two different Java Development Kits (JDKs) for the purpose of comparison.

Keywords: Aspect Bench Compiler (abc), Aspect OrientedProgramming (AOP), AspectJ, Aspects, Concurrency packages, Concurrent programming, Cross-cutting Concerns, Data race, Eclipse, Java, Java Development Kits (JDKs), Pointcuts

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Authors: Dursun Aydın, Bilgin Senel

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In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: Taiki Baba, Tomoaki Hashimoto

Abstract:

The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization.

Keywords: Model predictive control, stochastic systems, probabilistic constraints, random dither quantization.

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Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

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In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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