Discrete Cost Function Research Articles

\(\boldsymbol{\mathcal{L}_2}\)-Optimal Reduced-Order Modeling Using Parameter-Separable Forms

We provide a unifying framework for -optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive the gradients of the cost function with respect to the reduced matrices, which then allows a nonintrusive, data-driven, gradient-based descent algorithm to construct the optimal approximant using only output samples. By choosing an appropriate measure, the framework covers both continuous (Lebesgue) and discrete cost functions. We show the efficacy of the proposed algorithm via various numerical examples. Furthermore, we analyze under what conditions the data-driven approximant can be obtained via projection.

Discrete optimal quadratic AGC based cost functional minimization for interconnected power systems

The increasing complexity and difficulty of the Automatic generation control (AGC) problem has resulted from the increasing scale of interconnected power networks and changing daily demands. The primary goals of AGC are to control frequency variations at nominal levels and tie-line power variances at planned levels. To effectively deal with AGC control difficulties, this study introduces Discrete Optimal Quadratic Automatic Generation Control (OQAGC). One advantages of this method is the differentiation of quadratic cost function results into linear terms while minimizing control actions and minimizing state deviations. This developed control method leads to a simple and easy discrete control law that can be implemented for both linear and nonlinear systems. For optimizing the controller, this research work utilized an optimum control theorem using Lagrangian multipliers, while the functional minimization technique is used for systematically selecting the state and control weighting matrices in discrete form for N control regions (where N is the number of interconnected power systems). The discrete cost function needs are derived using this technique in terms of area control errors, integral area control errors, and control energy expenditure. Four interconnected power systems were analyzed with/without disturbances and area control errors, each with one thermal, hydro, and gas-generating unit. A two-area multi-source power system with renewable energy in control area 2 is analyzed for the performance of the proposed controller with generation rate constraints (GRCs). The functional minimization technique simplifies and eases the choosing of weighting matrices. Furthermore, the simulation findings suggest that the developed discrete optimum quadratic AGC control-based cost functional minimization approach enhances power system dynamics in terms of stability, steady-state performance, and the closed-loop control system's robustness to input load disturbances. As a result, the newly developed OQAGC approach demonstrates the significance of the discrete LQR controller for N multi-area power systems.

A novel discrete learning-based intelligent methodology for breast cancer classification purposes

Classification is one of the most significant subfields of data mining that has been successfully applied to various applications. The literature has expended substantial effort to present more efficient and accurate classification models. Despite the diversity of the proposed models, they were all created using the same methodology, and their learning processes ignored a fundamental issue. In all existing classification model learning processes, a continuous distance-based cost function is optimized to estimate the unknown parameters. The classification problem's objective function is discrete. Consequently, applying a continuous cost function to a classification problem with a discrete objective function is illogical or inefficient. This paper proposes a novel classification methodology utilizing a discrete cost function in the learning process. To this end, one of the most popular intelligent classification models, the multilayer perceptron (MLP), is used to implement the proposed methodology. Theoretically, the classification performance of the proposed discrete learning-based MLP (DIMLP) model is not dissimilar to that of its continuous learning-based counterpart. Nevertheless, in this study, to demonstrate the efficacy of the DIMLP model, it was applied to several breast cancer classification datasets, and its classification rate was compared to that of the conventional continuous learning-based MLP model. The empirical results indicate that the proposed DIMLP model outperforms the MLP model across all datasets. The results demonstrate that the presented DIMLP classification model achieves an average classification rate of 94.70 %, a 6.95 % improvement over the classification rate of the traditional MLP model, which was 88.54 %. Therefore, the classification approach proposed in this study can be utilized as an alternative learning process in intelligent classification methods for medical decision-making and other classification applications, particularly when more accurate results are required.

Automatic Transmission Upshift Control Using a Linearized Reduced-Order Model-Based LQR Approach

<div class="section abstract"><div class="htmlview paragraph">Automatic transmission (AT) upshift control performance in terms of shift duration and comfort can be improved during the inertia phase by coordinating the off-going clutch together with oncoming clutch and engine torque. The performance improvement is highest in low gear shifts (i.e., for high ratio steps), which are typically performed with open torque converter. In this paper, a discrete-time, linear quadratic regulation (LQR) is applied during the upshift inertia phase, as it provides an optimal multi-input/multi-output control action with respect to the prescribed cost function. The LQR law is based on a reduced-order drivetrain model, which is applicable to actual transmissions characterized by a limited number of available state measurements. The reduced-order model includes the linearized torque converter model. The shift duration is ensured by precise tracking of a linear-like oncoming clutch slip speed reference profile. To facilitate the tracking accuracy, the LQR law is extended by an integral action. A clipped optimal approach is applied to account for the clutch energy passivity. By using a set of differently weighted conflicting criteria in the discrete cost function, including shift duration, comfort, and efficiency, Pareto frontiers are obtained based on post-processing the multi-run simulation results. The Pareto frontiers are compared with benchmark frontiers determined off-line by applying a multi-objective genetic algorithm-based control parameter optimization relying on full-order, nonlinear drivetrain model. It is shown that the LQR approach results in comparable Pareto frontiers to those obtained by multi-objective optimization.</div></div>

Numerical Solutions for the Optimal Control Governing by Variable Coefficients Nonlinear Hyperbolic Boundary Value Problem Using the Gradient Projection, Gradient and Frank Wolfe Methods

This paper is concerned with studying the numerical solution for the discrete classical optimal control problem (NSDCOCP) governed by a variable coefficients nonlinear hyperbolic boundary value problem (VCNLHBVP). The DSCOCP is solved by using the Galerkin finite element method (GFEM) for the space variable and implicit finite difference scheme (GFEM-IFDS) for the time variable to get the NS for the discrete weak form (DWF) and for the discrete adjoint weak form (DSAWF) While, the gradient projection method (GRPM), also called the gradient method (GRM), or the Frank Wolfe method (FRM) are used to minimize the discrete cost function (DCF) to find the DSCOC. Within these three methods, the Armijo step option (ARMSO) or the optimal step option (OPSO) are used to improve the discrete classical control (DSCC). Finally, some illustrative examples for the problem are given to show the accuracy and efficiency of the methods.

Stochastic optimization of two-machine flow shop robotic cells with controllable inspection times: From theory toward practice

Abstract This paper considers the stochastic scheduling of a two-machine flow shop robotic cell with controllable inspection times. The inspection here is performed by a multi-function robot which can inspect identical parts with two alternatives for the inspection strategy: either at the back of the upstream machine or in transit between upstream and downstream machines. A characteristic of the inspection process is that its time is changed by altering the inspection cost. If the inspection time is reduced, more failures in parts may result regardless of when failures are identified. The challenge is therefore to find a suitable trade-off between inspection time and internal and external quality costs to increase reliability benefits. Initially, we complete a structural analysis of costs of quality and partial cycles, and then consider a simultaneous analysis of them. Then, through a sensitivity analysis, an epsilon-constraint method is used to find useful upper bounds on costs of quality and partial cycle times. The outcomes of the research are (i) an integrated framework for designing robotic cells with different levels of quality: low (e.g., disassembly industries), medium (e.g., automotive industries), and high (e.g., aerospace industries); and (ii) a sensitivity analysis for studying the impact of inspection strategies to assist production and quality managers with decision-making processes in stochastic environments. Finally, we extend the analysis to show that the given framework can be generalized for subtle variations found in practical applications with regard to (i) the quality of the part and (ii) accuracy of the inspection process. Robotic cells with scrap consideration and robotic cells with decreasing failure rates of the inspection process are studied as examples of the former, and robotic cells with either convex cost function or discrete cost function are studied for the latter.

Optimal charging strategy for a residential PEV battery considering bidirectional trade and frequency regulation

A practical charging strategy for an individual plug-in electric vehicle (PEV) is proposed. A cost function is constructed to reflect bidirectional electricity trade arising from surplus photovoltaic generation under the reward system called feed-in tariffs and time-of-use electricity pricing. It is then extended to include the revenue for providing vehicle-to-grid frequency regulation. In order to take advantages of high performance existing solvers, several mathematical techniques are applied to transform the discrete non-linear cost function to a differentiable continuous function. In the latter part of the paper, simulations are performed to verify and show the performance of the developed model. A quantitatively developed battery wear model is also applied during the simulations to calculate the effective operational cost, and to compare the costs for different control strategies. From the result of case study, the economic feasibility of the frequency regulation under the given circumstance is addressed as well.

Detection of Clone Node Attack in Mobile Wireless Sensor Network with Optimized cost Function

Clone attack is considered as the most important security challenge of wireless sensor networks. In this paper, an innovative distributed approach for the detection of clone node attack is proposed, that is robust against smart attacker in mobile wireless sensor networks. Previously proposed approaches suffer disadvantages such as memory and communication overheads, probability of false alarm and high detection time, however, the detection approach proposed here takes advantage of introducing the observer position concept and hence achieves clone node detection in one cycle of protocol execution leading to less communication overheads. Performance of the proposed approach is analysed in terms of security and cost. To improve performance, using a discrete model and detection cost function stated as a convex optimisation problem and parameters optimised values are calculated. Finally, the simulation results show that proposed approach has less communication overhead and false alarm probability and better performance compared to previously proposed approaches.

Efficient edit distance with duplications and contractions

We propose three algorithms for string edit distance with duplications and contractions. These include an efficient general algorithm and two improvements which apply under certain constraints on the cost function. The new algorithms solve a more general problem variant and obtain better time complexities with respect to previous algorithms. Our general algorithm is based on min-plus multiplication of square matrices and has time and space complexities of O (|Σ|MP (n)) and O (|Σ|n2), respectively, where |Σ| is the alphabet size, n is the length of the strings, and MP (n) is the time bound for the computation of min-plus matrix multiplication of two n × n matrices (currently, due to an algorithm by Chan).For integer cost functions, the running time is further improved to . In addition, this variant of the algorithm is online, in the sense that the input strings may be given letter by letter, and its time complexity bounds the processing time of the first n given letters. This acceleration is based on our efficient matrix-vector min-plus multiplication algorithm, intended for matrices and vectors for which differences between adjacent entries are from a finite integer interval D. Choosing a constant , the algorithm preprocesses an n × n matrix in time and space. Then, it may multiply the matrix with any given n-length vector in time. Under some discreteness assumptions, this matrix-vector min-plus multiplication algorithm applies to several problems from the domains of context-free grammar parsing and RNA folding and, in particular, implies the asymptotically fastest time algorithm for single-strand RNA folding with discrete cost functions.Finally, assuming a different constraint on the cost function, we present another version of the algorithm that exploits the run-length encoding of the strings and runs in time and space, where is the length of the run-length encoding of the strings.

An energy management system for off-grid power systems

Next generation power management at all scales will rely on the efficient scheduling and operation of both generating units and loads to maximize efficiency and utility. The ability to schedule and modulate the demand levels of a subset of loads within a power system can lead to more efficient use of the generating units. These methods become increasingly important for systems that operate independently of the main utility, such as microgrid and off-grid systems. This work extends the principles of unit commitment and economic dispatch problems to off-grid power systems where the loads are also schedulable. We propose a general optimization framework for solving the energy management problem in these systems. An important contribution is the description of how a wide range of sources and loads, including those with discrete states, non-convex, and nonlinear cost or utility functions, can be reformulated as a convex optimization problem using, for example, a shortest path description. Once cast in this way, solution are obtainable using a sub-gradient algorithm that also lends itself to a distributed implementation. The methods are demonstrated by a simulation of an off-grid solar powered community.

Max-flow segmentation of the left ventricle by recovering subject-specific distributions via a bound of the Bhattacharyya measure

This study investigates fast detection of the left ventricle (LV) endo- and epicardium boundaries in a cardiac magnetic resonance (MR) sequence following the optimization of two original discrete cost functions, each containing global intensity and geometry constraints based on the Bhattacharyya similarity. The cost functions and the corresponding max-flow optimization built upon an original bound of the Bhattacharyya measure yield competitive results in nearly real-time. Within each frame, the algorithm seeks the LV cavity and myocardium regions consistent with subject-specific model distributions learned from the first frame in the sequence. Based on global rather than pixel-wise information, the proposed formulation relaxes the need of a large training set and optimization with respect to geometric transformations. Different from related active contour methods, it does not require a large number of iterative updates of the segmentation and the corresponding computationally onerous kernel density estimates (KDEs). The algorithm requires very few iterations and KDEs to converge. Furthermore, the proposed bound can be used for several other applications and, therefore, can lead to segmentation algorithms which share the flexibility of active contours and computational advantages of max-flow optimization. Quantitative evaluations over 2280 images acquired from 20 subjects demonstrated that the results correlate well with independent manual segmentations by an expert. Moreover, comparisons with a related recent active contour method showed that the proposed framework brings significant improvements in regard to accuracy and computational efficiency.

Time-Cost Tradeoff Analysis in Project Management: An Ant System Approach

The time-cost tradeoff problem (TCTP) is an important issue in the scheduling of industrial projects; it is often possible to expedite the completion of certain activities by increasing the budget. This paper develops a new approach for the discrete TCTP (DTCTP) in program evaluation and review technique networks of project management, in which activities have multimode discrete cost functions and activity durations are normally distributed. Moreover, the first application of the ant colony system (ACS) is applied to the stochastic DTCTP, solving it as a nonlinear zero-one problem. To illustrate the suggested approach, a numerical example is discussed and an overall efficiency measure is developed to set the ACS parameters so as to reach more accurate results with less computational time. The results obtained from the computational study demonstrate the effectiveness of the suggested approach for the DTCTP.

Fringe-pattern denoising based on discrete topological analysis

We present an effective way to solve the denoising problem of fringe patterns in optics interferometry. The proposed method is based on the topological analysis of an appropriate cost function. To overcome the blurring drawback of the linear diffusion approach, the linear diffusion coefficient at each edge is perturbed successively. The total variation of a discrete cost function can be taken as an indicator function to pick out the most suitable edges of pixels at which the diffusion coefficients are to be perturbed. Then, a filtered image can be obtained by using selected diffusion coefficients associated to the edges. We demonstrate the performance of the proposed method via application to numerically simulated and experimentally obtained fringe patterns.

Ant colony optimization algorithm for stochastic project crashing problem in PERT networks using MC simulation

This paper describes a new approach based on ant colony optimization (ACO) metaheuristic and Monte Carlo (MC) simulation technique, for project crashing problem (PCP) under uncertainties. To our knowledge, this is the first application of ACO technique for the stochastic project crashing problem (SPCP), in the published literature. A confidence-level-based approach has been proposed for SPCP in program evaluation and review technique (PERT) type networks, where activities are subjected to discrete cost functions and assumed to be exponentially distributed. The objective of the proposed model is to optimally improve the project completion probability in a prespecified due date based on a predefined probability. In order to solve the constructed model, we apply the ACO algorithm and path criticality index, together. The proposed approach applies the path criticality concept in order to select the most critical path by using MC simulation technique. Then, the developed ACO is used to solve a nonlinear integer mathematical programming for selected path. In order to demonstrate the model effectiveness, a large scale illustrative example has been presented and several computational experiments are conducted to determine the appropriate levels of ACO parameters, which lead to the accurate results with reasonable computational time. Finally, a comparative study has been conducted to validate the ACO approach, using several randomly generated problems.

Optimal Design and Modelling of Stand-Alone Photovoltaic-Wind Hybrid System with Adaptive-Fuzzy Controller

This paper proposes an optimal approach for design of a hybrid photovoltaic (PV)- wind generating system with adaptive-fuzzy controller, which is based on discrete optimisation and energy balance calculations. The total capacity of the renewable system is determined based on estimated annual power consumption, average wind speed and sun radiation. Different structures of each unit are examined, and a discrete cost function is defined and optimised to determine the minimum number of PV and wind units. To improve system reliability under different operating and environmental conditions, a self-adjustable controller capable of maximum power point tracking (MPPT) of PV units and blade angle pitch control of wind turbines is designed, and energy balance calculation is performed. Using reference adaptive tables, the fuzzy controller allocates each decision unit and activates the required number of units in each farm to supply the average demand power. Simulation results are used to show the validity of the design and system behaviour under different environmental and loading conditions. Main contributions are the inclusion of renewable system configurations, capacities, environmental factors and maximum power point tracking in the optimisation procedure, as well as the utilisation of an adaptive-fuzzy controller.

Optimal precomputation for mapping service level agreements in grid computing

A complicated task running on the grid system is usually made up of many services, each of which typically offers a better service quality at a higher cost. Mapping service level agreements (SLAs) optimally is to find the most appropriate quality level for each service such that the overall SLA of a task is achieved at the minimum cost. This paper considers mapping the execution time SLA in the case of the discrete cost function, which is an NP-hard problem. Due to the high computation of mapping SLAs, we propose a precomputation scheme that makes the selection of each individual service level in advance for every possible SLA requirement, which can reduce the request response time greatly. We use a ( 1 + ε ) -approximation method, whose solution for any time bound is at most ( 1 + ε ) times of the optimal cost. Simulation results demonstrate the superiority of our method compared with others.

Costate prediction based optimal control for non-linear hybrid systems

This paper is derived for solving a non-linear discrete-continuous systems optimal control problem by iterating on a sequence of simplified problems in discrete form. A mixed approach with a discrete cost function and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local subsystem problems and a coordinator within a hierarchical framework. The correct optimal solution to a real system in which model-reality difference exists can be obtained from the system model by interconnected costate prediction iterative solution. The algorithm efficiency and convergence properties are demonstrated by simulation study.

Multiperiod network design with incremental routing

AbstractIn this paper, we study a special case of multiperiod network design (MPND) problems, multiperiod network design with incremental routing (MPNDI), as applied to the transmission layer of an optical network. We optimize simultaneously the network architecture and the link dimensioning under discrete cost functions in order to route all traffic demands in line with traffic growth over a discrete time horizon. Because of operational requirements, routing paths used at a given period to route some traffic demands have to be preserved over subsequent periods; this is called incremental routing with respect to incremental flow. To handle the high dimensionality, a compact formulation omitting explicitly written flow variables is given. We examine the dominant polyhedron of the incremental multicommodity flow and provide a polyhedral study of it. Finally, a solution approach taking advantage of the polyhedral structure of MPNDI is proposed, and computational results for a range of instances with 8 and 10 nodes are provided. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(1), 109–117 2007

Zigzag Oscillations in Variational Data Assimilation with Physical “On–Off” Processes

Abstract Using an idealized model of a partial differential equation with parameterization “on–off” switches in the forcing term, the impacts of on–off switches on the variational data assimilation (VDA) are investigated in this paper. It is shown that the traditional time discretization at the switches of the discrete forward model could induce awful zigzags in the associated discrete cost function (CF), which would cause the optimization to fail to work well in the VDA when using the adjoint method. In addition, it can also cause zigzag oscillations in the numerical solution of the model. A method, which is a generalization of Xu’s intermediate interpolation method, is proposed to eliminate the zigzag phenomenon. The potential merits of this treatment are examined by numerical experiments. The results show that through this treatment, the convergence in the minimization processes of the VDA is improved and the satisfactory optimization retrievals are obtained even though the adjoint models are constructed following Zou’s method from the discrete forward model with the traditional time discretization at the switches.

A grid layout algorithm for automatic drawing of biochemical networks

Visualization is indispensable in the research of complex biochemical networks. Available graph layout algorithms are not adequate for satisfactorily drawing such networks. New methods are required to visualize automatically the topological architectures and facilitate the understanding of the functions of the networks. We propose a novel layout algorithm to draw complex biochemical networks. A network is modeled as a system of interacting nodes on squared grids. A discrete cost function between each node pair is designed based on the topological relation and the geometric positions of the two nodes. The layouts are produced by minimizing the total cost. We design a fast algorithm to minimize the discrete cost function, by which candidate layouts can be produced efficiently. A simulated annealing procedure is used to choose better candidates. Our algorithm demonstrates its ability to exhibit cluster structures clearly in relatively compact layout areas without any prior knowledge. We developed Windows software to implement the algorithm for CADLIVE. All materials can be freely downloaded from http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/ http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/