Continuous Cost Function Research Articles

Improved A* Algorithm for Mobile Robots under Rough Terrain Based on Ground Trafficability Model and Ground Ruggedness Model.

Considering that the existing path planning algorithms for mobile robots under rugged terrain do not consider the ground flatness and the lack of optimality, which leads to the instability of the center of mass of the mobile robot, this paper proposes an improved A* algorithm for mobile robots under rugged terrain based on the ground accessibility model and the ground ruggedness model. Firstly, the ground accessibility and ruggedness models are established based on the elevation map, expressing the ground flatness. Secondly, the elevation cost function that can obtain the optimal path is designed based on the two types of models combined with the characteristics of the A* algorithm, and the continuous cost function is established by connecting with the original distance cost function, which avoids the center-of-mass instability caused by the non-optimal path. Finally, the effectiveness of the improved algorithm is verified by simulation and experiment. The results show that compared with the existing commonly used path planning algorithms under rugged terrain, the enhanced algorithm improves the smoothness of paths and the optimization degree of paths in the path planning process under rough terrain.

Cost-Based Decision Support System: A Dynamic Cost Estimation of Key Performance Indicators in Manufacturing

An attempt is made to translate five generic key performance indicators (KPIs) into a continuous real-time cost function in a batch order-based manufacturing environment. The challenge of controlling and optimizing resource utilization, production efficiency, product-process quality, environmental impact, and inventory was specified by microelectronics and hard metal composite manufacturers. The motivation is to facilitate decision-making by converting operations management data into dynamic financial cost models. The process of interpreting engineering data of the physical level and operations management level into financial metrics creates a common language between engineers, managers, and financial departments of the company whose common objective is the profitability of the company, each with their own priorities. The proposed method provides a realistic representation of the performance of the system in monetary value. The integration may become an instrument of effective and efficient tactical and strategic collective decision-making. The main outcome is a near real-time formulation and prediction of manufacturing cost with respect to the five KPIs. The resultant cost function is verified according to several production scenarios. The case study demonstrating the proposed cost modeling methodology utilizes real-time and historical information from two different industrial partners in Tungsten metallurgy and electronic circuit manufacturing industries.

A Comparative Study of Discrete Direction vs. Continuous Distance-Based Cost Function in Energy Classification

Over the past decades, different classification approaches with different characteristics have been developed to achieve more efficient and accurate results. Although the loss function used in the training procedure is a significant influential factor in the performance of classification models, it has been less considered. In general, in previous research, two main categories of continuous and semi-continuous distance-based loss functions are often applied to estimate the unknown parameters of classification models. Among these, continuous distance-based cost functions are among the most commonly used and most popular loss functions in diverse statistical and intelligent classifiers. In particular, the fundamental of this category of the loss functions is based on the continuous reduction of the distance between the fitted and actual values with the aim of improving the performance of the model. However, since the goal function of classification models belongs to the class of discrete ones, the application of learning procedures based on a continuous distance-based function is not coordinated with the nature of these problems. Consequently, it is theoretically illogical and practically at least inefficient. Accordingly, in order to fill this research gap, the discrete direction-based loss function in the form of mixed-integer programming is proposed in the training procedure of statistical, shallow/deep intelligent classifiers. In this paper, the impact of the loss function type on the classification rate of the classifiers in the energy domain is investigated. For this purpose, the logistic regression (LR), multilayer perceptron (MLP), and deep multilayer perceptron (DMLP), which are respectively among the most widely used statistical, shallow intelligent, and deep learning classifiers, are exemplarily chosen. Numerical outcomes from 13 benchmark energy datasets show that, in all benchmarks, the performances of the discrete direction learning-based classifiers, i.e., discrete learning-based logistic regression (DILR), discrete learning-based multilayer perceptron (DIMLP), and discrete learning-based deep multilayer perceptron (DIDMLP), is higher than its conventional versions. In addition, the proposed DILR, DIMLP, and DIDMLP models can on average yield an 89.88%, 94.53%, and 96.02% classification rate, which indicate a 6.78%, 5.90%, and 4.69% improvement from the classic versions, which only produce an 84.17%, 89.26%, and 91.72% classification rate. Consequently, the discrete direction-based learning methodology can be a more suitable, effective, and valuable alternative for training processes in statistical and shallow/deep intelligent classification models.

\(\boldsymbol{\mathcal{L}_2}\)-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.

A novel discrete deep learning-based intelligent methodology for energy consumption classification

Energy consumption classification is one of the most widely-used approaches in the energy area that is applied in various applications such as household, commercial, urban, rural, industrial, etc. Energy consumption due to its substantial positive influence on the quality of made decisions, production and distribution management, and cost reduction, has considerable literature. In the classification literature, numerous statistical, intelligence, and hybrid methods have been developed and proposed in order to yield more accurate results. The common point of all these models is that whole of techniques follow a prevalent and repetitive procedure of learning process based on continuous distance-based cost function. While the objective function of classification is discrete. While the mismatch of the continuous cost function in classification problems with the discrete objective function causes them to be illogical or inefficient. Therefore, in this paper, a novel discrete learning process is offered to eliminate the inconsistency between the cost function and the classification objective function. The main difference between the proposed learning methodology rather than conventional versions is its cost function. In the proposed learning methodology, a mismatching function is considered as a cost function, which is dissimilar to previously developed ones, which are continuous functions based on distance, is a discrete function based on direction. In this way, in the proposed learning process, unknown parameters are discretely adjusted and at once jumped to the target. This is in contrast to conventional continuous learning algorithms in which the unknown parameters are continuously adjusted and step-by-step near the target. In this paper, deep multilayer neural networks (DMNs) have been exemplarily applied to implement the proposed learning algorithm. Although more consistency of goal and cost functions will logically has not a negative effect on the classification rate of classifiers. However, in this paper, to show the superiority of the proposed discrete deep multilayer neural network (DDMN) over conventional continuous-based classifiers, four energy consumption benchmark data sets have been employed. These data sets include the Tamilnadu Electricity Board Hourly Readings, Tetouan City Energy Consumption, Household Electric Power consumption, and steel industry Energy Consumption. Empirical results indicate that the proposed DDMN model, as pre-expected, can yield better performance in all cases than the DMN model. The DDMN model can achieve a 93.27% classification rate on average and upgrade its classic version approximately by 4.77%.

An optimal transport problem with storage fees

We establish basic properties of a variant of the semi-discrete optimal transport problem in a relatively general setting. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support of the target measure, and a “storage fee” function. The goal is to find a map for which the total transport cost plus the storage fee evaluated on the masses of the pushforward of the source measure is minimized. We prove existence and uniqueness for the problem, derive a dual problem for which strong duality holds, and give a characterization of dual maximizers and primal minimizers. Additionally, we find some stability results for minimizers and a Γ-convergence result as the target set becomes denser and denser in a continuum domain.

Discrete learning-based intelligent methodology for heart disease diagnosis

Classification is one of the most frequently used data mining approaches which has been broadly applied in different fields of sciences, such as engineering, finance, energy, environments, transportation, etc., especially medicine, successfully. Over the years, various intelligent modeling techniques with different properties have been proposed to yield more accurate and more efficient classification results. However, in spite of the different appearance of all of the developed models, the same basic methodology is applied to the learning processes. Based on this methodology, a continuous distance-based cost function is considered and optimized for estimating the unknown parameters in the learning procedures. While using a continuous cost function in the classification field in which the goal function is discrete, is unreasonable or at least quite inefficient. In this paper, in contrast to conventional continuous distance-based methodologies, a novel discrete learning-based methodology is proposed for classification purposes. The main difference between the proposed learning methodology rather than conventional versions is its cost function. In the proposed learning methodology, a mismatching function is considered as a cost function, which is dissimilar to previously developed ones, which are continuous functions based on distance, is a discrete function based on direction. In this way, in the proposed learning process, unknown parameters are discretely adjusted and at once jumped to the target. This is in contrast to conventional continuous learning algorithms in which the unknown parameters are continuously adjusted and step-by-step near the target. The multilayer perceptron (MLP) which is one of the most widely-used intelligent classification approaches, is exemplarily chosen in order to implement the proposed methodology. Although it can be generally demonstrated that the classification rate of the proposed discrete learning-based MLP (DIMLP) model will not be worse than its conventional continuous learning-based one. However, in order to determine the superiority of the proposed DIMLP model, it is exemplarily evaluated on the heart disease diagnosis benchmark data set and several other medical datasets, and its performance is compared to the classic multilayer perceptron model. Empirical results illustrate that, as pre-expected, the classification rate of the proposed model is higher than its conventional version in all data sets. Obtained results indicate that the proposed DIMLP classifier can yield a 94.27 % classification rate in heart disease diagnosis, which approximately indicates a 9.35 % improvement over the classic version, which can only produce an 86.21 % classification rate. Therefore, the proposed methodology is an appropriate and effective alternative learning process for intelligent classification approaches, especially when more accurate results and/or a more reasonable model are required.

Intelligent Discrete Deep Learning Based Classification Methodology in Chemometrics.

In recent years, deep learning models have attracted much attention for classification purposes in chemometrics. The popularity of deep learning models in this field comes from their unique features like universal approximation capability with the desired accuracy. Deep learning classifiers use several intelligent processing layers to model mixed, complex, and nonlinear patterns in the underlying data sets, which is why the development of deep learning based models has never been stopped in the chemometrics literature. Despite the variety of deep learning classification models used in this field, they all use a continuous distance-based cost function in their learning processes. Although using a continuous cost function for learning deep classifiers is a common approach, it conflicts with the discrete nature of the classification problem. In fact, applying a continuous cost function for inherently discrete classification problems can reduce the performance of the classification. In this research, a novel discrete learning based classification approach is proposed and implemented on a deep feed-forward neural network as one of the most commonly used deep learning models to develop a different learning process for deep classification models. The basis of the proposed learning approach is maximizing a discrete matching function of the actual and fitted values instead of minimizing a continuous distance-based cost function. The proposed classification approach is evaluated on five benchmark data sets in the chemistry field. The empirical results indicated the superiority of the proposed discrete deep learning approach over its classic continuous form. The results of this study demonstrate the important effect of discrete learning processes on the performances of deep learning classification models. Therefore, the proposed methodology can be a powerful alternative to common classification approaches to analyze chemical data in the chemometrics field.

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.

State Estimation Moving Window Gradient Iterative Algorithm for Bilinear Systems Using the Continuous Mixed p-norm Technique

This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances. A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data. Based on the bilinear state observer, a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function. The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance. Furthermore, to improve the performance of the proposed algorithm, a dynamic moving window is designed which can update the dynamical data by removing the oldest data and adding the newest measurement data. A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.

Mixed-Cell-Height Placement With Complex Minimum-Implant-Area Constraints

Mixed-cell-height standard cells are prevailingly used in advanced technologies to achieve better design tradeoffs among timing, power, and routability. As feature size decreases, the placement of cells with multiple threshold voltages may violate the complex minimum-implant-area (MIA) layer rule arising from the limitations of patterning technologies. Existing works consider the mixed-cell-height placement problem only during legalization or handle the MIA constraints during detailed placement. In this article, we address the mixed-cell-height placement problem with MIA constraints in two major stages: 1) post-global placement (Post-GP) and 2) MIA-aware legalization. In the Post-GP stage, we first present a continuous and differentiable cost function to address the Vdd/Vss alignment constraints and add weighted pseudonets to MIA-violation cells dynamically. Then, we propose a proximal optimization method based on the given global placement result to simultaneously consider Vdd/Vss alignment constraints, MIA constraints, cell distribution, cell displacement, and total wirelength. In the MIA-aware legalization stage, we develop a graph-based method to cluster cells of specific threshold voltages and apply a strip-packing-based binary linear programming to reshape cells. Then, we propose a matching-based technique to resolve intrarow MIA violations and reduce filler insertion. Furthermore, we formulate inter-row MIA-aware legalization as a quadratic programming problem, which is efficiently solved by a modulus-based matrix splitting iteration method. Finally, MIA-aware cell allocation and refinement are performed to further improve the result. Experimental results show that without any extra area overhead, our algorithm still can achieve 5.4% shorter final total wirelength than the state-of-the-art work.

Escaping Braess's paradox through approximate Caratheodory's theorem

In selfish routing, Braess's paradox demonstrates the counterintuitive fact that removing a part of a network may improve the players' cost at equilibrium. In this work, we use the approximate version of Caratheodory's theorem (Barman, SICOMP 2018) and show how to efficiently approximate the best subnetwork on selfish routing instances with relatively short paths and Lipschitz continuous cost functions. Restriction to networks with short paths is necessary to escape the strong inapproximability result of (Roughgarden, JCSS 2006). We present the first polynomial-time algorithm that approximates (in a certain relaxed sense) the best subnetwork problem on such instances. Specifically, for any constant ε>0, our algorithm computes an ε-Nash flow with maximum latency at most (1+ε)L⁎+ε, where L⁎ is the equilibrium latency of the best subnetwork. Moreover, our algorithm runs in quasipolynomial time on networks with polylogarithmically long paths. As a corollary, we obtain the first polynomial-time approximation scheme for the best subnetwork in the class of random Gn,p instances proven prone to Braess's paradox by (Roughgarden and Valiant, RSA 2010) and (Chung Graham et al., RSA 2012).

FIR FILTER DESIGN WITH INERTIA WEIGHT AND COMPRESSION FACTOR APPROACH USING ADVANCED OPTIMIZATION TECHNIQUES

This paper includes the design of Finite impulse response filter with inertia weight and compression factor approach. The objective function of filter design involves accurate control of various parameters of frequency spectrum and is thus highly non-uniform, non-linear, non-differentiable and multimodal in nature. Classical optimization methods cannot converge to solutions. Because they have disadvantages such as highly sensitive to starting points, frequent convergence to local optimum solution or divergence or revisiting the same solution, requirement of continuous and differentiable objective cost function, requirement of the piecewise linear cost approximation and problem of convergence and algorithm. Evolutionary optimization methods for the design of optimal digital filters have better control of parameters and the highest stop band attenuation.

Incremental Cost Consensus Algorithm for On/Off Loads to Enhance the Frequency Response of the Power System

Flexible loads, most of which are on/off appliances, are playing an important role in keeping the balance between power generation and demand. In this paper, a distributed consensus-based control strategy is proposed for the economic load dispatch in the frequency regulation. In order to avoid the complexity caused by the discrete cost characteristics, the continuous cost function of each user is fitted by the least squares method in advance. To minimize the overall load dispatching costs during the frequency regulation, Incremental Cost Consensus (ICC) algorithm is proposed in the load control. The economic load dispatch is realized through the convergence of the Incremental Cost (IC) of users. Case studies are provided to verify the effectiveness of the proposed method, with comparisons of different discretization methods.

On the Equality of Values in the Monge and Kantorovich Problems

This paper is concerned with the study of conditions under which the Monge and Kantorovich problems with a continuous cost function on a product of two completely regular spaces and two given atomless Radon measures-projections on these spaces have equal values of the corresponding infima.

Research on Optimization of Multi-Commodity Supply and Demand Logistics Network Based on Supernetwork

For the realization, a qualitative and quantitative description of matching degree between the elements for logistics supply network and demand network, logistics super network models are constructed by the theory of super network. Faced with the problems of diverse demand and massive circulation for commodities, this article studies the structure of the logistics super network of multi-commodity circulation and establishes the continuous cost function of the logistics demand and supply, reflecting the logistics cost of different commodities in different phrases. This article aims to establish the optimization model of logistics supernetwork by aiming to maximize the matching of supply and demand of multi-commodity. The model is transformed into the variational inequality problem, and proves the existence and uniqueness of the equivalence solution. Use the case of the logistics supernetwork of coal, a modified projection algorithm is adopted and the fact is revealed that improving the supply capacity of the network matching may have the original 81.3% increase to 90.5%, improving the impact of the relationship between trades, matching degree can be increased to 90.1%.

On the inherent robustness of optimal and suboptimal nonlinear MPC

Suboptimal model predictive control (MPC) is a control algorithm that uses suboptimal solutions to optimal control problems to provide control actions quickly. In MPC, terminal control laws and terminal region constraints are frequently used to ensure recursive feasibility and stability. Suboptimal MPC was proven to be inherently robust for systems with soft terminal region constraints in Pannocchia et al. (2011). We extend that work to systems with hard terminal region constraints. If these hard constraints are defined as sublevel sets of appropriate terminal cost functions, a well-chosen initial guess (warm start) for the optimization algorithm is robustly feasible. As a result, the system controlled by suboptimal MPC admits an ISS-Lyapunov function and is therefore inherently robust.The authors of Yu et al. (2014) noted that the result in Pannocchia et al. (2011) applied only to systems with continuous optimal cost functions. However, discontinuous optimal cost functions may be present in systems with hard terminal region constraints. We include a simple example of a continuous dynamical system with a provably discontinuous optimal value function that, as a consequence of the main result of this work, is inherently robust. This example is to our knowledge the first such system reported in the literature.

APPLYING OPTIMAL CHOICES FOR REAL POWERTRAIN AND LIGHTWEIGHTING TECHNOLOGY OPTIONS TO PASSENGER VEHICLES UNDER UNCERTAINTY

This paper illustrates how cost-constrained optimization based on a set of real lightweighting and powertrain efficiency options can be used to guide decision-making for automotive manufacturers. The paper provides a method for answering the question posed by Original Equipment Manufacturers (OEMs): ‘given a maximum amount additional cost which can be passed on to consumers for fuel-saving technology with uncertain manufacturing cost, to what degree should it be spent on lightweighting versus powertrain efficiency improving technology’. The optimization is formulated as a 0–1 knapsack problem, and dynamic programming is used to find the global optimum technology combination at various levels of maximum up-front technology cost. This paper builds on previous work, which showed that for continuous marginal cost functions under uncertainty, a decision heuristic to either implement lightweighting technology or efficiency technology but not both under cost constraints was preferable. This work extends that result to provide more quantitative strategies for dealing with uncertainty, and finds that, despite uncertainty, optimum lightweighting and efficiency technology selections can be made for the real discrete cases studied. It is found that while the optimum efficiency technology set is highly sensitive to the up-front cost a consumer is willing to pay for future operational savings, lightweighting options are often selected preferentially to efficiency reduction measures. In the same sense, although both technologies are very sensitive to discount rate, lightweighting technologies are less sensitive. Fully hybridized vehicles emerge as a robust option, and, surprisingly, rank highly together with fully electric powertrains.

Design of fractional order modeling based extended non-minimal state space MPC for temperature in an industrial electric heating furnace

In this paper, an improved approach of extended non-minimal state space (ENMSS) fractional order model predictive control (FMPC) is presented and tested on the temperature model of an industrial heating furnace. In the fractional order model predictive control algorithm, fractional order single-input single-output (SISO) system is discretized via fractional order Grünwald-Letnikov (GL) definition. The ENMSS fractional order model that contains the state variable and the fractional order output tracking error is formulated by choosing appropriate state variables. Meanwhile, the fractional order integral is introduced into the cost function and the GL definition is used to obtain the discrete form of the continuous cost function. Then the control signals are derived by minimizing the fractional order cost function. Lastly, the temperature process control of a heating furnace is illustrated to reflect the performance of the proposed FMPC method. Simulation results show the effectiveness of the proposed FMPC method.

Duality results for iterated function systems with a general family of branches

Given [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] compact metric spaces, we consider two iterated function systems [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are contractions. Let [Formula: see text] be the set of probabilities [Formula: see text] with [Formula: see text]-marginal being holonomic with respect to [Formula: see text] and [Formula: see text]-marginal being holonomic with respect to [Formula: see text]. Given [Formula: see text] and [Formula: see text], let [Formula: see text] be the set of probabilities in [Formula: see text] having [Formula: see text]-marginal [Formula: see text] and [Formula: see text]-marginal [Formula: see text]. Let [Formula: see text] be the relative entropy of [Formula: see text] with respect to [Formula: see text] and [Formula: see text] be the relative entropy of [Formula: see text] with respect to [Formula: see text]. Given a cost function [Formula: see text], let [Formula: see text]. We will prove the duality equation: [Formula: see text] In particular, if [Formula: see text] and [Formula: see text] are single points and we drop the entropy, the equation above can be rewritten as the Kantorovich duality for the compact spaces [Formula: see text] and a continuous cost function [Formula: see text].