Cost Function Research Articles

Strategic Behavior and Optimal Inventory Level in a Make-to-Stock Queueing System with Retrial Customers

In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat customer repeats their demand after an exponential amount of time until they have been successfully served. We explore the equilibrium strategies of customers in both the almost observable and unobservable cases. Furthermore, we also analyze the expected costs of the entire system based on the customers’ behavior in these two cases. Additionally, we determine the optimal inventory levels in both cases through numerical experiments.

A hybrid physics-based and data-driven model for intra-day and day-ahead wind power forecasting considering a drastically expanded predictor search space

This work presents a novel hybrid (physics- and data-driven) model for short-term (intra-day and day-ahead, 3h-24h) wind power forecasting (STWPF). Traditionally, STWPF predictors admitted very few meteorological variables only from the grid points closest to the turbines. Here, with the aim to further capture the underlying atmospheric processes ruling the wind variability in the wind farm, the approach relies on drastically expanding the predictor space, composed of numerous meteorological variables throughout a large geographical domain, retrieved from a weather forecasting model (COSMO-1). An ad-hoc genetic algorithm that optimizes the selection of predictors is designed and combined with feed-forward artificial neural networks for its cost function evaluation. The introduced model is compared to multiple benchmark models in a 16-turbine wind farm in the Swiss Jura mountains. For +12h and +24h lead times, the new approach shows a root-mean squared error normalized to the installed wind farm capacity of 11% and 11.6%, respectively. These values entail ∼16% higher forecasting skill compared to state-of-the-art predictor frameworks. Results highlight the ability of the presented approach to systematically select as predictors different variables with a well-known impact on the wind farm performance, such as the turbulent kinetic energy or the vertical wind shear. Clustering the data according to the wind direction provides substantial benefit. In addition, it provides a better understanding of the attained improvement: largest performances occur in those wind directions affected by highly complex terrain. This indicates that the proposed model can be especially suitable for wind farms in complex terrain.

Data-driven optimization for microgrid control under distributed energy resource variability

The integration of renewable energy resources into the smart grids improves the system resilience, provide sustainable demand-generation balance, and produces clean electricity with minimal leakage currents. However, the renewable sources are intermittent in nature. Therefore, it is necessary to develop scheduling strategy to optimise hybrid PV-wind-controllable distributed generator based Microgrids in grid-connected and stand-alone modes of operation. In this manuscript, a priority-based cost optimization function is developed to show the relative significance of one cost component over another for the optimal operation of the Microgrid. The uncertainties associated with various intermittent parameters in Microgrid have also been introduced in the proposed scheduling methodology. The objective function includes the operating cost of CDGs, the emission cost associated with CDGs, the battery cost, the cost of grid energy exchange, and the cost associated with load shedding. A penalty function is also incorporated in the cost function for violations of any constraints. Multiple scenarios are generated using Monte Carlo simulation to model uncertain parameters of Microgrid (MG). These scenarios consist of the worst as well as the best possible cases, reflecting the microgrid’s real-time operation. Furthermore, these scenarios are reduced by using a k-means clustering algorithm. The reduced procedures for uncertain parameters will be used to obtain the minimum cost of MG with the help of an optimisation algorithm. In this work, a meta-heuristic approach, grey wolf optimisation (GWO), is used to minimize the developed cost optimisation function of MG. The standard LV Microgrid CIGRE test network is used to validate the proposed methodology. Results are obtained for different cases by considering different priorities to the sub-objectives using GWO algorithm. The obtained results are compared with the results of Jaya and PSO (particle swarm optimization) algorithms to validate the efficacy of the GWO method for the proposed optimization problem.

Topology-aware Parallel Joins

We study the design and analysis of parallel join algorithms in a topology-aware computational model. In this model, the network is modeled as a directed graph, where each edge is associated with a cost function that depends on the data transferred between the two endpoints and the link bandwidth. The computation proceeds in synchronous rounds and the cost of each round is measured as the maximum cost over all the edges in the network. Our main result is an asymptotically optimal join algorithm over symmetric tree topologies. The algorithm generalizes prior topology-aware protocols for set intersection and cartesian product to a binary join over an arbitrary input distribution with possible data skew.

Effective anti-submarine decision support system based on heuristic rank-based Dijkstra and adaptive threshold partitioning mechanism

Submarines possess strong covert striking capabilities, making anti-submarine warfare (ASW) a global naval priority. The Hidden Markov Anti-Submarine Model (HMASM) finds crucial applications in dynamic and uncertain ASW. The model delineates ASW into two phases: partitioning and search path planning. Current partitioning algorithms often include cells leading to redundant and competitive search, determined empirically. Additionally, in HMASM, the path planning algorithms based on genetic algorithm (GA) are time-consuming and exhibits unstable performance. This paper proposes a novel solution to these issues. For partitioning, a Reassigned k-Nearest Neighbour (RKNN) algorithm is introduced, identifying and reallocating units causing repeated and competing searches. For search path planning, heuristic rules for Dijkstra's cost function and goal point selection transform the NP-hard problem of maximizing the expected number of detections (ED) into a deterministic algorithm-compatible form. A heuristic rank-based selection model, Rank-Based Dijkstra under the Hidden Markov Model (HMM-R-Dijkstra), considering distance and probability, is added to Dijkstra. Furthermore, an Adaptive Threshold Partitioning (ATP) dynamically monitors searcher exploration by setting variables and thresholds to determine optimal partitioning timing, preventing untimely and excessive partitioning. Combining RKNN, HMM-R-Dijkstra, and ATP forms R-HRD-ATP, optimizing all parameters using parallel structures. Through three comparative experiments, R-HRD-ATP's performance steadily improves. Experiments comparing R-HRD-ATP to GA, Sparrow Search Algorithm (SSA)-GA, and Ant Colony Optimization (ACO)-GA reveal performance enhancements of 25–70.99% and time savings of 56–295 times for our model. Importantly, no parameter adjustments are required. The success of R-HRD-ATP indicates that its heuristic rules can support the establishment of robust applications of deterministic path planning algorithms in HMASM.

Optimization of a wind farm layout to mitigate the wind power intermittency

A multi-objective optimization method utilizing genetic algorithms is developed to optimize wind farm layout design with the dual objectives of enhancing the production of wind power and reducing hour-level intermittency in the generated power. This method introduces a novel metric for annual wind power intermittency based on the transition probability of wind conditions (i.e., speed and direction). The present multi-objective optimization method ensures that Pareto optimal layouts are evenly distributed according to multiple cost function values. To mitigate wind power intermittency, the spatial distribution of wake fields is strategically manipulated to counteract hourly fluctuations in wind conditions. In wind conditions favoring high power generation, it is found that increasing the overlap between wakes and turbines helps to minimize disparities in generated power compared to other wind conditions.

Hot‐spot aware multicost‐based energy‐efficient routing protocol for WBANs

SummaryWireless body area networks (WBANs) are becoming widely considered in remote healthcare monitoring applications. However, WBAN nodes have limited resources; therefore, effective and reliable routing protocols are pivotal research challenges. Furthermore, balancing the traffic load among sensor nodes is also highly required to increase network stability. In recent years, many interesting routing solutions have been proposed for WBANs; however, the significant feature in terms of stability and energy in these solutions has not been sufficiently addressed. Therefore, in this context, the Hot‐Sspot Aaware Multicost‐based Energy‐efficient Routing (H‐SAMER) protocol is proposed in this paper. The suggested protocol used multieffective cost function for next‐hop node selection based on the data type, where the patient's data are categorized into three classes: normal data, on‐demand data, and emergency data. Furthermore, the H‐SAMER protocol adds awareness to the transmission of control packets by adding the cost value to the RREQ packets. Thus, the simulation scenario shows that the H‐SAMER saves energy 8.57%, 88%, 98%, 97%, and 100% greater than E‐HARP, EH‐RCP, CO‐LAEEBA, EECBSR, and ELR‐W, respectively. Moreover, the first node death of the proposed H‐SAMER is delayed to round number 7500, which proves H‐SAMER to be a stable and reliable effective solution for WBANs.

Distributed finite-time optimization for networked Euler–Lagrange systems under a directed graph

In this paper, we investigate the finite-time distributed optimization problem for multiple Euler–Lagrange systems. A new distributed optimization control scheme is presented to achieve the state agreement in finite time while minimizing the sum of each agent’s local cost function. The proposed algorithm has the advantage of being able to achieve distributed finite-time optimization consensus under general unbalanced connected directed communication graphs. By virtue of finite-time Lyapunov theory and convex optimization, the finite-time convergence for the algorithm is analyzed. A numerical example is also presented to illustrate the effectiveness of the obtained results.

Intent inferring based human-machine game control strategy for spacecraft rendezvous

In this paper, we propose a game control method for a machine-controlled spacecraft to cooperate with a human-controlled spacecraft in near-circular orbit for a rendezvous mission. Inspired by the cooperative game theory, the two-spacecraft rendezvous process is formulated as a cooperative differential game (DG) with a common cost function. A challenging problem is that the intent of the human-controlled spacecraft represented by the weighting matrix in the cost function is not available to the machine-controlled spacecraft. To complete the rendezvous mission optimally, an intent inferring based game control algorithm is developed for the machine-controlled spacecraft. Specifically, an adaptive approach is proposed for the machine-controlled spacecraft to identify the feedback gain matrix of the human-controlled spacecraft online based on the system state alone with the concurrent learning (CL) technique; furthermore, the unknown weighting matrix representing the intent of the human-controlled spacecraft in the cost function is retrieved by an inverse differential game (IDG) method. Accordingly, the control law of the machine-controlled spacecraft is updated in real-time. The control strategies of the spacecraft converge to near the Nash equilibrium. Finally, the simulation result is presented to illustrate the effectiveness of the approach.

Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic

The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic.

Enhancing Battery Capacity Estimation Accuracy through the Neural Network Algorithm

Accurate estimation of battery metrics, such as state of health (SOH), is crucial for effective battery management systems (BMS) due to capacity degradation over time. This paper proposes a methodology to enhance battery capacity estimation accuracy by addressing uncertainties related to state of charge (SOC) estimation and measurement. The methodology employs the Neural Network Algorithm (NNA), an optimization algorithm inspired by artificial neural networks (ANNs). The NNA generates an initial population of pattern solutions and iteratively updates them using a weight matrix, bias operator, and transfer function operator. By combining the advantages of ANNs and optimization techniques, the NNA aims to find an optimal solution considering interdependent variables and incorporating global and local feedbacks. Leveraging the capabilities of the NNA, our objective is to identify the candidate that minimizes a specified cost function, ensuring up-to-date cell capacity through a memory forgetting factor. The algorithm's precision was validated using NASA's Prognostic Data, demonstrating outstanding performance by surpassing two aggressive algorithms in terms of accuracy. In the most severe case scenario, the algorithm achieved a peak error of less than 0.4%. Furthermore, the algorithm consistently demonstrated predictive performance measures that were superior to those of the compared algorithms.

Suppression of Initial Charging Torque for Electric Drive-Reconfigured On-Board Charger

This paper presents a new electric drive-reconfigured on-board charger and initial electromagnetic torque suppression method. This proposed reconfigured on-board charger does not need many components added to the original electric drive system: only a connector is needed, which is easy to add. Specifically, the inverter for propulsion is reconfigured as a buck chopper and a conduction path to match the reconfigured windings. Two of the machine phase windings serve as inductors, while the third phase winding is reutilized as a common-mode inductor. In addition, the initial charging torque is generated at the outset of the charging process, which may cause an instant shock or even rotational movement. In order to prevent vehicle movement, the reason for the charging torque and suppression method were analyzed. Further, predictive control of the model based on mutual inductance analysis was adopted, where the charging torque was directly used as a control object in the cost function. Finally, experimental performances were applied to verify the proposed reconfigured on-board charger under constant current and constant voltage charging.

Supporting load frequency control process by using adaptive model reference virtual inertia controller when connecting renewable energy plants

Virtual inertia control can be used in combination with conventional load frequency controllers to support the system's inertia against the attenuation caused by renewables. As fractional-order controllers add more degrees of freedom, leading to a better response and improved controller robustness, this work proposes the implementation of a developed fractional-order model reference adaptive virtual inertia controller when integrating renewables in combination with fractional-order ID-P with filter controller as secondary controllers. To validate the introduced controllers, their results have been compared to those of using integer and fractional-order PID controllers as secondary controllers, in combination with adaptive and fixed parameters virtual inertia controllers. The Artificial Rabbits heuristic algorithm is used for the purpose of tuning secondary controllers and fixed parameters virtual inertia controllers. The proposed combination of adaptive model reference virtual inertia control with fractional-order ID-P with a filter achieves the best response among all the studied combinations. Using the proposed combination shows a relative percentage improvement in the cost function value of 26% to 160% compared to all the studied combinations. Additionally, the proposed combination shows a maximum frequency overshoot value of 0.04 Hz and a minimum undershoot value of -0.06 Hz.

Real-time and hardware in the loop validation of electric vehicle performance: Robust nonlinear predictive speed and currents control based on space vector modulation for PMSM

The transport industry's environmental impact has prompted various stakeholders to focus more on electric vehicles as a potential solution. Extensive research on electric vehicle motor control reveals their complexity, highlighting the crucial role of the traction motor control mechanism being one of their essential subsystems. This study presents a novel approach to control the drive system of an electric vehicle's permanent magnet synchronous motor, using a robust non-linear model predictive control in a cascaded structure combined with a space vector modulation technique. The formulation of the robust non-linear model predictive control law involves optimizing a new cost function with the inclusion of an integral action in the controller to ensure zero steady-state error. An important aspect of this control approach is its ability to enhance robustness without needing information about external perturbations and parameter uncertainties. Moreover, the space vector modulation technique is designed to address the issue of current harmonic distortion by carefully selecting appropriate switching vectors. The appropriate selection for space voltage vectors for every sampling period maintains a consistent switching frequency. As a result, the SVM can enhance torque-rippled regulation and accomplish effective flux and torque control. The performance of the proposed control system is evaluated through a series of numerical simulations using MATLAB/Simulink. The simulation results are analyzed and compared to assess the effectiveness of the proposed control system in terms of tracking accuracy, disturbance rejection, robustness against parameter uncertainties, reduction of torque, and current ripples. To further validate the numerical simulation results, a hardware-in-the-loop (HIL) setup is established using the OPAL-RT platform. Furthermore, experimental validation on a PMSM utilizing the dSPACE DS1202 board is carried out, demonstrating the efficacy of the proposed control system. These findings validate the suggested control technique's robustness and efficiency.

Graph-based minimum error entropy Kalman filtering

When the Gaussian kernel function is chosen with a small kernel bandwidths, the minimum error entropy Kalman filter (MEEKF) exhibits excellent performance. However, further narrowing the kernel bandwidths leads to a degradation in performance. To address this issue, this paper proposed a Graph-based MEEKF (G-MEEKF) algorithm based on Graph Signal Processing (GSP) theory. The G-MEEKF algorithm addresses the problem by smoothing the errors using graph filtering and incorporating graph topology into the cost function. The convergence of the algorithm is theoretically analyzed and simulations demonstrate that G-MEEKF improves the performance of MEEKF under small kernel bandwidths. Furthermore, it is emphasized that the topology of the graph abstracted from the minimum error entropy (MEE) definition also influences the performance of the algorithm.

Enhancing Cryptographic Primitives through Dynamic Cost Function Optimization in Heuristic Search

The efficiency of heuristic search algorithms is a critical factor in the realm of cryptographic primitive construction, particularly in the generation of highly nonlinear bijective permutations, known as substitution boxes (S-boxes). The vast search space of 256! (256 factorial) permutations for 8-bit sequences poses a significant challenge in isolating S-boxes with optimal nonlinearity, a crucial property for enhancing the resilience of symmetric ciphers against cryptanalytic attacks. Existing approaches to this problem suffer from high computational costs and limited success rates, necessitating the development of more efficient and effective methods. This study introduces a novel approach that addresses these limitations by dynamically adjusting the cost function parameters within the hill-climbing heuristic search algorithm. By incorporating principles from dynamic programming, our methodology leverages feedback from previous iterations to adaptively refine the search trajectory, leading to a significant reduction in the number of iterations required to converge on optimal solutions. Through extensive comparative analyses with state-of-the-art techniques, we demonstrate that our approach achieves a remarkable 100% success rate in locating 8-bit bijective S-boxes with maximal nonlinearity, while requiring only 50,000 iterations on average—a substantial improvement over existing methods. The proposed dynamic parameter adaptation mechanism not only enhances the computational efficiency of the search process, but also showcases the potential for interdisciplinary collaboration between the fields of heuristic optimization and cryptography. The practical implications of our findings are significant, as the ability to efficiently generate highly nonlinear S-boxes directly contributes to the development of more secure and robust symmetric encryption systems. Furthermore, the dynamic parameter adaptation concept introduced in this study opens up new avenues for future research in the broader context of heuristic optimization and its applications across various domains.

An adjoint-based approach for the surgical correction of nasal septal deviations

Deviations of the septal wall are widespread anatomic anomalies of the human nose; they vary significantly in shape and location, and often cause the obstruction of the nasal airways. When severe, septal deviations need to be surgically corrected by ear–nose–throat (ENT) specialists. Septoplasty, however, has a low success rate, owing to the lack of suitable standardized clinical tools for assessing type and severity of obstructions, and for surgery planning. Moreover, the restoration of a perfectly straight septal wall is often impossible and possibly unnecessary. This paper introduces a procedure, based on advanced patient-specific Computational Fluid Dynamics (CFD) simulations, to support ENT surgeons in septoplasty planning. The method hinges upon the theory of adjoint-based optimization, and minimizes a cost function that indirectly accounts for viscous losses. A sensitivity map is computed on the mucosal wall to provide the surgeon with a simple quantification of how much tissue removal at each location would contribute to easing the obstruction. The optimization procedure is applied to three representative nasal anatomies, reconstructed from CT scans of patients affected by complex septal deviations. The computed sensitivity consistently identifies all the anomalies correctly. Virtual surgery, i.e. morphing of the anatomies according to the computed sensitivity, confirms that the characteristics of the nasal airflow improve significantly after small anatomy changes derived from adjoint-based optimization.

Weighted information entropy‐based Kalman filter for outliers and structural noise

AbstractStructural noise and outliers are widely present in real‐world state estimate scenarios, and they significantly degrade the performance of most filtering algorithms based on minimum mean square error (MMSE) criterion. To address this problem, this paper first models structural noise and outliers as independent and piecewise identical distribution (IPID). Then, a minimum error weighted entropy‐based Kalman filter (MEWE‐KF) is proposed, where a new cost function is constructed by introducing a weight function related to error location distances in an original information space into the minimum error entropy (MEE) criterion. Further, the iterative formulations of the proposed filter are derived, and the computational complexity and the convergence are also analyzed. Simulation results show that the proposed filter with adaptive weights has the superior performance for suppressing structural noise and outliers.

Domain Transformation of Distortion Costs for Efficient JPEG Steganography with Symmetric Embedding

Nowadays, most image steganographic schemes embed secret messages by minimizing a well-designed distortion cost function for the corresponding domain, i.e., the spatial domain for spatial image steganography or the JPEG (Joint Photographic Experts Group) domain for JPEG image steganography. In this paper, we break the boundary between these two types of schemes by establishing a theoretical link between the distortion costs in the spatial domain and those in the JPEG domain and thus propose a scheme for domain transformations of distortion costs for efficient JPEG steganography with symmetric embedding, which can directly convert the spatial distortion cost into its JPEG counterpart. Specifically, by formulating the distortion cost function for JPEG images in the decompressed spatial domain, a closed-form expression for a distortion cost cross-domain transformation is derived theoretically, which precisely characterizes the conversion from the distortion costs obtained by existing spatial steganographic schemes to those applied in JPEG steganography. Experimental results demonstrate that the proposed method outperforms other advanced JPEG steganographic schemes, e.g., JUNIWARD (JPEG steganography with Universal Wavelet Relative Distortion), JMiPOD (JPEG steganography by Minimizing the Power of the Optimal Detector), and DCDT (Distortion Cost Domain Transformation), in resisting the detection of various advanced steganalyzers.

Differential neural network robust constrained controller using approximate dynamic programming

This study focuses on developing a continuous differential neural network (DNN) approximating min–max robust control by applying dynamic neural programming. The suggested controller is applied to a class of nonlinear perturbed systems providing satisfactory dynamics for a given cost function depending on both the trajectories of the perturbed system and the designed constrained control actions. The min–max formulation for dynamic programming offers reliable control for restricted modeling uncertainties and perturbations. The suggested design considers control norm restrictions in the optimization problem. DNN’s approximation of the worst (with respect to the admissible class of perturbations and uncertainties) value function of the Hamilton–Jacobi–Bellman (HJB) equation enables the estimation of the closed-loop formulation of the controller. The robust version of the HJB partial differential equation is studied to create the learning law class for the time-varying weights in the DNN. The controller employs a time-varying Lyapunov-like differential equation and the solution of the corresponding learning laws. A recurrent algorithm based on the Kiefer–Wolfowitz technique can be used by modifying the weights’ initial conditions to fulfill the specified cost function’s end requirements. A numerical example tests the robust control proposed in this study, validating the robust optimal solution based on the DNN approximation for Bellman’s value function.