Nonlinear Optimization Problem Research Articles

A new optimal strategy for energy minimization in wireless sensor networks

In recent years, evolutionary and metaheuristic algorithms have emerged as crucial tools for optimization in the field of artificial intelligence. These algorithms have the potential to revolutionize various aspects of our lives by leveraging the multidisciplinary nature of wireless sensor networks (WSNs). This study aims to introduce genetic and simulated annealing algorithms as effective solutions for enhancing WSN performance. Our contribution entails two main phases. Firstly, we establish mathematical models and formulate objectives as a nonlinear constrained optimization problem. Secondly, we develop two algorithmic solutions to address the formulated optimization problem. The obtained results from multiple simulations demonstrate the positive impact of the proposed strategies on improving network performance in terms of energy consumption.

Optimal power dispatch in hybrid power system for medium- and large-scale practical power systems using self-adaptive bonobo optimizer algorithm

Incorporating renewable energy sources (RESs) introduces a notable amount of uncertainty in the optimal planning and operation of electrical power grids. Under these circumstances, this paper proposes the application of a recently introduced metaheuristic optimization technique to solve the stochastic optimal power flow (OPF) problem involving wind and solar power sources. The self-adaptive bonobo optimizer (SaBO) is used to minimize three distinct objective functions: (i) Total generation cost (TGC) minimization, including both thermal and wind/solar generation costs, (ii) Power loss minimization, (iii) Combined generation cost and emissions effect minimization. The costs associated with the stochastic generation of wind and solar power included direct costs, reserves and penalty costs from the overestimation and underestimation of available wind and solar power, respectively. The performance of the proposed algorithm is evaluated on two power systems: the modified IEEE 30-bus and the Algerian DZA 114-bus test systems. To demonstrate the efficacy of the SaBO, the obtained results have been compared with those obtained from the Kepler optimization algorithm (KOA) and other recently published optimizers under the same case studies and constraints. The comparative results clearly show the superiority of the SaBO algorithm over all other well-known optimization algorithms provided in the literature for solving the OPF problem. This is evidenced by minimizing total generation costs of 781.2363 $/h for the modified IEEE 30-bus and 16,706.1630 $/h for the Algerian DZA-114-bus system. Furthermore, the integration of RES led to a notable 2.33% and 11.67% reduction in total generation cost for the IEEE 30-bus and Algerian DZA 114-bus systems, respectively, compared to their initial configurations without RESs. The promising findings highlight the powerful of the optimizer to solve non-linear and complex optimization problems in power systems.

Evolutionary computation, an alternative solution to nonlinear optimization problems

Analytical and numerical methods have been applied to solve problems in engineering. However, in some practical cases, they usually fail when there is a certain degree of complexity, for instance, when there is a certain lack of information about the elements of the system and when the unknowns are functions. These types of problems are often called nonlinear optimization problems. As an alternative to solving them, evolutionary computation methods are usually implemented, although they do not generate an exact solution, and provide a series of approximations that are generally feasible. In this context, the objective of this work is to briefly highlight the most typical characteristics of these type of algorithms, some advantages, and the importance of its use today. Due to the wide variety of existing methods, it would become complex to explain all of them in detail, so only a description of the differential evolution (DE) algorithm will be made because it is one of the most used and because there is current research that seeks to improve its performance.

Mathematical Model and Statistical Assessment of Non Linear Scheduling Optimization in Cloud Environment using Improved Cuckoo Search Algorithm

The scheduling optimization subject is indeed one of the most effective solutions in cloud system area to ensure the high systems performance and resource usage. The novelty presented in this study is a mathematical model that draws on an Improved Cuckoo Search Algorithm as a scheduling non-linear optimizer for the cloud computing environment. The model under consideration takes into account the underlying complications as well as the varying nature of the use of cloud resources, primarily addressing the latency issue with priority given to the increase of the throughput. Improved Cuckoo Search (ICS) Algorithm, developed on 'cuckoo search' algorithm, uses adaptive step size and probabilistic switching, which, in turn, ensure that the solution space is both being properly examined and exploited. The applications’ utilization of the scheduling mathematical model is based on an elaborately designed theoretical background representing the task as a non-linear optimization problem that meets all the specific constraints and objectives important in cloud computing. Statistical reassessment involves the comparison of the proposed model with standard benchmarks. The proposed model superiority is evident in terms of convergence speed, solution quality and robustness against diverse workloads, as shown in varied tests. The findings of this research contributes to the field by deriving a specialized tool commonly used by the cloud service provider in designing resource scheduling, enhancing the service delivery and operational efficiency.

Optimal control in models of virus propagation

Based on the SEIRD model, we consider that when multiple viruses of different virulence coexist, the more virulent virus will reinfect nodes already infected by the less virulent virus, which we call here Superexposed. Based on the state transitions, the corresponding differential equations and cost functions are established, then building the corresponding optimal control problem, where the vaccine efficiency and drug efficiency are controlled variables. This nonlinear optimal control problem is solved by Pontryagin’s maximum principle to finding the structure of the optimal control strategies. Based on the definition of the basic regeneration number, yielding the R0 value for the model, then discussed the final epidemic size. In the numerical analysis section, we validate the accuracy of the structure, fitting the behavior of each state and the effect of different parameter values.

Optimal Unmanned Combat System-of-Systems Reconstruction Strategy with Heterogeneous Cost via Deep Reinforcement Learning

The unmanned combat system-of-systems (UCSoS) in modern warfare is comprised of various interconnected entities that work together to support mission accomplishment. The soaring number of entities makes the UCSoS fragile and susceptible to triggering cascading effects when exposed to uncertain disturbances such as attacks or failures. Reconfiguring the UCSoS to restore its effectiveness in a self-coordinated and adaptive manner based on the battlefield situation and operational requirements has attracted increasing attention. In this paper, we focus on the UCSoS reconstruction with heterogeneous costs, where the collaboration nodes may have different reconstruction costs. Specifically, we adopt the heterogeneous network to capture the interdependencies among combat entities and propose a more representative metric to evaluate the UCSoS reconstruction effectiveness. Next, we model the combat network reconstruction problem with heterogeneous costs as a nonlinear optimization problem and prove its NP-hardness. Then, we propose an approach called SoS-Restorer, which is based on deep reinforcement learning (DRL), to address the UCSoS reconstruction problem. The results show that SoS-Restorer can quickly generate reconstruction strategies and improve the operational capabilities of the UCSoS by about 20∼60% compared to the baseline algorithm. Furthermore, even when the size of the UCSoS exceeds that of the training data, SoS-Restorer exhibits robust generalization capability and can efficiently produce satisfactory results in real time.

Optimal coordination of directional overcurrent protection relays using hybrid optimizer

In order to minimize or maximize an objective function, electrical engineering problems might benefit from optimization methodologies inspired by nature. This study employs a hybrid particle swarm optimizer (HPSO) to get rid of local optimum solutions and find the best global one for directional overcurrent protection relays (DOPR) protection. DOPR coordination is a highly constrained, mixed-integral nonlinear optimization problem. An adaptive defense method has been created to counteract the intentionally challenging design. Therefore, design variables such as time multiplier setting (TMS) and plug setting (PS) are utilized for each relay in the circuit. The goal function is to reduce the amount of time spent to trace the fault by all the relays. Reducing the time required for each relay to trace the fault is the aim of function. After analyzing and comparing two test studies of the IEEE benchmark using various optimization strategies, we found that the results for the IEEE 15-bus system has minimum time of 8.9 s, which is improved by 22.92% to 82.89%, and those for the IEEE 30-bus system minimum time of 22.45 s that is improved by 4.41% to 39.6%. In terms of overall DOPR operation and computational time needed to get the global optimum solution, the acquired results are demonstrably superior to those obtained using conventional and state-of-the-art methods.

Physics-informed deep learning and linear programming for efficient optimization of combined cycle power plants

Efficient operation of combined cycle power plants (CCPP) involves solving mixed-integer nonlinear optimization problems, constrained by thermodynamic differential equations, thermal constraints, and temporal dependencies between variables. The optimization problem aims to maximize profit for day-ahead operation by minimizing short-term and long-term costs, and accounting for volatility in ambient conditions and energy price. In operational terms, the challenge lies in developing an efficient and robust optimization algorithm capable of determining optimal values for thousands of temporal variables. It must also have the capacity to evaluate a multitude of scenarios encompassing various weather and market conditions. To address this challenge, this paper proposes a hybrid optimizer that utilizes deep learning models trained on historical operational data of a real CCPP, along with a surrogate physics-driven piecewise-linear model of CCPP, to determine the optimal values of thousands of control setpoints, with strong temporal co-dependencies, within a two-minute runtime required by industry constraints. A multi-resolution architecture is proposed to efficiently implement this optimizer. The algorithm sequentially solves the problem in coarse and fine resolutions to accelerate convergence. Final results are checked for feasibility using pre-trained deep learning models, ensuring accuracy and validity. The study shows that the proposed model provides comparable results to the exact solution while reducing computational costs, up to 95%. This research has practical implications for power plant system operators, as well as traders and dispatchers, enabling them to make optimal decisions for day-ahead contracting purposes and CCPP operation in a reasonable time, ultimately leading to more efficient and cost-effective power plant management. Furthermore, the methodology introduced in this work could potentially be extended to other industrial applications that require large-scale, complex optimizations, where the precise governing principles of a process can be approximated by piecewise-linear functions.

Various duality models associated with some constrained robust nonlinear optimal control problems

This paper deals with various duality results for a new class of constrained robust nonlinear control problems. Concretely, we introduce a minimisation problem associated with a vector of functionals of multiple integral type. In addition, the considered multi-objective controlled optimisation problem is governed by several mixed constraints generated by partial derivatives of second order and uncertain data. For this new class of control problems, we establish and characterise Wolfe, Mond-Weir and mixed type robust dual models. To this aim, by using the notion of convex multiple integral functional, generated by a controlled second-order Lagrangian with uncertain data, and the concept of robust weak efficient solution to the problem under study, we build a new mathematical context to state and prove the duality theorems.

Blockchain for urban governance: Enhancing trust in smart city systems with advanced techniques

The rapid urbanization and increasing energy demands necessitate innovative solutions for efficient energy governance in smart cities from the social science perspective. This paper introduces a comprehensive framework for Urban Energy Governance (UEG), focusing on the collaboration of three urban systems in energy exchange considering social and environmental impacts. To address the challenges of security, energy forecasting, and nonlinear optimization, we employ advanced techniques, including blockchain technology, Long Short-Term Memory (LSTM) networks for accurate energy forecasting, and a modified Particle Swarm Optimization (PSO) algorithm for solving the proposed nonlinear optimization problem. The utilization of blockchain enhances the security and transparency of energy transactions, fostering trust among stakeholders. Additionally, LSTM models leverage historical data to provide precise energy forecasts, optimizing resource utilization. The modified PSO algorithm tailors optimization to the specific nonlinearities of the proposed problem, ensuring efficient and effective decision-making in the context of Urban Energy Governance. Through a multi-faceted approach, our framework contributes to the advancement of smart city systems, providing a secure, forecast-driven, and optimized energy governance model for sustainable urban development.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Multi-level optimal energy management strategy for a grid tied microgrid considering uncertainty in weather conditions and load

Microgrids require efficient energy management systems to optimize the operation of microgrid sources and achieve economic efficiency. Bi-level energy management model is proposed in this paper to minimize the operational cost of a grid-tied microgrid under load variations and uncertainties in renewable sources while satisfying the various technical constraints. The first level is day ahead scheduling of generation units based on day ahead forecasting of renewable energy sources and load demand. In this paper, a recent meta-heuristic algorithm called Coronavirus Herd Immunity Optimizer (CHIO) is used to solve the problem of day-ahead scheduling of batteries, which is a complex constrained non-linear optimization problem, while the Lagrange multiplier method is used to determine the set-point of the Diesel Generator (DG). The second level of the proposed EMS is rescheduling and updating the set-points of sources in real-time according to the actual solar irradiance, wind speed, load, and grid tariff. In this paper, a novel real-time strategy is proposed to keep the economic operation during real-time under uncertainties. The obtained results show that the CHIO-based bi-level EMS demonstrates an optimal economic operation for a grid-connected microgrid in real-time when there are uncertainties in weather, utility tariffs, and load forecasts.

Three-stage energy trading framework for retailers, charging stations, and electric vehicles: A game-theoretic approach

Electric vehicle (EV) load integration and environmental concerns in recent years have motivated energy users to step forward in reducing carbon footprints by promoting energy trading. In the energy trading market, different energy stakeholders participate in trading energy with each other to maximize their utilities and improve trading efficiency. The social welfare (SW) of the energy market plays a significant role in keeping the market going and motivating new users to engage in energy trading. The SW of the energy market depends on its structure, where energy flows from producer to end user in a fair way. This paper introduces a hierarchical energy trading framework, formulated as a three-stage Stackelberg game, to enhance SW. In the first stage of this hierarchy, the retailer, acting as the sole leader, seeks to maximize profits through optimized energy sales to charging stations (CS). Subsequently, in the second stage, each CS operates as a leader for EVs, aiming to maximize profits by minimizing energy trading costs, while also acting as a follower in response to the retailer’s strategies. The third and final stage involves EVs collaboratively acting as a unified strategic agent to minimize their trading costs through optimized charging and discharging schedules. This paper also introduces an average price penalty function to further enhance SW in the energy market. The proposed model, addressing the complexities of energy trading interactions, is formulated as a non-linear optimization problem with constraints. It has been implemented in a Python environment and solved using the Gurobi optimization solver, demonstrating its potential to improve the efficiency, fairness, and overall social welfare of the energy trading market.

Data-driven hierarchical collaborative optimization method with multi-fidelity modeling for aerodynamic optimization

The aerodynamic optimization of aircraft based on evolutionary algorithms generally requires thousands or even tens of thousands of iterations. Moreover, it faces challenges such as high-dimensional design variables and high computational costs, leading to low efficiency in algorithm search and poor optimization results. In order to enhance the efficiency of aerodynamic optimization, a data-driven collaborative optimization and multi-fidelity hierarchical modeling method is proposed. Firstly, a Clustering-Enhanced Teaching-Learning-Based Optimization (CETLBO) algorithm is introduced to improve its exploration and exploitation capabilities. By employing a collaborative optimization strategy, a divide-and-conquer paradigm is utilized to efficiently solve high-dimensional, nonlinear, and complex engineering optimization problems. Secondly, a two-stage hierarchical aerodynamic optimization framework is designed to reduce computational costs by integrating data from different fidelity levels. Stage 1 adopts a data-driven approximate optimization method to provide prior knowledge for the high-fidelity optimization of stage 2. Finally, the proposed method is applied to the optimization design of supersonic wing shapes. Compared to traditional optimization design systems, it demonstrates high efficiency in high-dimensional aerodynamic optimization problems, yielding better optimization results.

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

Regression based stochastic energy management strategy for a grid connected microgrid using Artificial Electric Field Algorithm

Recent decade has witnessed steep technological advancement in the renewable energy sector due to growing concern of climate change and emission cut target. The lack of availability of fossil fuels and the high price of the same have made the use of Renewable Energy Sources (RES) as a promising approach for generating clean and sustainable energy at local level. This persuades the implementation of Microgrid (MG) supported with RES, to cater various types of load demand. However, planning and optimizing a MG operation have become challenging due to the intermittent nature of RES and uncertain loads. To address this issue, this paper introduces a Stochastic Energy Management Strategy (SEMS) for a grid connected MG comprising Photovoltaic, Wind Turbine, Fuel Cell, Micro Turbine, Battery Energy Storage and electrical as well as heat energy demand. The volatilities of RES power output and energy demand are modeled via Gaussian Process Regression (GPR) and Monte Carlo Simulation (MCS) respectively. The problem is framed as non-linear (NL) dynamic stochastic optimization problem and solved using ‘Artificial Electric Field Algorithm (AEFA)’. Here, minimization of expected value of operational and emission cost are taken as objective functions; while various practicality aspects are modeled as constraints in the problem. Further, the efficacy of the proposed approach is validated around the first central moment of the load. Various case studies are performed to estimate the day ahead optimum operating schedule of the Distributed Energy Resources (DER) and to assess the impact of load uncertainties on DER operation and total MG operation cost. Further, the efficacy of the GPR is verified through comparison with MCS based result.

A centralized EMPC scheme for PV-powered alkaline electrolyzer

Photovoltaic (PV)-powered alkaline electrolyzer system (PVPAES) is an advanced technique to convert the off-grid and intermittent PV-based solar energy into the storable and transportable electrolyzer-based hydrogen energy with zero carbon emissions. However, it is difficult to realize the coordinated control of the off-grid PV module and the alkaline electrolyzer, due to the multiple timescale dynamics. To address this challenge, the PVPAES is decomposed into slow part and fast part based on the dynamic time scale. Exploiting the decomposed subsystems, the slow one is assumed to be managed well by the auxiliary controller. For the fast one, a centralized economic model predictive control (CEMPC) scheme is constituted. This CEMPC integrates the energy management system and local feedback control into a single optimal control framework. A mathematical model of the PVPAES is established, on the basis of which the CEMPC directly adopts the economic indices as the cost function to realize the flexible power point tracking, power supply–demand balance, and dynamic economic optimization. Moreover, the inherent strong nonlinearity of PVPAES results in the nonconvex mixed-integer nonlinear programming optimization problem in the CEMPC. The exhaustive search algorithm utilizing finite converter switching states is adopted to achieve the global economic optimum. The effectiveness of the proposed CEMPC controller is illustrated through simulations under varying irradiance conditions.

Successive upper approximation methods for generalized fractional programs

The majorization approximation procedure consists in replacing the resolution of a nonlinear optimization problem by solving a sequence of simpler ones, whose objective and constraint functions upper estimate those of the original problem. For generalized fractional programming, i.e., constrained minimization programs whose objective functions are maximums of finite ratios of functions, we propose an adapted scheme that simultaneously upper approximates parametric functions formed by the objective and constraint functions. For directionally convex functions, that is, functions whose directional derivatives are convex with respect to directions, we will establish that every cluster point of the generated sequence satisfies Karush-Kuhn-Tucker type conditions expressed in terms of directional derivatives. The proposed procedure unifies several existing methods and gives rise to new ones. Numerical problems are solved to test the efficiency of our methods, and comparisons with different approaches are given.

Optimised Congestion Management Using Curative Measures in Combined AC/DC Systems with Flexible AC Transmission Systems

Due to the increasing demand for transport of electrical energy, measures for power flow control, congestion management, and higher utilisation of the existing grid play a decisive role in the transformation of the power system. Hence, enormous efforts must be undertaken using measures of congestion management. Modelling and integration of corresponding measures in optimisation tools to support grid and system operation and therewith reduce the resulting efforts become more important. This is especially true because of the high intermittency and decentralisation of renewable generation leading to increased complexity of the power system, higher loading of assets, and a growing need for control over flexible alternating current transmission systems (FACTS) and high-voltage direct current (HVDC) converters. This work therefore describes the implementation of optimised congestion management in an A Mathematical Programming Language (AMPL)-based nonlinear optimisation problem. AMPL is an effective tool to deal with highly complex problems of optimisation and scheduling. Therefore, the modelling of assets and flexibilities for power flow control in AC/DC systems in combination with an innovative grid operation strategy using predefined curative measures for the optimised use of the existing grid is introduced. The nonlinear mathematical optimisation aims at the optimal cost selection of flexibility measures. The application of the optimisation technique in a combined AC/DC system shows the optimal preventive and curative use of measures in operational congestion management. Simulation results prove that, by using predefined curative measures, the volume of cost-intensive preventive measures can significantly be reduced, especially in association with power flow control.

Planar Reconstruction of Indoor Scenes from Sparse Views and Relative Camera Poses

Planar reconstruction detects planar segments and deduces their 3D planar parameters (normals and offsets) from the input image; this has significant potential in the fields of digital preservation of cultural heritage, architectural design, robot navigation, intelligent transportation, and security monitoring. Existing methods mainly employ multiple-view images with limited overlap for reconstruction but lack the utilization of the relative position and rotation information between the images. To fill this gap, this paper uses two views and their relative camera pose to reconstruct indoor scene planar surfaces. Firstly, we detect plane segments with their 3D planar parameters and appearance embedding features using PlaneRCNN. Then, we transform the plane segments into a global coordinate frame using the relative camera transformation and find matched planes using the assignment algorithm. Finally, matched planes are merged by tackling a nonlinear optimization problem with a trust-region reflective minimizer. An experiment on the Matterport3D dataset demonstrates that the proposed method achieves 40.67% average precision of plane reconstruction, which is an improvement of roughly 3% over Sparse Planes, and it improves the IPAA-80 metric by 10% to 65.7%. This study can provide methodological support for 3D sensing and scene reconstruction in sparse view contexts.