Solving Optimization Problems Research Articles

Parameter Estimation Method for Virtual Power Plant Frequency Response Model Based on SLP

In adapting to the double-high development trend of high-voltage direct current (HVDC) receiving-end power systems and solving optimization problems in emergency frequency control (EFC) supporting virtual power plants (VPPs) in large-scale power systems, a parameter estimation method for a VPP frequency response model based on a successive linear programming (SLP) method is proposed. First, a “centralized/decentralized” hierarchical control architecture for VPP participation in EFC is designed. Second, the frequency response characteristics of multiple flexible resources are scientifically analyzed, and the system frequency response (SFR) model and equivalent model of VPP are constructed. Subsequently, parameter estimation of the VPP frequency response model is carried out based on the SLP method, aiming to balance the accuracy and computational efficiency of the model. Finally, the effectiveness of the proposed methodology is verified by using PSD-BPA to simulate and test the three-zone HVDC recipient area grid.

Multi-scale information transport generative adversarial network for human pose transfer

Human pose transfer, a challenging image generation task, aims to transfer a source image from one pose to another. Existing methods often struggle to preserve details in visible regions or predict reasonable pixels for invisible regions due to inaccurate correspondences. In this paper, we design a novel multi-scale information transport generative adversarial network, composed of Information Transport (IT) blocks to establish and refine the correspondences progressively. Specifically, we compute a transport matrix to warp the source image features by integrating an optimal transport solver in our proposed IT block, and use IT blocks to refine the correspondences in different resolutions to preserve rich details of the source image features. The experimental results and applications demonstrate the effectiveness of our proposed method. We further present an image-specific optimization using only a single image. The code is available for research purposes athttps://github.com/Zhangjinso/OT-POSE.

ROSMOSE: A web-based decision support tool for the design and optimization of industrial and urban energy systems

Energy efficiency is crucial for the sustainable operation of industrial and urban sectors. However, practicing engineers seldom have access to open-source tools that can readily evaluate and compare scenarios. In this work, a novel web-based tool called ROSMOSE is developed and proposed for analyzing the energy efficiency of industrial and urban systems and comparing potential process integration options. This optimization framework computes and graphically represents the minimum energy requirements, the pinch temperatures, and the Grand and integrated Carnot composite curves of process systems. Results are used to design utility systems that meet energy demands, while minimizing a specified objective function, such as total cost or environmental impacts. The Quarto environment, in which ROSMOSE is built upon, allows the integration of various open-source software and tools, such as database handling software, process modeling suites, and optimization solvers, along with interactive data visualization and reporting tools. This paper discusses the application of ROSMOSE for the energy integration and total site optimization of a dairy process consisting of milk treatment, and cream and cheese production to demonstrate the tool features. Other integration options, such as the use of heat pumps or solar panels, and the production of soft drinks or biogas as value-added byproducts, are also proposed and evaluated. As a result, from 75 % to 90 % in fuel savings and up to 80 % CO2 emissions reduction in the dairy plant are identified by optimizing the utility systems integration. Moreover, complete electrification via heat pumps eliminates any fossil fuel needs and it results in 85 % energy savings and up to 96 % CO2 emissions reduction. The activation of renewable electricity sources, such as solar power, made plausible this fully electrified scenario. Finally, optimized waste management strategies led to in-house fuel production and net export of biogas to the grid, but they also reduce cheese yield by prioritizing the biogas production from whey upgrading process. In this way, decision-makers have access to a clear performance comparison for a list of system configurations to draw informed trade-offs. A similar approach could be adopted to aid decision-making for the design and operation of other industrial and urban energy systems using ROSMOSE.

A performance indicator-based evolutionary algorithm for expensive high-dimensional multi-/many-objective optimization

Surrogate-assisted multi-objective evolutionary algorithms have shown considerable potential for solving optimization problems in which only a small number of expensive function evaluations are available. However, most existing research remains restricted to low-/medium-dimensional problems, with very little attention paid to addressing problems involving decision variables with more than 100 dimensions. In this study, a performance indicator-based evolutionary algorithm (PIEA) is proposed for expensive high-dimensional multi-/many-objective optimization. A surrogate model is employed to approximate the performance indicator rather than directly predicting the objective function, thus simplifying the optimization complexity and mitigating the impact of cumulative errors. An efficient indicator-based optimization strategy emphasising the balance between exploration and exploitation is designed for surrogate-assisted evolution and infill sampling. A history-based selection strategy is implemented to select a suitable indicator from the preset pool for each optimization cycle. An empirical study was conducted on two well-known benchmark suites, and the results demonstrate the superiority of the proposed algorithm over several state-of-the-art algorithms. Moreover, we integrate this concept into a classification-based framework, which further verifies its effectiveness.

From low-rank retractions to dynamical low-rank approximation and back

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well, including interpolation tasks. In this work, we consider the application of retractions to the numerical integration of differential equations on fixed-rank matrix manifolds. This is closely related to dynamical low-rank approximation (DLRA) techniques. In fact, any retraction leads to a numerical integrator and, vice versa, certain DLRA techniques bear a direct relation with retractions. As an example for the latter, we introduce a new retraction, called KLS retraction, that is derived from the so-called unconventional integrator for DLRA. We also illustrate how retractions can be used to recover known DLRA techniques and to design new ones. In particular, this work introduces two novel numerical integration schemes that apply to differential equations on general manifolds: the accelerated forward Euler (AFE) method and the Projected Ralston–Hermite (PRH) method. Both methods build on retractions by using them as a tool for approximating curves on manifolds. The two methods are proven to have local truncation error of order three. Numerical experiments on classical DLRA examples highlight the advantages and shortcomings of these new methods.

A robust [formula omitted] fault-tolerant control approach for time-delay LPV systems with uncertain parameters and unknown disturbances

The article proposes a H∞ fault-tolerant control approach for a series of uncertain linear parameter-varying (LPV) time-delay models to obtain disturbance suppressions. Specifically, by applying the Lyapunov functions, a series of feedback controllers are provided to ensure the robust performance of LPV models with actuator faults. Meanwhile, a convex optimization strategy is developed for resolving optimization problems in the presence of bilinear matrix inequalities (BMIs), where the robustness conditions are improved to guarantee the stability of LPV model under uncertain factors. By resolving a class of linear matrix inequalities (LMIs), the gain matrices for LPV systems can be obtained. Furthermore, the less conservative conditions are developed and supported by strict theoretical derivation. Ultimately, the validity of proposed approach is confirmed by simulation analyses of truck–trailer systems.

Exploration of Solving Methods and Applications of Neural Network Models in Optimization Problems

With the booming growth of artificial intelligence (AI) technology, machine learning (ML) as its core component has shown enormous potential and application value in solving optimization problems. Among numerous ML algorithms, neural networks (NN) have become one of the preferred tools for handling optimization problems due to their high flexibility and powerful learning ability. This article focuses on the application of NN in the field of image recognition, exploring its solution methods and application exploration. Image recognition, as an important branch in the field of AI, aims to recognize and understand information in images through computer algorithms. NN can automatically learn features in images and construct complex classification models by simulating the connections and working modes of human brain neurons. By applying the NN model, the performance of the image recognition system has been significantly improved. NN can accurately recognize objects, scenes, and text information in images, providing strong technical support for fields such as intelligent security, autonomous driving, and medical diagnosis. With the continuous progress of technology and the expansion of application scenarios, NN will play an important role in more fields, promoting the rapid growth of AI technology.

A novel modified Cheetah Optimizer for designing fractional-order PID-LFC placed in multi-interconnected system with renewable generation units

Establishing robust electrical interconnections between nations is a pivotal foundation for significant investments and addressing energy shortfalls in regions grappling with generational challenges. However, developing electrical load disruptions within interconnected systems can lead to substantial variations in frequencies and energy transmission. Load Frequency Control (LFC) is a crucial mechanism to mitigate these disruptions and ensure stable operations in interconnected regions. While meta-heuristics have been employed for LFC design, some techniques face challenges like early convergence and poor accuracy due to a lack of population diversity. In this study, a novel Modified Cheetah Optimizer (mCO) is proposed to optimize the parameters of LFC system, incorporating fractional-order proportional integral derivative (FOPID) controllers within multi-interconnected system with renewable energy integration. The mCO integrates learning-from-experience and random contraction strategies to enhance convergence accuracy and overcome local optima, demonstrating superior efficiency in solving optimization problems. The proposed mCO is evaluated by solving twelve functions from the CEC2022 test suite, showcasing its effectiveness. The optimization problem involves minimizing the Integral Time Absolute Error (ITAE) of the area control error, considering changes in frequencies and exchanged power, with controller parameters λd, kd, ki, kp, and μ to be identified. Two interconnected systems, photovoltaic (PV)-thermal and thermal-wind turbine (WT)-thermal-PV, are assessed under various load disturbances. The mCO is compared with other methods, including Modified Hunger Games Search Optimizer (MHGS), Driving Training-Based Optimizer (DTBO), Grey Wolf Optimizer (GWO), Aquila Optimal Search (AOS), and Cheetah Optimizer (CO). In the case of PV-thermal linked system, the proposed mCO succeeded in mitigating the ITAE by 19.21% compared to the reported MHGS and 8.63% compared to the conventional CO. In the four interconnected systems, the suggested approach reduced the ITAE by 89.21% and 15.26% compared to the reported MHGS and conventional CO, respectively. This confirmed the efficacy of FOPID-LFC, which was designed using the proposed mCO in all examined scenarios.

Photovoltaic Model Parameters Estimation Via the Fully Informed Search Algorithm

Effective parameter estimation for photovoltaic (PV) systems holds significant importance for both researchers and industry professionals. An accurate understanding of PV models, achieved through modeling and simulation, plays a pivotal role in optimizing the design, control, testing, and forecasting of PV system performance. Developing a precise and robust parameter identification method significantly contributes to enhancing the modeling, control, and optimization of photovoltaic systems. In this context, our research contribution introduces a novel version of Rao metaheuristic algorithm named the Fully Informed Search Algorithm (FISA). Which demonstrate acceptable performance to solving optimization problems in several applied fields. While, maintaining the simplicity and non-parametric nature of the original algorithm. The proposed algorithm holds promise for various industrial applications, particularly in optimizing complex systems such as photovoltaic (PV) systems. For which, we used it to efficiently identifying the parameters of the single-diode model (SDM). Thus, we demonstrate its effectiveness through the application in two distinct case studies within our simulation research. in the end, we compared the results of FISA algorithm to seven other well-known algorithms, the obtained results indicate the superiority of the proposed algorithm in term of the stability of the system, a faster convergence and higher accuracy.

Quantum algorithm for time-dependent differential equations using Dyson series

Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence of the complexity on the error and derivative. As usual, there is an exponential improvement over classical approaches in the scaling of the complexity with the dimension, with the caveat that the solution is encoded in the amplitudes of a quantum state. Our method is to encode the Dyson series in a system of linear equations, then solve via the optimal quantum linear equation solver. Our method also provides a simplified approach in the case of time-independent differential equations.

A Bilevel Optimization Approach for Tuning a Neuro-Fuzzy Controller

This work presents a methodology to solve optimization problems with dynamic-size solution vectors containing continuous and integer variables. It is achieved by reformulating the original problem through a bilevel optimization approach and implementing metaheuristic techniques to solve it. In the selected case study, the optimization problem corresponds to tuning a neuro-fuzzy controller (NFC) that operates in a biodiesel production system for controlling temperature. The NFC performs well and is especially robust to disturbances, but due to its complexity, it is difficult to determine the best set of parameters for its use. This has led to biased searches based on criteria such as the experiences of designers. With the proposed method, it was possible to obtain a tuning that—when implemented in a simulation—led to results that surpassed those documented in the literature. Finally, the proposal offers flexibility for implementation with other controllers that have similar architectures and can be integrated into various other plants or processes.

Introducing a Parallel Genetic Algorithm for Global Optimization Problems

The topic of efficiently finding the global minimum of multidimensional functions is widely applicable to numerous problems in the modern world. Many algorithms have been proposed to address these problems, among which genetic algorithms and their variants are particularly notable. Their popularity is due to their exceptional performance in solving optimization problems and their adaptability to various types of problems. However, genetic algorithms require significant computational resources and time, prompting the need for parallel techniques. Moving in this research direction, a new global optimization method is presented here that exploits the use of parallel computing techniques in genetic algorithms. This innovative method employs autonomous parallel computing units that periodically share the optimal solutions they discover. Increasing the number of computational threads, coupled with solution exchange techniques, can significantly reduce the number of calls to the objective function, thus saving computational power. Also, a stopping rule is proposed that takes advantage of the parallel computational environment. The proposed method was tested on a broad array of benchmark functions from the relevant literature and compared with other global optimization techniques regarding its efficiency.

A sensitivity-based estimation method for investigating control co-design relevance

Abstract. Control co-design is a promising approach for wind turbine design due to the importance of the controller in power production, stability, load alleviation, and the resulting coupled effects on the sizing of the turbine components. However, the high computational effort required to solve optimization problems with added control design variables is a major obstacle to quantifying the benefit of this approach. In this work, we propose a methodology to identify if a design problem can benefit from control co-design. The estimation method, based on post-optimum sensitivity analysis, quantifies how the optimal objective value varies with a change in control tuning. The performance of the method is evaluated on a tower design optimization problem, where fatigue load constraints are a major driver, and using a linear quadratic regulator targeting fatigue load alleviation. We use the gradient-based multi-disciplinary optimization framework Cp-max. Fatigue damage is evaluated with time-domain simulations corresponding to the certification standards. The estimation method applied to the optimal tower mass and optimal cost of energy show good agreement with the results of the control co-design optimization while using only a fraction of the computational effort. Our results additionally show that there may be little benefit to using control co-design in the presence of an active frequency constraint. However, for a soft–soft tower configuration where the resonance can be avoided with active control, using control co-design results in a taller tower with reduced mass.

Data-Driven and Domain Adaption Framework for Optimizing Energy Usage Forecasting in Smart Buildings Using ARIMA Model

Building energy demand and energy system supply are increasingly balanced by energy storage and short-term DSM. This is necessary due to fluctuating renewable energy supplies and rising building power use. Worldwide, structures utilize tons of energy. Greenhouse gas emissions and operational expenses decrease with construction energy efficiency. Forecasting and optimization algorithms can solve challenges, including supply chains (inventory optimization), traffic, and sustainable energy system battery/load/production scheduling for carbon-free energy generation. We often solve optimization problems that need forecasting due to uncertain future values. Predicting and optimizing are challenging; therefore, little research has been done. Our method uses building energy modeling professionals' data to forecast neighboring building types for new or unknown building types. After training, we utilize the models to estimate energy usage for the k-closest building types and combine the predictions using a weighted average. We used time-series decomposition to detect uncertainty and a hybrid model to close this gap: The concepts encode static features and predictable patterns in time-series simulation results. The model learns latent performance differences and calibrates output using outcomes and history records. Historical data predicts public building energy ARIMA use. Our method covers data processing, training, validation, and forecasting. We measured our method. Mixed integer linear optimization and ARIMA projected most accurately.

An adaptive strategy based multi-population multi-objective optimization algorithm

An algorithm is sensitive to parameters; different parameter settings for solving optimization problems can thus have a serious impact on algorithm performance. This leads to an inability to determine the optimal set of parameters for the algorithm to solve the problem at hand. In this study, we propose an adaptive strategy with a multi-population multi-objective algorithm (A-MPMO) framework to select the appropriate set of genetic settings according to the problem to be solved and eliminate the sensitivity of the algorithm to the parameters. Multi-population are often combined with Evolutionary Algorithms (EAs) as an effective strategy to maintain population diversity. First, we divided the population generated by the algorithm into multiple subpopulations to expand the search range and updated them iteratively using operators with different genetic parameters. Second, based on multi-population, subpopulations compete for limited computational resources, implying that the size of each subpopulation adaptively adjusts according to the degree of its contribution to problem solving. Finally, a set of subpopulations that are best suited to solve the problem is selected to improve the adaptability to different problems. For DTLZ, ZDT, and UF, compared to the other algorithms, A-MPMO was experimentally shown to produce better performance.

On the automatic generation of metaheuristic algorithms for combinatorial optimization problems

Metaheuristic algorithms have become one of the preferred approaches for solving optimization problems. Finding the best metaheuristic for a given problem is often difficult due to the large number of available approaches and possible algorithmic designs. Moreover, high-performing metaheuristics often combine general-purpose and problem-specific algorithmic components. We propose here an approach for automatically designing metaheuristics using a flexible framework of algorithmic components, from which algorithms are instantiated and evaluated by an automatic configuration method. The rules for composing algorithmic components are defined implicitly by the properties of each algorithmic component, in contrast to previous proposals, which require a handwritten algorithmic template or grammar. As a result, extending our framework with additional components, even problem-specific or user-defined ones, automatically updates the design space. Furthermore, since the generated algorithms are made up of components, they can be easily interpreted. We provide an implementation of our proposal and demonstrate its benefits by outperforming previous research in three distinct problems from completely different families: a facility layout problem, a vehicle routing problem and a clustering problem.

Scheduling stochastic distributed flexible job shops using an multi-objective evolutionary algorithm with simulation evaluation

The trend of reverse globalisation prompts manufacturing enterprises to adopt distributed structures with multiple factories for improving production efficiency, meeting customer requirements, and responding disturbance events. This study focuses on scheduling a distributed flexible job shop with random job processing time to achieve minimal makespan and minimal total tardiness. First, a stochastic programming model is established to formulate the concerned problems. Second, in accordance with the natures of two objectives and randomness, an evolutionary algorithm incorporating an evaluation method is designed. In it, population-based and external archive-based search processes are developed for searching candidate solutions, and the evaluation method integrates stochastic simulation and discrete event simulation to calculate objective values of acquired solutions. Finally, a mathematical optimisation solver, CPLEX, is employed to validate the developed model and optimisation approach. A set of cases is solved to verify the performance of the proposed method. The comparisons and discussions show the superiority of the proposed method for handling the problems under study.

Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Functions

Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Functions

A chaotic map with two-dimensional offset boosting.

A chaotic map with two-dimensional offset boosting is exhaustively studied, which is derived from the Lozi map and shows the controllability of amplitude control. The mechanism of two-dimensional offset boosting is revealed based on the cancelation of offset-involved feedback terms. Furthermore, the coexistence of homogeneous multistability and heterogeneous multistability is disclosed when the offset boosting turns to the initial condition. It is also found that the independent constant term rescales the amplitude of all the sequences without changing the Lyapunov exponents. More strikingly, the parameters for amplitude control and offset boosting are bound together introducing hybrid control. The circuit implementation based on the microcontroller unit is used to validate the theoretical analysis and numerical simulations. This chaotic map is applied for particle swarm optimization showing its stronger performance and robustness in solving optimization problems.

Optimal schedules for annealing algorithms.

Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e., finding ground states). For both statistical mechanics and optimization, additional parameters beyond temperature are often needed such as chemical potentials, external fields, or Lagrange multipliers enforcing constraints. In this paper we derive a formalism for optimal annealing schedules in multidimensional parameter spaces using methods from nonequilibrium statistical mechanics. The results are closely related to work on optimal control of thermodynamic systems [Sivak and Crooks, Phys. Rev. Lett. 108, 190602 (2012)0031-900710.1103/PhysRevLett.108.190602]. Within the formalism, we compare the efficiency of population annealing and multiple weighted runs of simulated annealing ("annealed importance sampling") and discuss the effects of nonergodicity on both algorithms. Theoretical results are supported by numerical simulations of spin glasses.