Optimization Objective Function Research Articles

Optimized Evaluations of Irrigation Profits and Balance of Irrigation Water Demand and Supply Under Climate Change

Optimizing irrigation profit is essential for enhancing agricultural productivity and ensuring sustainable water resource management, especially under the uncertainties caused by climate variability. It signifies that maximizing irrigation profits has become the primary consideration of current agricultural irrigation systems. By discussing the change in irrigation profits with irrigation fraction , which represents the proportion of irrigated farmland per unit area of cultivated land, a new method of qualitative diagnosis of irrigation supply and demand balance was proposed by means of the optimal irrigation fraction corresponding to the objective function and the correlation coefficient between irrigation water demand anomalies and irrigation water withdrawal anomalies (). It will serve as a new attempt to optimize irrigation profits. We argue that the optimal objective function represents the state of equilibrium of irrigation supply and demand. This study proposes a reverse optimization idea, which includes two comparison methods, to estimate the comprehensively optimal irrigation fraction that maximizes irrigation profits and irrigation profit per unit area while minimizing risks associated with climatic anomalies. By demonstrating that performs exceptionally well in meeting the objectives of maximizing irrigation profits and minimizing risks across various climatic scenarios, we suggest a robust method for optimizing irrigation profits, which simply calculates because is the function of . Since could capture the optimal solution to the greatest extent. It can serve as a simple and effective solution to determine the optimal objective function and diagnose the state of balance between irrigation water demand and supply. This method offers practical implications for water resource management and agricultural planning in the face of climate change.

A robust and computationally efficient guided wave tomography of pipes

ABSTRACT Guided wave ultrasonic tomography of pipe usually uses the helical modes propagated between parallel transducer arrays to compensate for the missing incident angle . Nevertheless, separating mixed signals from various helical modes during inversion is challenging, and this method necessitates multiple replications of the two-dimensional unfolding area , leading to high computational costs. It also faces practical problems such as environmental noise, transducer differences, and poor coupling . To address these problems, this paper proposes a finite difference method that utilizes helical mode information without multiple replications or the need to separate signals. Additionally, an objective function based on zero-delay cross-correlation is employed to mitigate the effects of noise, transducer inconsistencies, and coupling issues that distort signal amplitudes. The proposed method reduces the inversion space of high-order helical modes of the pipeline to the area of a two-dimensional unfolding, and improves the reliability and accuracy of inversion through objective function optimisation. In numerical simulations, the algorithm achieves thickness loss imaging with errors less than 0.1 mm and demonstrates good performance in experimental tests .

Label Deconvolution for Node Representation Learning on Large-Scale Attributed Graphs Against Learning Bias.

Node representation learning on attributed graphs-whose nodes are associated with rich attributes (e.g., texts and protein sequences)-plays a crucial role in many important downstream tasks. To encode the attributes and graph structures simultaneously, recent studies integrate pre-trained models with graph neural networks (GNNs), where pre-trained models serve as node encoders (NEs) to encode the attributes. As jointly training large NEs and GNNs on large-scale graphs suffers from severe scalability issues, many methods propose to train NEs and GNNs separately. Consequently, they do not take feature convolutions in GNNs into consideration in the training phase of NEs, leading to a significant learning bias relative to the joint training. To address this challenge, we propose an efficient label regularization technique, namely Label Deconvolution (LD), to alleviate the learning bias by a novel and highly scalable approximation to the inverse mapping of GNNs. The inverse mapping leads to an objective function that is equivalent to that by the joint training, while it can effectively incorporate GNNs in the training phase of NEs against the learning bias. More importantly, we show that LD converges to the optimal objective function values by the joint training under mild assumptions. Experiments demonstrate LD significantly outperforms state-of-the-art methods on Open Graph Benchmark datasets.

Multi-objective optimization of a biogas-fired gas turbine incorporated with closed Brayton and ejector power/cooling co-generation cycles

Fossil fuels have long been the primary source of energy for human consumption. However, with increasing population growth and industrialization, electricity demand continues to rise, necessitating a sustainable and clean energy supply to mitigate environmental damage and support global development. This research proposes a gas turbine-based power plant that utilizes renewable biogas as its fuel source. To enhance the plant’s efficiency, the gas turbine is integrated with a closed Brayton cycle, complemented by compressor intake cooling. This cooling process is achieved through a combined power and ejector refrigeration unit, which recovers waste heat from the gas turbine. The energy, exergy, and economic performance of the proposed plant are thoroughly analyzed, with exergy efficiency and unit product cost serving as the objective functions for multi-criteria optimization. The results demonstrate that compressor intake cooling improves both thermodynamic and economic performance under all operating conditions. At the optimal design point, the system with intake cooling achieves an exergy efficiency of 39.38%, compared to 33.64% for the system without it. Additionally, while the system with intake cooling requires higher initial investment, it offers lower unit product costs, making it a more economically viable option.

Regime‐Switching Density Forecasts Using Economists' Scenarios

ABSTRACTWe propose an approach for generating macroeconomic density forecasts that incorporate information on multiple scenarios defined by experts. We adopt a regime‐switching framework in which sets of scenarios (“views”) are used as Bayesian priors on economic regimes. Predictive densities coming from different views are then combined by optimizing objective functions of density forecasting. We illustrate the approach with an empirical application to quarterly real‐time forecasts of the US GDP growth rate, in which we exploit the Fed's macroeconomic scenarios used for bank stress tests. We show that the approach achieves good accuracy in terms of average predictive scores and good calibration of forecast distributions. Moreover, it can be used to evaluate the contribution of economists' scenarios to density forecast performance.

Multi-objective optimization and prediction of strength along with durability in acid-resistant self-compacting alkali-activated concrete

Sustainability in concrete production reduces the environmental impact and conserves resources, yielding durable concrete. This study focuses on developing and analyzing an acid-resistant Self-Compacting alkali-activated concrete (SCAC). Optimization of mix proportions of SCAC containing GGBFS as a binder was performed through experimental methods and multi-objective optimization. The fresh and mechanical characteristics of SCAC were evaluated, examining the impact of sodium hydroxide (NaOH) molarity and sodium silicate to sodium hydroxide (SS/SH) ratio on strength loss under acid exposure. Optimal mix proportions were identified experimentally for both M25 and M45 SCAC grades. A comprehensive database of 120 observations from experimental findings was used to develop a machine learning (ML) model to predict compressive strength and loss of strength due to acid attack. The gradient boost regression with R2 of 0.96 and the long short-term memory (LSTM) model with R2 of 0.93 were established to be best performing in predicting strength and strength loss respectively. These models were then used as objective functions in a multi-objective optimization to maximize strength and minimize acid-induced strength loss. A cost-based comparison of experimentally and analytically optimized mix proportions was provided. The established optimal NaOH molarity and SS/SH ratio for both M25 and M45 grade SCGC were 12 M and 2.3 along with 12 M and 2.5 respectively. This research offers valuable insights for further experimental work on sustainable and resilient SCAC.

Optimization of A Dynamic Program for Water Resources Utilization in the Mambal Irrigation Area

The Irrigation Area (D. I.) Mambal, which passes through Badung Regency, Denpasar City, and Tabanan Regency, is the largest irrigation water supplied by the Ayung River, covering an area of 5.963 Ha. Despite the Ayung River’s substantial water potential, the D. I. Mambal experiences water shortages during certain months. This research aims to improve the effectiveness and efficiency of irrigation water use based on the Global Planting Management Plan (RTTG) using simulation methods and dynamic program optimization. Simulations were carried out under low conditions, normal and sufficient dependable discharges, using both existing and alternative RTTG. The objective function of the dynamic optimization seeks to maximize revenue gain from the applied RTTG. The existing cropping pattern at the beginning of planting in October showed an average proportion of fulfillment of water irrigation needs at 85%. Under the Alternative I condition, with planting beginning in November, the average proportion of fulfillment of irrigation water needs was 89%. In Alternative II conditions, with planting beginning in December, the average proportion of fulfillment of irrigation water needs was 87%. By optimizing the water discharge using the dynamic program, the irrigation profit for the existing cropping pattern (October) amounted to IDR 491,816,154,938. The highest profit was obtained using the Alternative II cropping pattern (December), totaling IDR 606,675,369,830. Meanwhile, the lowest profit was obtained in the Alternative I cropping pattern (November), which was IDR 360,767,292,361. The analysis showed that the Alternative II cropping pattern, starting with the first rice planting period in December, yields the most optimal results. The analysis considers the optimized air allocation and irrigation benefits obtained from the third cropping pattern.

Fault diagnosis for multi-axis carving machine systems with Gaussian mixture hidden Markov models: A data-model interactive perspective

This paper is concerned with sensor fault diagnosis problems for multi-axis carving machine systems (MACMSs) with repetitive machining tasks. A novel fault diagnosis method that combines the multi-feature fusion technology and Gaussian mixture hidden Markov models (GMHMMs) is proposed, which is inspired by a data- and model-driven collaborative perspective. With fault-sensitive features first extracted from both the time domain and time–frequency domain, the composite health index (CHI) is constructed to facilitate the understanding of the time-varying evolution. Then, GMHMMs are established to characterize the probabilistic relationship between the hidden states and CHI. To achieve high-precision fault classification, a well-designed global objective function is adopted to dynamically optimize both the CHI construction and classifier model training in a closed-loop feedback mechanism. Specifically, the fusion coefficients with range and equality constraints are integrated as part of the model parameters into the global optimization objective function, thereby reducing the search range and improving convergence speed. Besides, the well-trained GMHMMs interact with each other to capture the correlation information between different faults, and are utilized for online fault diagnosis. Finally, experiments are conducted on a self-developed multi-axis carving machine platform. The results exhibit outstanding performance in comparison with existing methods, particularly attaining a diagnostic accuracy of 95.37%.

Stochastic Normal Orientation for Point Clouds

We propose a simple yet effective method to orient normals for point clouds. Central to our approach is a novel optimization objective function defined from global and local perspectives. Globally, we introduce a signed uncertainty function that distinguishes the inside and outside of the underlying surface. Moreover, benefiting from the statistics of our global term, we present a local orientation term instead of a global one. The optimization problem can be solved by the commonly used numerical optimization solver, such as L-BFGS. The capability and feasibility of our approach are demonstrated over various complex point clouds. We achieve higher practical robustness and normal quality than the state-of-the-art methods.

Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots

Aiming at the problem that it is difficult for an orbital photovoltaic panel cleaning robot to span a large distance between photovoltaic panels, a method of designing and optimizing a non-coplanar orbit based on Bezier curves is proposed. Firstly, the robot’s motion law is analyzed to obtain trajectory data for a single work cycle. Then, Bezier curves are utilized for trajectory design to ensure a smooth transition during the spanning motion phase. Thirdly, with the average value of the minimum distance between the Bezier curve and the point set data of the spanning motion phase as the optimization objective function, the nonlinear planning based on the SQP algorithm was adopted for the optimization of the upper and lower trajectories. Finally, the results of the case calculations indicate that the standard deviation of the optimized upper and lower trajectories was reduced by 35.63% and 40.57%, respectively. Additionally, the ADAMS simulation validation demonstrates that the trajectory errors of the four wheels decreased by a maximum of 8.79 mm, 23.78 mm, 10.11 mm, and 14.97 mm, respectively, thereby confirming the effectiveness of the trajectory optimization.

Group Forward–Backward Orthogonal Matching Pursuit for General Convex Smooth Functions

This paper introduces the Group Forward–Backward Orthogonal Matching Pursuit (Group-FoBa-OMP) algorithm, a novel approach for sparse feature selection. The core innovations of this algorithm include (1) an integrated backward elimination process to correct earlier misidentified groups; (2) a versatile convex smooth model that generalizes previous research; (3) the strategic use of gradient information to expedite the group selection phase; and (4) a theoretical validation of its performance in terms of support set recovery, variable estimation accuracy, and objective function optimization. These advancements are supported by experimental evidence from both synthetic and real-world data, demonstrating the algorithm’s effectiveness.

Optimization algorithm of UAV‐assisted federated learning resources based on wireless energy harvesting

AbstractFederated learning (FL) enhances data privacy and security by enabling multiple terminals to collaboratively train a global model without transferring data to a central location. To tackle the challenges of limited terrestrial communication resources and device energy in FL, a UAV‐assisted federated learning and energy collection resource optimization algorithm is proposed. This algorithm harvests the working energy of FL terminals from radio frequency signals transmitted by the UAV via wireless energy collection. Considering energy causality and limited resources, we formulate a problem aimed at minimizing the completion time of FL training tasks. As this problem is NP‐hard, we initially employ a greedy algorithm to optimize the UAV's position, then decompose it into three sub‐problems: computing resources, power control, and bandwidth allocation. We derive and establish the optimization objective function for computing resources as convex, obtaining the expression for optimal computing resources. The Brent algorithm, based on golden section interpolation, iteratively solves the power distribution sub‐problem, while the Lagrange‐quasi‐Newton algorithm optimizes bandwidth allocation for each user. Simulation results demonstrate that the proposed algorithm effectively reduces training completion time while maintaining training quality.

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

ABSTRACTAnnual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free‐stream wind conditions. Physics‐based estimates of wind farm power production typically rely on low‐fidelity engineering wake models that approximate the steady‐state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed‐form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient‐based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

A piecewise smooth version of the Griewank function

The Griewank test function for global unconstrained optimization has multiple local minima clustered around the global minimum at the origin. A new version of this test function is proposed that has a similar structure, but whose behavior at the local minima and maxima is non-smooth. This piecewise smooth version of the Griewank function represents an abs-factorable test case of objective functions for global non-smooth optimization as, for example, observed in the training of neural networks.

Research on parameter optimization method of thrust vector/aerodynamic rudder composite control law based on singular value method

Advanced aircraft with thrust vectoring/aerodynamic rudder layout have significant control coupling problems. The traditional single-loop control parameter design method cannot take into account the performance of multiple control loops in this scenario. Therefore, a control law parameter optimization method based on the singular value of the hysteresis matrix is proposed. First, the control parameter optimization interval is determined using the time domain control performance index. Then, the singular value method is used to measure the stability margin of the multiple-input multiple-output (MIMO) system on this basis, and the corresponding optimal objective function is established to optimize the controller parameters. The feasibility of this method is verified by numerical simulation. The results show that the designed control parameter optimization algorithm has better time domain control performance and larger system stability margin than the traditional single-loop control parameter design method.

High robust eddy current tuned tandem mass dampers-inerters for structures under the ground acceleration

In this work, a novel eddy current tuned tandem mass dampers-inerters, referred to as EC-TTMDI is proposed, a theoretical analysis model of the vibration control mechanism is established, and parameterized analysis and design are conducted using the intelligent optimization algorithm. This model is the single-degree-of-freedom (SDOF) structure with EC-TTMDI subjected to Gaussian white noise base excitation. Specifically, the expression for the displacement variance of the SDOF structure-EC-TTMDI system was firstly obtained with resorting to both the equivalent linearization of eddy current damper (ECD) and residue theorem. The optimization objective function was then defined as minimization of the displacement variance, which is product of the white noise intensity and the square of H2 norm of the model transfer function. Employing the pattern-search algorithm, the variation trends of the objective function and the optimum design parameters were subsequently scrutinized. The vibration damping mechanism of EC-TTMDI is then revealed in terms of control effectiveness, robustness, structural frequency response, suppression bandwidth, and stroke. Finally, the time history response analysis of the SDOF structure-EC-TTMDI system subjected to the near-field impulse, near-field non-impulse, and far-field earthquakes was conducted to further confirm the performance superiority of EC-TTMDI. Results demonstrates that EC-TTMDI offers higher robustness and better control effectiveness compared to TTMDI and TMDI. Furthermore, EC-TTMDI features the damping force limiting characteristic, which enhances the integrity and reliability of TTMDI.

An innovative quick-decision strategy for evaluating the applicability of extractive distillation process with a preconcentration column in separating high-concentration organic waste liquid

In the face of the high energy consumption challenge in separating high-concentration organic waste liquid through extractive distillation (ED), the concept of preconcentration provides a new strategic direction. Therefore, it has become crucial to determine the suitability of the ED process with a preconcentration column for processing such complex mixture. Taking this into consideration, the study proposes an innovative quick-decision method that utilizes thermodynamic analysis of ternary phase diagram to determine the ratio of theoretical product flowrate at the bottom of the preconcentration column to the feed flowrate, which serves as the basis for deciding whether to choose the ED process with a preconcentration column for handling such separation tasks. Three azeotropic systems with different thermodynamic characteristics are chosen as case studies: cyclohexane/ethyl acetate/ethanol (Case 1), ethyl acetate/ethanol/water (Case 2), and n-hexane/ethyl acetate/acetonitrile (Case 3). The task of separating the above three systems is accomplished through the application of both three-column extractive distillation configuration (TCED), and four-column extractive distillation configuration (FCED). The objective functions for multi-objective optimization of all separation configurations include the minimum total annual cost (TAC), the minimum entropy generation and the minimum CO2 emissions. The research findings indicate that when the ratio of theoretical product flowrate at the bottom of the preconcentration column to the feed flowrate is not less than 0.56, or when there is a significant concentration difference among the components in the feed stream, the FCED configuration exhibits clear advantages over the TCED configuration in terms of economic, environmental, and thermodynamic aspects.

Reservation and allocation model considering the user cost and the utilization of parking space

In order to alleviate the problem of imbalance between parking supply and demand by improving the utilization rate of parking resources, and considering the game relationship between user benefits and system benefits in parking allocation, the optimization objective function of maximum parking space utilization and minimum user cost in parking reservation mode is established from the two aspects which are system optimization and user optimization respectively. Then, the optimal allocation parking integer programming model (OPA) considering users' preferences is established. An Augmented Lagrangian-Alternating Direction Method of Multipliers Algorithm is designed to solve the optimal solution of the model. Finally, in order to test the validity of the model, the proposed model and the classical distribution model are compared and analyzed under different supply and demand conditions. The results show that the performance of the proposed model in three performance metrics which are parking utilization, average user cost and request acceptance rate is significantly better than that of the classical allocation model. The research results of this paper can provide theoretical reference for the management of parking reservation platform.

Identifying effective evolutionary strategies-based protocol for uncovering reaction kinetic parameters under the effect of measurement noises

BackgroundThe transition from explanative modeling of fitted data to the predictive modeling of unseen data for systems biology endeavors necessitates the effective recovery of reaction parameters. Yet, the relative efficacy of optimization algorithms in doing so remains under-studied, as to the specific reaction kinetics and the effect of measurement noises. To this end, we simulate the reactions of an artificial pathway using 4 kinetic formulations: generalized mass action (GMA), Michaelis–Menten, linear-logarithmic, and convenience kinetics. We then compare the effectiveness of 5 evolutionary algorithms (CMAES, DE, SRES, ISRES, G3PCX) for objective function optimization in kinetic parameter hyperspace to determine the corresponding estimated parameters. ResultsWe quickly dropped the DE algorithm due to its poor performance. Baring measurement noise, we find the CMAES algorithm to only require a fraction of the computational cost incurred by other EAs for both GMA and linear-logarithmic kinetics yet performing as well by other criteria. However, with increasing noise, SRES and ISRES perform more reliably for GMA kinetics, but at considerably higher computational cost. Conversely, G3PCX is among the most efficacious for estimating Michaelis–Menten parameters regardless of noise, while achieving numerous folds saving in computational cost. Cost aside, we find SRES to be versatilely applicable across GMA, Michaelis–Menten, and linear-logarithmic kinetics, with good resilience to noise. Nonetheless, we could not identify the parameters of convenience kinetics using any algorithm.ConclusionsAltogether, we identify a protocol for predicting reaction parameters under marked measurement noise, as a step towards predictive modeling for systems biology endeavors.

Optimal scheduling of battery energy storage system operations under load uncertainty

This paper investigates the optimal scheduling of battery energy storage system operations considering energy load uncertainty. We develop a novel two-stage distributionally robust optimization model to determine an optimal battery usage schedule that minimizes the worst-case energy costs considering peak load costs. The model leverages deep-learning-based probabilistic forecasting in the construction of the ambiguity set. Specifically, we develop a Deep Autoregressive Recurrent Networks model to generate a probabilistic forecast of energy loads over a time horizon. The output of the forecasting model is then used to construct a marginal-moment ambiguity set for the distributionally robust optimization model. To solve the proposed model, we establish a closed-form characterization of the optimal second-stage objective function value. Leveraging this closed-form expression and using second-order conic duality, we derive an exact single-level mixed integer second-order conic reformulation of the problem. Extensive computational experiments, conducted on a real dataset, demonstrate the value of our proposed model and the effectiveness of the resulting battery schedule. The results show that the proposed model outperforms several benchmarks, including two-stage stochastic programming. Furthermore, the accuracy of the load forecast significantly impacts the effectiveness of the optimal battery schedule in eliminating peak loads by achieving up to 18% reduction in the maximum energy load.