Optimization Objective Function Research Articles

Optimisation of Pre-Engineered Buildings

In traditional building practice, a lot of construction material is wasted, because the structures are often grossly over-dimensioned. Inevitably, optimisation is a fundamental aspect of human life as well as a feature of nature. Although numerical optimisation methods have the potential to minimise the usage of structural materials, their application in routine design practice is limited by the absence of tailored algorithms. Structural optimisation based on mathematical computing is one of the approaches for sustainable and effective design in the field of civil engineering. It includes the formulation of the optimisation problem, defining variables, objective functions and constraints followed by a suitable optimisation method with mathematical programming to achieve structural optimisation resulting in reduced overall weight and cost of the structure. The current study includes an overview of prior research on structural optimisation and provides an analysis of the optimisation objectives, optimisation process and different methods and their limitations. The paper includes a numerical study to suggest an optimal design solution for a structural element which is part of a considered pre-engineered building. Topology optimisation of a conventional steel beam (I- section) is performed by numerical analysis along with the finite element method in ABAQUS. The topology optimisation of the beam in terms of decreasing the profile volume reduces the overall material consumed, thereby reducing the cost of the structure. The current numerical analysis helps in arriving at a cost-effective and efficient design solution for a typical pre-engineered building alternative to experimental tests and conventional trials.

Model updating method for offshore jacket platforms using improved DNN and OOA considering non-uniform corrosion and structural responses

During the service life of offshore jacket platforms, the harsh marine environment leads to severe structural corrosion and damage, necessitating structural health monitoring. Ensuring the accuracy of numerical finite element models (FEM) requires critical model updating. This study introduces an improved DNN-OOA model updating method by incorporating actual structural responses into the optimization objective function and considering non-uniform corrosion of the structure. We utilized Pyansys to automatically generate large-scale datasets, simplifying the simulation process. An accurate and responsive surrogate model is generated using the improved deep neural network (DNN), and the optimal solution for the parameters to be corrected is sought through the Osprey optimization algorithm (OOA), completing the FEM updating. The main innovation of this study lies in incorporating non-uniform corrosion caused by the real marine physical environment into the model updating process. This phenomenon is employed to determine the updating range for different structural members. Furthermore, the parameters subject to updating include structural damage to the members and changes in the upper mass. Incorporating the structural response under static loading into the optimization objective function allows for a more comprehensive reflection of the structure’s dynamic and static behavior, addressing the regression confusion problem in the optimization process of purely modal frequency updating. Experimental results demonstrate that the proposed improved DNN-OOA model updating method effectively eliminates inaccuracies in simulated structural responses and mitigates the local optimum problem inherent in pure modal frequency updating. In the updated scaled jacket platform FEM, the maximum relative error of the modal frequencies is reduced to 2.624%, and the maximum error in structural response is reduced to 3.510%. This approach provides a more accurate and reliable FEM for the maintenance and safety assessment of offshore jacket platforms.

Study on the Optimal Allocation of Supercapacitor Capacity for Oil Drilling Winch Energy Recovery Microgrid System

The application of supercapacitor energy storage device in the microgrid system of ultra-deep well oil drilling rig can effectively recover the regenerative energy generated when the winch lowers the drilling tools. Firstly, a microgrid system model of super capacitor energy recovery for ultra-deep well oil drilling rigs was established; the theoretical recoverable energy during a complete operation of ultra-deep well drilling rigs was calculated; the economic efficiency of energy recovery was calculated by taking into consideration of a variety of economic factors, such as storage cost, pollutant emission reduction benefit, and storage loss, etc. was taken into account as the objective function of energy management and capacity allocation optimisation of super capacitor energy storage devices. Using genetic algorithm to solve the supercapacitor capacity configuration, when the well depth is 9000 m, the economic efficiency can reach 26.4% by using 5×377 supercapacitor combination; when the well depth is 12000 m, the economic efficiency can reach 32.7% by using 5×650 supercapacitor combination. It provides a corresponding reference to help improve the economic efficiency of the microgrid system for energy recovery of oil drilling rigs in ultra-deep wells.

Fitting Copulas with Maximal Entropy.

We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions.

Many-Objective Truss Structural Optimization Considering Dynamic and Stability Behaviors

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss).

An Optimization Coverage Strategy for Wireless Sensor Network Nodes Based on Path Loss and False Alarm Probability.

In existing coverage challenges within wireless sensor networks, traditional sensor perception models often fail to accurately represent the true transmission characteristics of wireless signals. In more complex application scenarios such as warehousing, residential areas, etc., this may lead to a large gap between the expected effect of actual coverage and simulated coverage. Additionally, these models frequently neglect critical factors such as sensor failures and malfunctions, which can significantly affect signal detection. To address these limitations and enhance both network performance and longevity, this study introduces a perception model that incorporates path loss and false alarm probability. Based on this perception model, the optimization objective function of the WSN node optimization coverage problem is established, and then the intelligent optimization algorithm is used to solve the objective function and finally achieve the optimization coverage of sensor nodes. The study begins by deriving a logarithmic-based path loss model for wireless signals. It then employs the Neyman-Pearson criterion to formulate a maximum detection probability model under conditions where the cost function and prior probability are unknown, constraining the false alarm rate. Simulated experiments are conducted to assess the influence of various model parameters on detection probability, providing comparative analysis against traditional perception models. Ultimately, an optimization model for WSN coverage, based on combined detection probability, is developed and solved using an intelligent optimization algorithm. The experimental results indicate that the proposed model more accurately captures the signal transmission and detection characteristics of sensor nodes in WSNs. In the coverage area of the same size, the coverage of the model constructed in this paper is compared with the traditional 0/1 perception model and exponential decay perception model. The model can achieve full coverage of the area with only 50 nodes, while the exponential decay model requires 54 nodes, and the coverage of the 0/1 model is still less than 70% at 60 nodes. According to the simulation experiments, it can be basically proved that the WSN node optimization coverage strategy based on the proposed model provides an effective solution for improving network performance and extending network lifespan.

A study on the optimal allocation of photovoltaic storage capacity for rural new energy microgrids based on double-layer multi-objective collaborative decision-making

Aiming at the problems of low energy efficiency and unstable operation in the optimal allocation of optical storage capacity in rural new energy microgrids, this paper proposes an optimization method based on two-layer multi-objective collaborative decision-making. First, an outer optimization objective function containing constraints on capacity allocation, line transmission security, charging and discharging power of the energy storage system, microgrid security, and power supply reliability was constructed, and an inner optimization objective function containing constraints on energy storage self-discharge correction and power balance was constructed. The quantum-behaved particle swarm optimization algorithm is used to solve the optimal solution set of the objective function, and the interactive multi-criteria decision-making method is used to select the compromise solution to realize efficient optimal allocation of optical storage capacity. The test results show that this method can obtain the Pareto optimal solution set of multi-objective functions in the model. Comprehensive prospect value calculation results are obtained according to each configuration scheme, and a compromise scheme is obtained. The total energy consumption, power deviation rate, light rejection rate, and load loss cost were significantly reduced, with maximum values of 90.5%, 2.03% and 114,700 yuan, respectively, and the load loss probability was lower than 2.2%. The results show that the proposed method can effectively improve the total energy consumption utilization of the microgrid, reduce the power deviation rate and light abandonment rate, and provide significant advantages in different lighting and load demand scenarios.

AEGD: adaptive gradient descent with energy

We propose AEGD, a new algorithm for optimization of non-convex objective functions, based on a dynamically updated 'energy' variable. The method is shown to be unconditionally energy stable, irrespective of the base step size. We prove energy-dependent convergence rates of AEGD for both non-convex and convex objectives, which for a suitably small step size recovers desired convergence rates for the batch gradient descent. We also provide an energy-dependent bound on the stationary convergence of AEGD in the stochastic non-convex setting. The method is straightforward to implement and requires little tuning of hyper-parameters. Experimental results demonstrate that AEGD works well for a large variety of optimization problems. Specifically, it is robust with respect to initial data, capable of making rapid initial progress. The stochastic AEGD shows comparable and often better generalization performance than SGD with momentum for deep neural networks. The code is available at https://github.com/txping/AEGD.

Optimization of the Screw Conveyor Device Based on a GA-BP Neural Network

As technology advances, so does digital farming, revolutionizing the industry. Drones, sprayers equipped with GPS and other sensors, combine harvesters, and other machinery can greatly improve agricultural productivity. This paper studies the impact of the straw baler screw conveyor on the efficiency of the baler. Via theoretical analysis, GA—BP (Genetic Algorithm—Back Propagation) simulation, and comparative experiments, the structural parameters and rotational speed of the spiral shaft in the screw conveying device are optimized. In this paper, we analyze the force and velocity components acting on the straw, give the design principles for the screw’s conveying parameters under the premise of ensuring maximum conveying capacity and minimum power consumption, and determine the optimal design variables, objective functions, and constraints according to the specific optimization problem; we establish a specific mathematical model, and introduce algorithm optimization for nonlinear problems with many variables and large amounts of calculations. In MATLAB, an optimization calculation and analysis were performed. The optimization results of the traditional BP (Back Propagation) and GA—BP were compared. It was proven that GA—BP could effectively compensate for the deficiencies of the BP neural network and substantially enhance the model’s accuracy. Through an analysis of the optimization results, the conclusion of attaining the optimization objective was drawn. Specifically, when the outer diameter of the spiral for screw conveyance in the straw baler was D=320 mm, the pitch was S=200 mm, and the rotational speed of the pickup shaft was n=138 r/min, the straw baler could achieve the maximum conveying capacity and the minimum power consumption. At this moment, the power consumption was P=0.079 kW, and the conveying capacity was Qm=23.98 t/h. Subsequently, the optimization results were contrasted with those of other mainstream domestic models, and a comparative experiment was conducted. The experimental results indicated that the model’s prediction results were reliable and exhibited higher efficiency compared to other combinations. The results could provide a reference for the research on screw conveyance of balers.

Methodology for optimizing high-viscosity oil production using a nature-inspired algorithm

To maintain reservoir pressure above the saturation pressure of oil with gas and effectively displace oil from the reservoir, flooding remains an established operating practice in the fields of the Russian Federation. In recent years, theoretical and practical research into this method of operation has been actively developing. Thus, the low efficiency of oil displacement by flooding has been established in conditions of low oil mobility compared to water, which is especially evident in heterogeneous reservoirs. The highest reduction in the efficiency of the process of replacing oil with water is observed during the development of highly viscous oil fields. For these difficult conditions, polymer flooding technology is especially promising, because the polymer, thickening the water, increases its viscosity, increasing the displacing ability of water. However, for the practical application of polymer flooding, it is necessary to optimize the process by justifying technological parameters (polymer concentration, injection rate) to achieve maximum efficiency. For this purpose, the paper presents a methodological approach based on the use of a nature-inspired optimization algorithm ‒ a flock of migratory birds, used to solve a number of practical nonlinear optimization problems. Keywords: flooding; polymer compositions; mathematical modeling; optimization objective function; nature-inspired algorithms; migrating bird algorithm; net present value.

Research on the Optimal Control of Working Oil Pressure of DCT Clutch Based on Linear Quadratics Form

The control of the vehicle transmission system is of great significance to driving comfort. In order to design a controller for smooth shifting and comfortable driving, a dynamic model of dual-clutch transmission is established in this paper. An optimal control strategy for clutch oil pressure based on linear quadratics is proposed, which is used to optimally control the oil pressure of two clutches in the torque stage and inertia stage. The control strategy selects the slipping work and jerk as evaluation indices of shift quality and establishes an optimization objective function. On the premise of optimizing the input torque, the relative speed difference between the engine and the sliding clutch in the inertia stage is adjusted. Through the optimal trajectory control of the wet clutch oil pressure, slipping work and jerk are reduced, thereby improving driving comfort. The simulation results show that the slipping work and jerk generated by the system during the shift stage are reduced, and the shift quality is improved. Additionally, compared with the controller using the MATLAB particle swarm optimization algorithm, the response speed of the proposed controller is faster, the slipping work and jerk are better reduced, and the shift quality is improved.

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 f, 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 f0 corresponding to the objective function yf and the correlation coefficient ρ between irrigation water demand anomalies D^ and irrigation water withdrawal anomalies I^ (ρD^,I^=0). It will serve as a new attempt to optimize irrigation profits. We argue that the optimal objective function yf0 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 f0 that maximizes irrigation profits and irrigation profit per unit area while minimizing risks associated with climatic anomalies. By demonstrating that f0 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 ρD^,I^f=0 because ρD^,I^ is the function of f. Since f0 could capture the optimal solution to the greatest extent. It can serve as a simple and effective solution to determine the optimal objective function yf0 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.

A Novel Variance Reduction Proximal Stochastic Newton Algorithm for Large-Scale Machine Learning Optimization

Abstract This paper introduces the Variance Reduction Proximal Stochastic Newton Algorithm (SNVR) for solving composite optimization problems in machine learning, specifically minimizing F(w) + Ω(w), where F is a smooth convex function and Ω is a non-smooth convex regularizer. SNVR combines variance reduction techniques with the proximal Newton method to achieve faster convergence while handling non-smooth regularizers. Theoretical analysis establishes that SNVR achieves linear convergence under standard assumptions, outperforming existing methods in terms of iteration complexity. Experimental results on the "heart" dataset (N=600, d=13) demonstrate SNVR's superior performance: Convergence speed: SNVR reaches optimal solution in 5 iterations, compared to 14 for ProxSVRG, and >20 for proxSGD and ProxGD. Solution quality: SNVR achieves an optimal objective function value of 0.1919, matching ProxSVRG, and outperforming proxSGD (0.1940) and ProxGD (0.2148). Efficiency: SNVR shows a 10.5% reduction in objective function value within the first two iterations. These results indicate that SNVR offers significant improvements in both convergence speed (180-300% faster) and solution quality (up to 11.9% better) compared to existing methods, making it a valuable tool for large-scale machine learning optimization tasks.

Interactive Prognosis Framework Between Deep Learning and a Stochastic Process Model for Remaining Useful Life Prediction.

Uncertainty quantification of the remaining useful life (RUL) for degraded systems under the big data era has been a hot topic in recent years. A general idea is to execute two separate steps: deep-learning-based health indicator (HI) construction and stochastic process-based degradation modeling. However, there exists a critical matching defect between the constructed HI and a degradation model, which seriously affects the RUL prediction accuracy. Toward this end, this article proposes an interactive prognosis framework between deep learning and a stochastic process model for the RUL prediction. First, we resort to stacked contractive autoencoders to fuse multiple sensor information of historical systems for constructing the HI in a typical unsupervised manner. Then, considering the nonlinear characteristic of the constructed HI, an exponential-like degradation model is introduced to construct its degradation evolving model, and theoretical expressions of the prediction results are derived under the concept of the first hitting time. Furthermore, we design an optimization objective function by integrating the HI construction and degradation modeling for the RUL prediction. To minimize the designed objective function of the proposed interactive prognosis framework, a gradient descent algorithm is employed to update the model parameters. Based on the well-trained interactive prognosis model, we can obtain the HI of a field system from stacked contractive autoencoders with sensor data and the probability density function (pdf) of the predicted RUL on the basis of the estimated parameters. Finally, the effectiveness and superiority of the proposed interactive prognosis method are verified by two case studies associated with turbofan engines.

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

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

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

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

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.