Objective Function Research Articles

A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem

We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy.

Applying the Expectation-Maximization Algorithm to Multivariate Signal Extraction

Understanding time series signal extraction is vital for federal agencies, especially as data collection accelerates. One natural extension is moving from univariate to multivariate signal extraction, which offers the promise of reducing extraction error by exploiting cross-sectional relationships. However, such an extension ushers in new computational challenges, viz. larger parameter spaces and more complicated objective functions. The Expectation-Maximization (EM) algorithm provides a methodology to implicitly compute (or approximate) maximum likelihood estimates (MLEs). This paper provides methodology for applying the EM algorithm to a class of latent component multivariate time series models that allow for a nuanced specification of the unobserved signal. We derive an explicit formula for the maximization step, which facilitates computation speed while also improving the stability of the algorithm. Numerical studies demonstrate EM’s ability to efficiently compute MLEs in low-dimensional systems, while also providing feasible estimates in moderate-dimensional systems where MLEs are infeasible to compute. Applications to monthly housing starts and daily immigration are provided.

Balancing Economic Growth, Carbon Emissions, and Sequestration: A Multi-Objective Spatial Optimization in Zhengzhou Metropolitan Area in China

As China’s “Dual Carbon” strategy is implemented and the new urbanization advances, balancing economic development, emission reduction, and carbon sequestration has become an important issue during the growth of emerging metropolitan areas, and it is also important for achieving high-quality urban development. Therefore, this study had three major objective functions: economic growth, carbon emission reduction, and increased carbon storage. The multi-objective land use quantity structure was solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), and the best solution in the solution set was introduced using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for evaluation. Finally, combined with the Future Land Use Simulation (FLUS) model, the low-carbon evolution of the metropolitan area was predicted on a spatial scale. The trade-off plan results show that by 2035, the economic benefits will reach CNY 7.65 trillion, carbon emissions will be kept under 99.24 million tons, and carbon storage will steadily increase by 15.2 million tons. Therefore, optimizing land use from the perspective of balancing carbon emissions, carbon sequestration, and economic development can provide valuable references for planning low-carbon development and the rational use of spatial resources in future metropolitan areas.

Alignment of a 360° image with posed color images for locally accurate texturing of 3D mesh

With the popularity of 3D content like virtual tours, the challenges of 3D data registration have become increasingly significant. The registration of heterogeneous data obtained from 2D and 3D sensors is required to create photo-realistic 3D models. However, the alignment of 2D images with 3D models introduces a significant challenge due to their inherent differences. This article introduces a rigorous mathematical approach to align a 360° image with its corresponding 3D model generated from images with known camera poses followed by texture projection on the model. We use Scale-Invariant Feature Transform (SIFT) feature descriptors enhanced with a homography-based metric to establish correspondences between the faces of a cubemap and the posed images. To achieve optimal alignment, we use a non-linear least squares optimization technique with a custom objective function. Subsequently, the outcomes of the alignment process are evaluated through texturing using a customized raytracing algorithm. The resulting projections are compared against the original textures, with a comprehensive assessment of the alignment's fidelity and precision.

Robust Direction Estimation of Terrestrial Signal via Sparse Non-Uniform Array Reconfiguration under Perturbations

DOA (Direction of Arrival), as an important observation parameter for accurately locating the Signals of Opportunity (SOP), is vital for navigation in GNSS-challenged environments and can be effectively obtained through sparse arrays. In practical application, array perturbations affect the estimation accuracy and stability of DOA, thereby adversely affecting the positioning performance of SOP. Against this backdrop, we propose an approach to reconstruct non-uniform arrays under perturbation conditions, aiming to improve the robustness of DOA estimation in sparse arrays. Firstly, we theoretically derive the mathematical expressions of the Cramér–Rao Bound (CRB) and Spatial Correlation Coefficient (SCC) for the uniform linear array (ULA) with perturbation. Then, we minimize CRB as the objective function to mitigate the adverse effects of array perturbations on DOA estimation, and use SCC as a constraint to suppress sidelobes. By doing this, the non-uniform array reconstruction model is formulated as a high-order 0–1 optimization problem. To effectively solve this nonconvex model, we propose a polynomial-time algorithm, which can converge to the optimal approximate solution of the original model. Finally, through a series of simulation experiments utilizing frequency modulation (FM) signal as an example, the exceptional performance of this method in array reconstruction has been thoroughly validated. Experimental data show that the reconstructed non-uniform array excels in DOA estimation accuracy compared to other sparse arrays, making it particularly suitable for estimating the direction of terrestrial SOP in perturbed environments.

Optimal boundary control in a micromixer

This work studies mathematical foundations for optimal boundary control of mixers which mix two fluid phases. Existence of optima is proved and the influence of common objective functionals is discussed.

Demand-Side Flexibility in Power Systems, Structure, Opportunities, and Objectives: A Review for Residential Sector

The integration of renewable energy sources (RESs) is rapidly increasing within energy systems worldwide. However, this shift introduces intermittency and uncertainty on the supply side. To hedge against RES intermittency, demand-side flexibility introduces a practical solution. Therefore, further studies are required to unleash demand-side flexibility in power systems. This flexibility is relevant across various sectors of power systems, including residential, industrial, commercial, and agricultural sectors. This paper reviews the key aspects of demand-side flexibility within the residential sector. To achieve this objective, a general introduction to demand flexibility across the four sectors is provided. As a contribution of this paper, and in comparison with previous studies, household appliances are classified based on their flexibility and controllability. The flexibility potential of key residential demands, including heat pumps, district heating, electric vehicles, and battery systems, is then reviewed. Another contribution of this paper is the exploration of demand-side flexibility scheduling under uncertainty, examining three approaches: stochastic programming, robust optimization, and information-gap decision theory. Additionally, the integration of demand flexibility into short-term electricity markets with high-RES penetration is discussed. Finally, the key objective functions and simulation software used in the study of demand-side flexibility are reviewed.

A survey of deep causal models and their industrial applications

The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but not limited to computer science, medicine, economics, and industrial applications. Given the continous advancements in deep learning methodologies, there has been a notable surge in its utilization for the estimation of causal effects using counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective functions to estimate counterfactual data unbiasedly. Different from the existing surveys on causal models in machine learning, this review mainly focuses on the overview of the deep causal models based on neural networks, and its core contributions are as follows: (1) we cast insight on a comprehensive overview of deep causal models from both timeline of development and method classification perspectives; (2) we outline some typical applications of causal effect estimation to industry; (3) we also endeavor to present a detailed categorization and analysis on relevant datasets, source codes and experiments.

DentAge: Deep learning for automated age prediction using panoramic dental X-ray images.

Age estimation plays a crucial role in various fields, including forensic science and anthropology. This study aims to develop and validate DentAge, a deep-learning model for automated age prediction using panoramic dental X-ray images. DentAge was trained on a dataset comprising 21,007 panoramic dental X-ray images sourced from a private dental center in Slovenia. The dataset included subjects aged 4 to 97 years with various dental conditions. Transfer learning was employed, initializing the model with ImageNet weights and fine-tuning on the dental image dataset. The model was trained using stochastic gradient descent with momentum, and mean absolute error (MAE) served as the objective function. Across the test dataset, DentAge achieved an MAE of 3.12 years, demonstrating its efficacy in age prediction. Notably, the model performed well across different age groups, with MAEs ranging from 1.94 (age group [10-20]) to 13.40 years (age group [90-100]). Visual evaluation revealed factors contributing to prediction errors, including prosthetic restorations, tooth loss, and bone resorption. DentAge represents a significant advancement in automated age prediction within dentistry. The model's robust performance across diverse age groups and dental conditions underscores its potential utility in real-world scenarios. Our model will be accessible to the public for further adjustments and validation, ensuring DentAge's effectiveness and trustworthiness in practical scenarios.

Particle swarm optimization based on data driven for EV charging station siting

Charging stations are an important support facility for electric vehicles (EVs). Nowadays, the EV industry is developing rapidly, however, the imperfect construction of charging stations or the unreasonable choice of location has seriously reduced the desire of people to buy EVs and led to the problem of difficult charging of EVs in many areas. At present, the research field of EV charging station siting suffers from the inability to quickly and accurately calculate the optimal solution for charging station siting. In this regard, a particle swarm optimization based on deep neural networks modified boundaries (DNNMBPSO) is proposed for solving the problem. DNNMBPSO reduces the convergence value of the objective function by applying deep learning to modify the boundary of the particle swarm optimization. DNNMBPSO is an algorithm that combines heuristic and data driven. In this study, DNNMBPSO is applied for siting study in a system having 50 alternative points, 500 alternative points, and 1000 alternative points and a case of siting of electric vehicle charging stations in Nanning, Guangxi, China. The convergence value of the DNNMBPSO-based objective function is found to be at least 5.5 %, 1.7 %, 8.23 % and 14.7 %, lower compared to genetic algorithms, African vulture optimization algorithm, particle swarm optimization, and grey wolf optimization algorithms, respectively. Traditional heuristic optimization algorithms cannot find optimal solutions in large-scale systems, while DNNMBPSO shows feasibility in large-scale systems.

Failure Probability-Based Optimal Seismic Design of Reinforced Concrete Structures Using Genetic Algorithms

Artificial intelligence (AI) has enabled several optimization techniques for structural design, including machine learning, evolutionary algorithms, as in the case of genetic algorithms, reinforced learning, deep learning, etc. Although the use of AI for weight optimization in steel and concrete buildings has been extensively studied in recent decades, multi-objective optimization for reinforced concrete (RC) and steel buildings remains challenging due to the difficulty in establishing independent objective functions and obtaining Pareto fronts. The well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is an efficient genetic algorithm approach for multi-objective optimization. In this work, the NSGA-II approach is considered for the multi-objective structural optimization of three-dimensional RC buildings subjected to earthquakes. For the objective of this study, two function objectives are considered: minimizing total cost and the probability of structural failure, which are obtained via several nonlinear seismic analyses of the RC buildings. Beams and columns’ cross-sectional dimensions are selected as design variables, and the Mexican Building Code (MBC) specifications are imposed as design constraints. Pareto fronts are obtained for two RC-framed buildings located in Mexico City (soft soil sites), which demonstrate the efficiency and accuracy of NSGA-II for structural optimization.

Existence, uniqueness, and efficiency of numerically unbiased attenuation pathlength estimators for photon counting detectors at low count rates.

The first step in computed tomography (CT) reconstruction is to estimate attenuation pathlength. Usually, this is done with a logarithm transformation, which is the direct solution to the Beer-Lambert Law. At low signals, however, the logarithm estimator is biased. Bias arises both from the curvature of the logarithm and from the possibility of detecting zero counts, so a data substitution strategy may be employed to avoid the singularity of the logarithm. Recent progress has been made by Li etal. [IEEE Trans Med Img 42:6, 2023] to modify the logarithm estimator to eliminate curvature bias, but the optimal strategy for mitigating bias from the singularity remains unknown. The purpose of this study was to use numerical techniques to construct unbiased attenuation pathlength estimators that are alternatives to the logarithm estimator, and to study the uniqueness and optimality of possible solutions, assuming a photon counting detector. Formally, an attenuation pathlength estimator is a mapping from integer detector counts to real pathlength values. We constrain our focus to only the small signal inputs that are problematic for the logarithm estimator, which we define as inputs of<100 counts, and we consider estimators that use only a single input and that are not informed by adjacent measurements (e.g., adaptive smoothing). The set of all possible pathlength estimators can then be represented as points in a 100-dimensional vector space. Within this vector space, we use optimization to select the estimator that (1) minimizes mean squared error and (2) is unbiased. We define "unbiased" as satisfying the numerical condition that the maximum bias be less than 0.001 across a continuum of 1000 object thicknesses that span the desired operating range. Because the objective function is convex and the constraints are affine, optimization is tractable and guaranteed to converge to the global minimum. We further examine the nullspace of the constraint matrix to understand the uniqueness of possible solutions, and we compare the results to the Cramér-Rao bound of the variance. We first show that an unbiased attenuation pathlength estimator does not exist if very low mean detector signals (equivalently, very thick objects) are permitted. It is necessary to select a minimum mean detector signal for which unbiased behavior is desired. If we select two counts, the optimal estimator is similar to Li's estimator. If we select one count, the optimal estimator becomes non-monotonic. The oscillations cause the unbiased estimator to be noise amplifying. The nullspace of the constraint matrix is high-dimensional, so that unbiased solutions are not unique. The Cramér-Rao bound of the variance matches well with the expected scaling law and cannot be attained. If arbitrarily thick objects are permitted, an unbiased attenuation pathlength estimator does not exist. If the maximum thickness is restricted, an unbiased estimator exists but is not unique. An optimal estimator can be selected that minimizes variance, but a bias-variance tradeoff exists where a larger domain of unbiased behavior requires increased variance.

Multi-Spectral Radiation Temperature Measurement: A High-Precision Method Based on Inversion Using an Enhanced Particle Swarm Optimization Algorithm with Multiple Strategies

Multi-spectral temperature measurement technology has been found to have extensive applications in engineering practice. Addressing the challenges posed by unknown emissivity in multi-spectral temperature measurement data processing, this paper adds emissivity constraints to the objective function. It proposes a multi-spectral radiation temperature measurement data processing model realized through a particle swarm optimization algorithm improved based on multiple strategies. This paper simulates six material models with distinct emissivity trends. The simulation results indicate that the algorithm calculates an average relative temperature error of less than 0.3%, with an average computation time of merely 0.24 s. When applied to the temperature testing of silicon carbide and tungsten, experimental data further confirmed its accuracy: the absolute temperature error for silicon carbide (tungsten) is less than 4 K (7 K), and the average relative error is below 0.4% (0.3%), while two materials maintain an average computation time of 0.33 s. In summary, the improved particle swarm optimization algorithm demonstrates strong performance and high accuracy in multi-spectral radiation thermometry, making it a feasible solution for addressing multi-spectral temperature measurement challenges in practical engineering applications. Additionally, it can be extended to other multi-spectral systems.

Control Method for Ultra-Low Frequency Oscillation and Frequency Control Performance in Hydro–Wind Power Sending System

In a hydropower-dominated power grid, the primary frequency regulation (PFR) capability of hydropower units is typically compromised to suppress ultra-low frequency oscillations (ULFOs). However, as renewable wind power is further integrated, a practicable solution to damp ULFOs has emerged, which is to adjust the frequency control parameters of wind turbine (WT) units. Driven by the goals of overall damping enhancement and ULFO suppression, this paper first establishes an extended unified frequency model (EUFM) of a hydro–wind power sending system. Based on EUFM, the damping torque of the hydro–wind power sending system is derived, and the specific impact of WT control parameters on ULFOs and PFR characteristics is investigated. Then, a novel optimization objective function considering damping in the ultra-low frequency band and PFR is formulated and solved using an intelligence algorithm. By optimizing the parameters of the WT to suppress ULFOs, the PFR capability of hydropower units can be released. Finally, simulation results verify that the optimized WT parameters can simultaneously address the ULFO problem and guarantee PFR performance, thereby enhancing the frequency dynamic stability of the sending system.

Research on Trajectory Planning and Tracking Algorithm of Crawler Paver

The implementation of unmanned intelligent construction on the concrete surfaces of an airport effectively improves construction accuracy and reduces personnel investment. On the basis of three known common tracked vehicle dynamics models, reference trajectory planning and trajectory tracking controller algorithms need to be designed. In this paper, based on the driving characteristics of the tracked vehicle and the requirements of the stepping trajectory, a quartic polynomial trajectory planning algorithm was selected with the stability of the curve as a whole and the end point as the optimization goal, combining the tracked vehicle dynamics model, collision constraints, start–stop constraints and other boundary conditions. The objective function of trajectory planning was designed to effectively plan the reference trajectory of the tracked vehicle’s step-by-step travel. In order to realize accurate trajectory tracking control, a nonlinear model predictive controller with transverse-longitudinal integrated control was designed. To improve the real-time performance of the controller, a linear model predictive controller with horizontal and longitudinal decoupling was designed. MATLAB 2023A and CoppeliaSim V4.5.1 were used to co-simulate the two controller models. The experimental results show that the advantages and disadvantages of the tracked vehicle dynamics model and controller design are verified.

Budget allocation problem for projects with considering risks, robustness, resiliency, and sustainability requirements

Budget Allocation Problem (BAP) for projects is considered one of the critical risks that necessitate the completion of projects in the shortest possible duration. This aspect is significant in extensive projects such as national endeavors directly impacting people's livelihoods. This research focuses on introducing Sustainable, Robust, Resilient, and Risk-averse Budget Allocation for Projects (S3RBAP). A hybrid robust stochastic optimization approach was employed, incorporating Weighted VaR (WVaR) and the minimum function as risk criteria to ensure the robustness of the objective function. This model is designed to minimize the weighted expected value, WVaR, and the minimum progress function, thereby promoting the 3R and sustainability framework to tackle budget fluctuations and enhance project viability. The case study revolves around the construction of national projects in Iran. Ultimately, the project's required budget was allocated within the budgetary constraints. Sensitivity analysis found that the integration of 3R and sustainability led to a 13.5 % reduction in the progress function compared to scenarios without these principles. Furthermore, increasing the conservatism coefficient to 20 % decreased the progress function to −0.58 %. Reducing the resiliency coefficient had an adverse effect by disrupting the budget allocation process. The computational time is increased gradually with the escalation of problem complexity, while the progress function decreases due to the increased number of projects. The findings demonstrate that using an exponential function promotes risk aversion, whereas a sine function encourages risk-seeking behaviour within this research context.

Multi-objective optimization of inerter-based building mass dampers

The building mass damper (BMD) is a design concept in which a structure is substructured in such a way that the upper substructure behaves as a large-mass tuned mass damper for the lower one. Its correct tuning usually requires softening (partial isolating) the upper substructure, which limits its application for retrofitting. The recently proposed inerter-based building mass damper (IBMD) solves, reasonably, the softening dynamically through the use of an inerter. This implies an in parallel intervention, which drastically simplifies the practicability of the BMD for retrofitting. The present paper involves comprehensive numerical simulations for multi-objective optimization of an IBMD, accounting for inherent structural damping. In particular, the deformation of the upper substructure is an additional objective function, besides the deformation of the lower substructure as considered in a previous work. Results demonstrate that the IBMD outperforms various benchmark interventions, including dampers, stiffeners, softening devices, and inerters without dampers. Additionally, it was found that the inherent structural damping partially replaces the need for additional damping. Finally, it was also shown that emphasizing the optimization of the lower substructure deformation enhances the overall structural safety in most cases. Nevertheless, the multi-objective optimization increases the versatility of the design concept in the case of substructures with different allowable deformations.

An Intelligent Proofreading for Remote Skiing Actions Based on Variable Shape Basis

AbstractThe current proofreading algorithms for action regulation mainly recover the 3D structure and action information of non-rigid objects from image sequences by factorization. Most of algorithms assume that the camera model is an affine model. This assumption only holds if the size and depth of the object change very little relative to the distance from the object to the camera, which is in the case of fixed-shape basis. When the object is very close to the camera, this assumption causes a large reconstruction error. This paper solves this problem by the intelligent proofreading algorithms for remote skiing teaching actions based on variable shape basis. Firstly, the improved Retinex algorithm is used to enhance the multi-frame video images of skiing actions to make the action details more prominent. Then, measurement matrix is calculated after eliminating the translation vector by coordinate transformation. Under the condition of rank constraint, the measurement matrix is decomposed by singular value decomposition algorithm, and the correct shape basis structure of 3D action features can be obtained by using the variable shape basis. Finally, by randomly initializing a parameter, the optimized parameter and the least square algorithm are used to optimize the randomly initialized parameter further. The iteration until the convergence of the objective function can be used to calculate the deformation degree of the actions. The test results show that this algorithm improves the proofreading accuracy of action regulation in skiing teaching, and the proofreading results of various uploaded sliding actions are correct, which can be applied to remote skiing teaching and community learning.

Maintenance strategy for urban micro wind farm considering maintenance route and resource allocation

Emerging urban wind farms (UMWF) are becoming increasingly prevalent, and optimizing maintenance strategy for UMWF has become crucial for reducing costs and improving wind power efficiency. This research formulates an optimization problem of UMWF by considering the maintenance route and resources. To solve this problem, firstly, the Efficient Maintenance Value (EMF) is proposed as an objective function to measure the maintenance value, based on which a novel Random Variable Neighborhood Descent and Cuckoo Search-based Hybrid Discretized Artificial Fish Swarm Algorithm (RVNDCS-HDAFSA) is proposed to search the optimal maintenance strategy. Experiments are conducted to verify the local search capabilities of the hybrid algorithm, and extensive comparison experiments with the other algorithms are conducted at different scales to validate the effectiveness of the RVNDCS-HDAFSA algorithm; the result of the comparison experiments and the ANOVA shows that the HDAFSA demonstrates a superior capability in solving the medium-scale and large-scale problems compared to the existing algorithm. In conclusion, the practical application experiments validate the effectiveness of our proposed approach.

Improved Parameter Estimation of Three-Phase Squirrel-Cage Induction Motors Using the Nelder-Mead Simplex Algorithm

This work presents a technique for precisely determining the characteristics of a squirrel-cage three-phase induction motor using the Nelder-Mead simplex algorithm. This approach is a frequently employed numerical optimization technique for determining the minimal value of a multi-dimensional objective function. An advantageous feature of the Nelder-Mead simplex algorithm is its independence from the need to calculate partial derivatives of the objective function. Nevertheless, similar to several optimization techniques, the Nelder-Mead simplex approach can also exhibit sensitivity to the initial conditions. Thus, the initial estimation of the parameters of the approximated equivalent circuit of the induction motor was used as the starting point for the Nelder-Mead optimization approach. The experiment's results are compared to those obtained using the polynomial regression approach to demonstrate the efficacy of the proposed method.