Objective Function Research Articles

Deep-learning optimization using the gradient of a custom objective function: A full-waveform inversion example study on the convolutional objective function

The integration of conventional high-performance full-waveform inversion (FWI) algorithms with deep-learning frameworks is an innovative and promising research direction with the potential to enhance and broaden the application prospects of this field significantly. Automatic differentiation with backpropagation techniques can derive the gradients of model parameters in an equivalent manner to that of adjoint methods; however, it requires a substantial amount of computer memory, particularly when considering the time-step layers. In addition, some excellent objective functions suitable for FWI are not available in deep-learning frameworks. In comparison, the adjoint method, based on effective boundary storage technology, offers greater practicality for calculating the gradients of various objective functions. Therefore, this paper develops a novel approach toward FWI that integrates deep-learning optimization with high-performance gradient computation. In particular, our method inputs model parameter gradients from a custom objective function into the deep-learning framework. Herein, we use the acoustic equation with variable density as an example to demonstrate how a convolutional objective function, along with its corresponding velocity and density gradients, can be used for optimized inversion, multiscale inversion, and deep network parameterization-based multiscale inversion within the deep-learning framework. This approach provides a paradigm for deep-learning-optimized FWI, which we apply to synthetic and field data scenarios.

Adaptive Neighbors Graph Learning for Large-Scale Data Clustering using Vector Quantization and Self-Regularization

In traditional adaptive neighbors graph learning (ANGL)-based clustering, the time complexity is more than O(n2), where n is the number of data points, which is not scalable for large-scale data problems in real applications. Subsequently, ANGL adds a balance regularization to its objective function to avoid the sparse over-fitting problem in the learned similarity graph matrix. Still, the regularization may leads to many weak connections between data points in different clusters. To address these problems, we propose a new fast clustering method, namely, Adaptive Neighbors Graph Learning for Large-Scale Data Clustering using Vector Quantization and Self-Regularization (ANGL-LDC), to perform vector quantization (VQ) on original data and feed the VQ data as the input in the n×n similarity graph matrix learning. Hence, the n×n similarity graph matrix learning problem is simplified to weighted m×m(m≪n) graph learning problem, where m is the number of distinct points and weight is the duplicate times of distinct points in VQ data. Consequently, the time complexity of ANGL-LDC is much lower than that of ANGL. At the same time, we propose a new ANGL objective function with a graph connection self-regularization mechanism, where the ANGL-LDC objective function will get an infinity value if the value of one graph connection is equal to 1. Therefore, ANGL-LDC naturally avoids obtaining the sparse over-fitting problem since we need to minimize the value of ANGL-LDC’s objective function. Experimental results on synthetic and real-world datasets demonstrate the scalability and effectiveness of ANGL-LDC.

Optimization of high-speed angular contact ball bearing for aircraft gearbox utilizing an evolutionary multi-objective algorithm, NSGA-III

We develop a program for predicting bearing performance, including the maximum contact stress, bearing power loss, minimum lubricating film thickness, static safety factor, and dynamic life, and an optimal design for high-speed angular contact ball bearings in aircraft gearboxes using optimization algorithms. A program is developed to predict bearing performance by calculating the loads and displacements of individual balls based on the bearing’s kinematic and static equilibrium equations. Next, an optimization program is developed with non-dominated sorting genetic algorithm III (NSGA-III), wherein calculated bearing performance indicators serve as constraints or objective functions. The performance of individuals within the final Pareto front is evaluated using the inter-criteria correlation (CRITIC) and weighted product methods. The optimization performances of NSGA-III and NSGA-II are compared based on their hypervolume indicators. A solution of the kinematic and static equilibrium equations under the load cases and duty cycles of real aircraft gearboxes is obtained, enhancing the prediction accuracy. Furthermore, optimization, including bearing performance metrics rarely considered in previous studies, is performed. Optimal specifications superior to reference bearings employed in aircraft gearboxes are obtained, enhancing all three objective functions or specific objective functions. The optimization performance of NSGA-III is confirmed to surpass that of conventional NSGA-II.

Unreliable association between self-reported sense of direction and peripheral vestibular function.

Uni- or bilateral peripheralvestibular impairment causes objective spatial orientation deficits, which can be measured using pen-and-paper-tests or sensorimotor tasks (navigation or pointing). For patients' subjective orientation abilities, questionnaires are commonly used (e.g., Santa Barbara sense of direction scale [SBSODS]). However, the relationship between subjective assessment of spatial skills and objective vestibular function has only been scarcely investigated. A total of 177 patients (mean age 57.86±17.53 years, 90 females) who presented in our tertiary Center for Vertigo and Balance Disorders underwent neuro-otological examinations, including bithermal water calorics, video head impulse test (vHIT), and testing of the subjective visual vertical (SVV), and filled out the SBSODS (German version). Correlation analyses and linear multiple regression model analyses were performed between vestibular test results and self-assessment scores. Additionally, groupwise vestibular function for patients with low, average, and high self-report scores was analyzed. Forty-two patients fulfilled the diagnostic criteria for bilateral vestibulopathy, 93 for chronic unilateral vestibulopathy (68 unilateral caloric hypofunction and 25 isolated horizontal vestibulo-ocular reflex deficits), and 42 patients had normal vestibular test results. SBSODS scores showed clear sex differences with higher subjective skill levels in males (mean score males: 4.94±0.99, females 4.40±0.94; Student's t-test: t-3.78, p<.001***). No stable correlation between objective vestibular function and subjective sense of spatial orientation was found. A multiple linear regression model could not reliably explain the self-reported variance. The three patient groups with low, average, and high self-assessment-scores showed no significant differences of vestibular function. Self-reported assessment of spatial orientation does not robustly correlate with objective peripheral vestibular function. Therefore, other methods of measuring spatial skills in real-world and virtual environments are required to disclose orientation deficits due to vestibular hypofunction.

Enhancing renewable energy utilization and energy management strategies for new energy yachts

Hydrogen energy, due to its clean and efficient nature, has shown great potential during the current transition period in the shipbuilding industry. However, the application of hydrogen energy in ship energy systems is influenced by variations in operational load and the integration of new energy sources during actual navigation. To address these issues, this paper focuses on optimizing and scheduling the operation of ships under various navigation conditions, considering the distributed nature of hydrogen energy. System simulations were conducted to model the photovoltaic (PV), proton exchange membrane fuel cells (PEMFCs), lithium batteries (LIBs), electrolytic cells (ECs), and energy storage modules of yacht energy systems. Component boundaries and objective functions were set, and two cases (excess photovoltaic state and constant power state) were designed to optimize and regulate the energy balance of hydrogen-powered yachts, enhancing their comprehensive utilization of renewable energy. By comparing the changes in ship energy under the two cases, it was concluded that case 1 ensures the maximum utilization of renewable energy. When photovoltaic power generation is insufficient, the PEMFC and LIB in the system provide the required power to achieve a supply-demand balance. Moreover, when PV power generation is sufficient, hydrogen energy is used to store renewable energy. The optimization method designed in this study can, to some extent, maximize the application of renewable energy in new energy yachts, ensuring the efficiency of the comprehensive energy system of new energy yachts, reducing emissions, and improving the sustainability and economic efficiency of the ships.

Suppressed Possibilistic Fuzzy C-Means Clustering Based on Shadow Sets for Noisy Data with Imbalanced Sizes

Possibilistic fuzzy c-means clustering (PFCM) algorithm generates fewer overlapping clustering centers than the possibilistic c-means clustering (PCM) algorithm and possesses better noise immunity than fuzzy c-means clustering (FCM) algorithm. However, with the increasing noise intensity and number of clusters, PFCM still faces the problem of getting partially overlapping clustering centers or mislocated centers in noise regions. Moreover, the sample-size imbalance increasingly intensifies the difficulty of positioning centers of small clusters. To solve the above problems, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets (S-SPFCM) is proposed by introducing the shadow set theory and the "suppressed competitive learning" strategy. Firstly, KL divergence is introduced in the objective function of PFCM to increase the anti-noise robustness of fuzzy memberships against long-range noise and outliers. Secondly, to reduce the number of overlapping centers caused by possibilistic memberships, the shadow set theory is introduced to divide each class adaptively into three regions (core, shadow, and exclusion regions) by an uncertainty balance method. The suppressed competitive learning method is extended by modifying the memberships of points within the three regions, thus artificially guiding the iterative track of clustering centers. Meanwhile, to further reduce the influence of imbalanced sizes, a scheme to reset mislocated centers in the core and shadow regions is also designed. In addition, to improve the segmentation performance of S-SPFCM for noisy images, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets and local information (SL-SPFCM) is also proposed. The SL-SPFCM first improves the Euclidean distance by a distance filtering scheme. Then SL-SPFCM introduces the local median membership of each pixel which is regarded as a point-by-point prior probability into the KL divergence of the objective function. Finally, experiments on synthetic datasets and color images characteristic of imbalanced sizes and noise injection demonstrate the proposed S-SPFCM and SL-SPFCM algorithms achieve smaller center deviations and higher clustering accuracy compared with several state-of-the-art clustering algorithms.

Dynamic Neural Network Predictive Compensation-Based Point-to-Point Iterative Learning Control With Nonuniform Batch Length.

This article discusses the problem of nonuniform running length in incomplete tracking control, which often occurs in industrial processes due to artificial or environmental changes, such as chemical engineering. It affects the design and application of iterative learning control (ILC) that relies on the strictly repetitive property. Therefore, a dynamic neural network (NN) predictive compensation strategy is proposed under the point-to-point ILC framework. To handle the difficulty of establishing an accurate mechanism model for real process control, the data-driven approach is also introduced. First, applying the iterative dynamic linearization (IDL) technique and radial basis function NN (RBFNN) to construct the iterative dynamic predictive data model (IDPDM) relies on input-output (I/O) signal, and the extended variable is defined by a predictive model to compensate for the incomplete operation length. Then, a learning algorithm based on multiple iteration errors is proposed using an objective function. This learning gain is constantly updated through the NN to adapt to changes in the system. In addition, the composite energy function (CEF) and compression mapping prove that the system is convergent. Finally, two numerical simulation examples are given.

Transfer learning-accelerated network slice management for next generation services

The current trend in user services places an ever-growing demand for higher data rates, near-real-time latencies, and near-perfect quality of service. To meet such demands, fundamental changes were made to the traditional radio access network (RAN), introducing Open RAN (O-RAN). This new paradigm is based on a virtualized and intelligent RAN architecture. However, with the increased complexity of 5G applications, traditional application-specific placement techniques have reached a bottleneck. Our paper presents a Transfer Learning (TL) augmented Reinforcement Learning (RL) based networking slicing (NS) solution targeting more effective placement and improving downtime for prolonged slice deployments. To achieve this, we propose an approach based on creating a robust and dynamic repository of specialized RL agents and network slices geared towards popular user service types such as eMBB, URLLC, and mMTC. The proposed solution consists of a heuristic-controlled two-module-based ML Engine and a repository. The objective function is formulated to minimize the downtime incurred by the VNFs hosted on the commercial-off-the-shelf (COTS) servers. The performance of the proposed system is evaluated compared to traditional approaches using industry-standard 5G traffic datasets. The evaluation results show that the proposed solution consistently achieves lower downtime than the traditional algorithms.

A novel multi-objective dung beetle optimizer for Multi-UAV cooperative path planning

Path planning for multiple unmanned aerial vehicles (UAVs) is crucial in collaborative operations and is commonly regarded as a complicated, multi-objective optimization problem. However, traditional approaches have difficulty balancing convergence and diversity, as well as effectively handling constraints. In this study, a directional evolutionary non-dominated sorting dung beetle optimizer with adaptive stochastic ranking (DENSDBO-ASR) is developed to address these issues in collaborative multi-UAV path planning. Two objectives are initially formulated: the first one represents the total cost of length and altitude, while the second represents the total cost of threat and time. Additionally, an improved multi-objective dung beetle optimizer is introduced, which integrates a directional evolutionary strategy including directional mutation and crossover, thereby accelerating convergence and enhancing global search capability. Furthermore, an adaptive stochastic ranking mechanism is proposed to successfully handle different constraints by dynamically adjusting the comparison probability. The effectiveness and superiority of DENSDBO-ASR are demonstrated by the constrained problem functions (CF) test, the Wilcoxon rank sum test, and the Friedman test. Finally, three sets of simulated tests are carried out, each including different numbers of UAVs. In the most challenging scenario, DENSDBO-ASR successfully identifies feasible paths with average values of the two objective functions as low as 637.26 and 0. The comparative results demonstrate that DENSDBO-ASR outperforms the other five algorithms in terms of convergence accuracy and population diversity, making it an exceptional optimization approach to path planning challenges.

An Improved Artificial Electric Field Algorithm for Determining the Maximum Length of Gravel Packing in Deep-Water Horizontal Well

Gravel packing in deep-water horizontal wells is an effective and practical sand control method, which is a key technical method to ensure efficient exploitation of deep-water oil and gas. To ensure the successful implementation of gravel packing in deep water horizontal wells, it is crucial to carry out effective optimization design of packing parameters. This paper proposes a novel optimization design approach for gravel packing in deep-water horizontal wells. In the proposed approach, an optimization model is proposed for gravel packing in deep-water horizontal wells, in which the gravel packing length is regarded as the objective function. Then, an improved artificial electric field algorithm (IAEFA) is introduced for optimizing the key gravel packing parameters so as to determine the maximum gravel packing length. For a specific case study, we conducted optimization calculations for gravel packing in a deep-water horizontal well. Results of the case study demonstrate that the optimization design approach based on the IAEFA algorithm can effectively address the parameter optimization problem of deep-water horizontal well gravel packing. For the target well of the case study, the maximum packing length obtained by the IAEFA algorithm could reach 1000.22 m, and the corresponding 3 sets of optimal packing parameters were also obtained. In the scenario of optimal packing parameters, the total time of gravel packing in target well is 566.6 min, and the total amount of sand consumption is 54,050.94 lbs. The bottom hole pressure during the injection stage remains stable with about 9780 psi, then slowly rises from 9788 psi to 9837 psi in the α-wave packing stage, and rapidly increases from 9837 psi to 9986 psi in the β-wave packing stage. The proposed approach provides an efficient and practical optimization tool for the optimal design of gravel packing in deep water horizontal wells.

Petrophysical parameter estimation using a rock-physics model and collaborative sparse representation

The estimation of petrophysical parameters is key in the identification of underground reservoirs. Current petrophysical parameter estimation methods are typically constrained by the choice of particular rock-physics models, necessitating the use of distinct models for various reservoirs. Furthermore, the inherent pronounced nonlinearity of these models presents significant challenges to the solution process in reservoir parameter inversion. Although linearized petrophysical inversion methods can simplify the solving process, they can introduce errors due to linearization. To address these limitations, we develop a petrophysical parameter estimation method driven by a rock-physics model and collaborative sparse representation (CSR). In this approach, the rock-physics model governs the fundamental pattern of the petrophysical parameters, with the CSR introducing perturbations to minimize model errors. Our method maximizes the use of well-log data and the rock-physics model, thereby reducing errors associated with linearized rock-physics (LRP) models and enhancing the method’s adaptability. We use the joint dictionary method to learn features and correlations among multiple parameters from the existing well-log data. This learned dictionary is then used as a CSR regularization constraint and applied to refine the LRP inversion objective function. Finally, the objective function is minimized using the block coordinate descent method to predict the petrophysical parameters. The effectiveness of this method in enhancing the adaptability and accuracy of petrophysical parameter estimation is confirmed through synthetic and field data tests.

Efficient adaptive learning rate for convolutional neural network based on quadratic interpolation egret swarm optimization algorithm

Convolutional neural network (CNN) has recently become popular for addressing multi-domain image classification. However, most existing methods frequently suffer from poor performance, especially in performance and convergence for various datasets. Herein, we have proposed an algorithm for multi-domain image classification by introducing a novel adaptive learning rate rule to the conventional CNN. Specifically, we adopt the CNN to extract rich feature representations. Given that the hyperparameters of the learning rate have a positive effect on the prediction error, the Egret Swarm Optimization Algorithm (ESOA) is introduced to update the learning rate, which can jump out of local extrema during exploration. Therefore, combined with quadratic interpolation, the objective function can be approximated by a polynomial, thereby improving its prediction accuracy. To verify the robustness of the proposed algorithm, we conducted comprehensive experiments in five domain public datasets to fulfil the task of image classification. Meanwhile, the highest accuracy rate of 97.15 % was obtained on the test set. The performances of our method on 24 benchmark functions (CEC2017 and CEC2022) are compared with Particle Swarm Optimization (PSO), Genetic Algorithm(GA), Whale Optimization Algorithm(WOA), Catch Fish Optimization Algorithm(CFOA), GOOSE Algorithm(GO) and ESOA. In two benchmark sets, the performance metric values of our algorithm rank no. 1, especially in all unimodal functions in contrast with other baseline algorithms.

A Novel Methodology for GB-SAR Estimating Parameters of the Atmospheric Phase Correction Model Based on Maximum Likelihood Estimation and the Gauss-Newton Algorithm.

Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method.

A Linear Programming Aggregation Method Based on Generalized Zhenyuan Integral in q-ROFN Environment and the Application of Talent Recruitment in Universities

The reasonable ranking of binary pairs that characterize fuzzy information in many fuzzy decision problems is very important. To overcome some defects of the existing score functions for the q-rung orthopair fuzzy numbers (q-ROFNs), a novel score function and ranking criterion are proposed by the q-compression transformation and hesitation factor. The main motivation is to introduce the generalized Zhenyuan (GZ)-integral into the q-ROFN environment, and cleverly transform the aggregation operations into a linear programming problem through the arithmetic operations of q-ROFNs. The main contribution is to solve the aggregation problem of q-rung orthopair fuzzy generalized Zhenyuan integral ordered weighted average (q-ROFGZIOWA) operator through the optimization technique of linear programming, and a new decision making method is established by using the q-ROFGZIOWA operator and ranking criterion. The main innovation is to map all q-ROFNs to the unit triangle in the first quadrant (converted into intuitionistic fuzzy numbers, IFNs) according to the q-compression transformation in geometric significance, and the novel score function and its ranking criterion are proposed by combining hesitation factor, and then the aggregation operation based on generalized Z-integral is converted to an optimization problem in linear programming. Finally, the superiority of the proposed method are verified by comparing the aggregation results of two integral operators through an example, and apply the proposed method to the optimal decision-making of talent recruitment in universities. The proposed method can not only correct some flaws in the ranking of existing q-ROFNs, but also overcomes some defects of existing Choquet integral average (geometric) operators in a q-ROFN environment. These results are of great significance for further research on the widespread application of q-ROFNs.

MRDPDA: A multi-Laplacian regularized deepFM model for predicting piRNA-disease associations.

PIWI-interacting RNAs (piRNAs) are a typical class of small non-coding RNAs, which are essential for gene regulation, genome stability and so on. Accumulating studies have revealed that piRNAs have significant potential as biomarkers and therapeutic targets for a variety of diseases. However current computational methods face the challenge in effectively capturing piRNA-disease associations (PDAs) from limited data. In this study, we propose a novel method, MRDPDA, for predicting PDAs based on limited data from multiple sources. Specifically, MRDPDA integrates a deep factorization machine (deepFM) model with regularizations derived from multiple yet limited datasets, utilizing separate Laplacians instead of a simple average similarity network. Moreover, a unified objective function to combine embedding loss about similarities is proposed to ensure that the embedding is suitable for the prediction task. In addition, a balanced benchmark dataset based on piRPheno is constructed and a deep autoencoder is applied for creating reliable negative set from the unlabeled dataset. Compared with three latest methods, MRDPDA achieves the best performance on the pirpheno dataset in terms of the five-fold cross validation test and independent test set, and case studies further demonstrate the effectiveness of MRDPDA.

Scattered storage for retail e-commerce fulfilment warehouses with consideration for product turnover

Storage assignment policy of a warehouse controls how the stocks are assigned to various storage locations. Traditionally used storage policies, such as dedicated or random storage, do not address the specific needs of retail e-commerce fulfillment warehouses that store a wide assortment of products and service a large number of single-unit orders under strict timelines. This has led to the development of scattered storage assignment policy, which deliberately spreads the stocks of every product across the warehouse. However, the available approaches towards scattering have largely ignored product turnover, which is a significant determinant of order picking travel. To fill this research gap, we propose a new, turnover-incorporated scattered storage policy. More specifically, we develop a new measure of scattering of stocks and a mathematical model that optimizes the measure by scattering the stocks across the warehouse, while considering product turnover. Certain important properties of this measure are proved and eventually exploited in developing a heuristic approach to solve the proposed mathematical model for large problem instances. An upper bound for the objective function of the mathematical model is used as a benchmark to evaluate the performance and computation time of the proposed heuristic, as well as solutions obtained through genetic algorithms and surrogate optimization. We conduct a simulation study using the proposed heuristic to analyze the impact of the scattering of stocks on order picking performance in a single block, low level, picker to parts warehouse. We also present the impact of warehouse operating parameters on the performance of the proposed scattered storage policy.

Worst-case robust optimization based on an adaptive incremental Kriging metamodel

Worst-case robust optimization problem is concerned with finding a candidate solution that is insensitive to uncertainty. This problem involves nested-loop structure based on the worst-case analysis. It is an expensive optimization problem which has large computational complexity. This paper presents a robust optimization method of reduced computational complexity. Firstly, the state transition algorithm (STA) is utilized to explore and exploit the candidate solutions of the search space. Then, an adaptive incremental Kriging (IKriging) metamodel is proposed to replace the evaluation functions for evaluating the robustness of candidate solutions. Finally, a preferential selection strategy is presented to select the optimal solution in terms of objective function value, constraint and robustness violation. Four engineering examples are studied to analyze the performance of the proposed robust optimization method. Experimental results illustrate that the proposed method can find a better robust solution with a high computational efficiency.

Assessing PEM fuel cell performance in a geothermal Cogeneration system for peak-time energy storage

In this investigation, a novel geothermal power plant was designed, combining absorption chiller units, PEMFC, EPEM, and ORC. We conducted a comprehensive case study across four continents—Asia, Oceania, Europe, and America—leveraging weather data from various cities to evaluate the system's efficacy. Our modeling utilized EES (Engineering Equation Solver) software, optimizing the setup via the RSM with three key objective functions: exergy efficiency, hydrogen production, and cost rate. The primary focus was on delivering electricity to residential properties during peak demand periods. Exploring six scenarios for organic fluids in organic Rankine cycles, we gauged energy, exergy, and overall system performance. The TOPSIS method led us to select scenario 3, employing R123 and R134a refrigerants, as the optimal choice. The results of the optimization showcased impressive figures: an exergy efficiency of 81.816%, a hydrogen production rate of 25.119 kg/h, and a cost rate of 15.967 $/h for the system's most efficient configuration. Economic analysis highlighted the organic Rankine cycle units 1 and 2 as the components with the highest costs. Our evaluation extended to various cities—Aomori, Grosseto, Lhasa, Wellington, and San Diego—assessing the electricity, heating, and cooling needs of residential complexes based on the system's performance.

Probabilistic branch and bound considering stochastic constraints

In this paper, we investigate a simulation optimization problem that poses challenges due to (i) the inability to evaluate the objective and multiple constraint functions analytically; instead, we rely on stochastic simulation to estimate them, and (ii) a discrete and potentially vast solution space. Rather than providing a single optimal solution, our aim is to identify a set of near-optimal solutions within a specific quantile, such as the top 10%. Our investigation covers two different problem settings or frameworks. The first framework is focused solely on a stochastic objective function, disregarding any stochastic constraints. In this context, we propose employing a probabilistic branch-and-bound algorithm to discover a level set of solutions. Alternatively, the second framework involves stochastic constraints. To address such stochastically constrained problems, we utilize a penalty function methodology in conjunction with a probabilistic branch-and-bound algorithm. Furthermore, we establish a convergence analysis of both algorithms to demonstrate their asymptotic validity and highlight their theoretical properties and behavior. Our experimental results provide evidence of the efficiency of our proposed algorithms, showing that they outperform existing approaches in the field of simulation optimization.

Online Distributed Optimization With Nonconvex Objective Functions Under Unbalanced Digraphs: Dynamic Regret Analysis

Online Distributed Optimization With Nonconvex Objective Functions Under Unbalanced Digraphs: Dynamic Regret Analysis