Uncertain Problem Research Articles

A study of uncertain 4D transportation problems with rough interval parameters and additional real-life factors

In developing countries like India and Nepal, a vehicle document verification system is implicated at the checkpoints and border crossings that allows users to authenticate and verify the validity of vehicle related documents such as registration certificates, driving licenses, pollution under control certificates, and insurance policies. This results in the formation of long queues of the vehicles and hence a significant time wastage. These vehicles waiting in the long queues, continue to emit carbon dioxide and other greenhouse gases into the atmosphere. To address these issues, the government has introduced the Automated Number Plate Recognition (ANPR) technology which plays a significant role in the efficient and accurate document verification by identifying and validating vehicle registration details. It also automates toll collection by capturing the vehicle’s number plate, reducing waiting times and congestion at toll barriers. To analyze all these benefits, in this study, for the first time, ANPR technology has been introduced in the multi-objective model of transportation problem and its impact on various objectives has been observed. Also, real-life factors: fixed-charge cost, carbon emission, multiple routes have been considered in the proposed model and the problem is named as multi-objective fixed-charge four dimensional green transportation problem. Rough set theory has been employed as a tool for effectively addressing the indeterminacy and facilitating the modeling of real-life transportation problems. Two methods: the expected value method and the rough chance constrained programming method, are proposed to transform the suggested model of multi-objective transportation problem into a deterministic form. To solve these transformed models, a new multi-objective optimization approach based on the neutrosophic theory, named as neutrosophic goal programming has been introduced. To further demonstrate the practicality of the proposed study, an application for the apple fruit transportation has been solved. Detailed comparisons between obtained results are done on the basis of different modeling perspectives, different solution techniques and also with/and without ANPR technology. Based on the outcomes, the suggested neutrosophic goal programming technique proved to be superior to the existing techniques in the literature.

Modified dung beetle optimizer with multi-strategy for uncertain multi-modal transport path problem

Abstract Uncertain multi-modal transport path optimization (UMTPO) is a combined optimization non-deterministic polynomial-time hard problem. Its goal is to determine a path with the lowest total transportation cost and carbon emissions from the starting point to the destination. To effectively address this issue, this article proposes a modified dung beetle optimizer (DBO) to address it. DBO is a swarm-based metaheuristic optimization algorithm that has the features of a fast convergence rate and high solution accuracy. Despite this, the disadvantages of weak global exploration capability and falling easily into local optima exist. In this article, we propose a modified DBO called MSHDBO for function optimization and to solve the UMTPO problem. However, for the vast majority of metaheuristic algorithms, they are designed for continuous problems and cannot directly solve discrete problems. Therefore, this article employs a priority based encoding and decoding method to solve the UMTPO problem. To verify the performance and effectiveness of the MSHDBO algorithm, we compared it with other improved versions of the DBO algorithm used in the literature. We confirmed the excellent performance of MSHDBO using 41 benchmark test functions from the IEEE CEC 2017 test suite and IEEE CEC 2022 test suite. Additionally, we compared the MSHDBO algorithm with 10 other state-of-the-art metaheuristic optimization algorithms through a practical UMTPO problem. The experimental results indicated that the MSHDBO algorithm achieved very good performance when solving the UMTPO problem.

Three-way decision based island harmony search algorithm for robust flow-shop scheduling with uncertain processing times depicted by big data

This paper discusses an uncertain two-machine permutation flow-shop scheduling problem (2PFSP) with total weighted tardiness and common due date. Uncertain processing times are described by a large set of discrete scenarios, which is a type of big data. The objective is to minimize the schedule performance under the worst-case scenario. Identifying the worst-case scenario for each evaluated schedule is quite time-consuming in the situation that the scenario set size is large so that the objective evaluation might be computationally expensive. To handle this difficulty, three-way decision is used to preprocess the large-size scenario set to get a reduced scenario set so that the concept of surrogate worst-case scenario is adopted. A hybrid harmony search algorithm of combining three-island framework and the scenario-based local search is developed to solve the discussed problem. Based on the single-scenario knowledge of 2PFSP, a problem-specific scenario-dependent neighborhood structure is constructed under the surrogate worst-case scenario. An extensive experiment was carried out. The computational results show that the application of surrogate worst-case scenario based on three-way decision is effective in reducing the time consuming while keeping schedule performance evaluation. Being compared to the worst-case scenario objective evaluation, for an example in the case of the middle bad-scenario ratio, the surrogate worst-case scenario objective evaluation made the solution algorithm save 12.95 % in average CPU time for all instances while the relative performance difference is only 1.809 % in average. Being compared to possible alternative algorithms derived from the state-of-the-art algorithms, the developed algorithm is advantageous for the addressed problems.

Bayesian network structure learning with a new ensemble weights and edge constraints setting mechanism

Bayesian networks (BNs) are highly effective in handling uncertain problems, which can assist in decision-making by reasoning with limited and incomplete information. Learning a faithful directed acyclic graph (DAG) from a large number of complex samples of a joint distribution is currently a challenging combinatorial problem. Due to the growing volume and complexity of data, some Bayesian structure learning algorithms are ineffective and lack the necessary precision to meet the required needs. In this paper, we propose a new PCCL-CC algorithm. To ensure the accuracy of the network structure, we introduce the new ensemble weights and edge constraints setting mechanism. In this mechanism, we employ a method that estimates the interaction between network nodes from multiple perspectives and divides the learning process into multiple stages. We utilize an asymmetric weighted ensemble method and adaptively adjust the network structure. Additionally, we propose a causal discovery method that effectively utilizes the causal relationships among data samples to correct the network structure and mitigate the influence of Markov equivalence classes (MEC). Experimental results on real datasets demonstrate that our approach outperforms state-of-the-art methods.

Prediction of the process capability for compression rubber part forming in the automotive supply chain

The paper proposes predicting production process capability for the compression rubber part in automotive supply chain management. Delivery of parts to tier 1 and OEM on time is the most important part of supply chain management, together with the delivery of on-quality and on-cost control to maintain the competitiveness of the supply chain. There are many suppliers to produce many automotive parts for tier 1. Therefore, the simulation approach properly predicts and prevents the process from getting into trouble during the actual production time. Production process quality control is critical to ensure that the good quality of the parts purchased can be delivered on time. Rubber parts are used widely in automotive, motorcycles, trucks, and other types of vehicles, with small sizes but in huge quantities to support general OEM brands and specific parts. The rubber part manufacturing process is complex and uncertain with compression moulding and rubber curing conditions. Therefore, good conditions can predict the production process's capability to commission and deliver on schedule.A neuro-fuzzy system is adopted and developed to deal with the uncertain process capability under multi-criteria decision-making.The methodology development can be used in the actual rubber part manufacturing supply chain environment and can predict uncertain problems that might occur in the subcontractor factories.The prediction of the production process capability of the rubber part supply chain might be more effective on the real-time monitoring control system and can be tracking location part progress for further planning both success or rescheduling.The platform can be applied to audit and test the actual industrial supply chain, and problem and research questions are brought about from the real supply chain in the local country.The methodology development was originally created for the particular supply chain in rubber automotive parts that can replace the existing system to obtain a more efficient performance evaluation process.

A novel penalty function-based interval constrained multi-objective optimization algorithm for uncertain problems

To directly address problems involving uncertain objectives and constraints, a novel penalty function-based interval constrained multi-objective optimization algorithm (PF-ICMOA) was developed. It comprises three main components: an uncertainty propagation-based interval constraint solver, an interval constraint violation function, and a two-stage penalty function. The uncertainty violation of interval constraints can be accurately evaluated by the proposed advanced multi-objective optimization algorithm using a segmentation function without requiring multiple interval analyses. Additionally, by applying penalties to infeasible solutions in the two-stage process, partially feasible and superior infeasible solutions are retained in the early stages of evolution, while superior feasible solutions are favored in the later stages. A novel benchmark was designed and the effect of the imprecision factor on the Pareto front was examined in details. Comparisons with seven deterministic constraint handling techniques demonstrated the effectiveness of the proposed method for solving interval constrained multi-objective optimization problems, demonstrating that PF-ICMOA is a highly competitive method for balancing the feasibility, convergence, and diversity performance characteristics.

Hellinger distance measures on Pythagorean fuzzy environment via their applications

Pythagorean fuzzy sets (PFSs) are a versatile tool for handling uncertain problems and have proven effective in practical applications. However, many existing Pythagorean fuzzy distance measures have counter-intuitive situations, making it challenging to measure the difference between PFSs accurately. To address this issue, we propose two distance measures for PFSs inspired by the Hellinger distance measure. We also explore the properties of the proposed measures and provide several comparative examples with existing measures for PFSs, illustrating their superior performance in processing fuzzy information from PFSs. Finally, we further develop a new decision-making method on top of the proposed measures and evaluate its performance in two applications.

Next track point prediction using a flexible strategy of subgraph learning on road networks

Accurately predicting the next track point of vehicle travel is crucial for various Intelligent Transportation System (ITS) applications, such as travel behavior studies, traffic control, and traffic congestion monitoring. Recent works on trajectory prediction follow a paradigm that first represents the raw trajectory and subsequently makes predictions based on that representation. Currently, trajectory representation methods tend to project trajectory points to road networks by map matching and represent trajectories based on the representation of matched roads. However, precisely matching trajectories to roads is a challenge in ITS, as the matching precision is greatly affected by the quality of the trajectory. Meanwhile, since it is difficult to discern whether trajectory matching results are accurate or confounded, how to effectively utilize this type of uncertain geographic context information is also a challenge, which is defined as the Uncertain Geographic Context Problem (UGCoP) in geographic information science. Therefore, we propose a flexible strategy of subgraph learning, referred to as SLM, for predicting the next track point of vehicles. Specifically, a subgraph generation module is first proposed to extract topology contextual information of the roads around historical trajectory points. Secondly, a subgraph learning module is designed to learn rich spatial and temporal features from generated subgraphs. Finally, the extracted spatiotemporal features will be fed into a prediction module to predict the next track points of vehicles on road networks. Our model enables the effective utilization of uncertain geographic context information of trajectories on road networks while avoiding the error brought by map matching. Extensive experiments based on trajectory datasets in two different cities confirm the effectiveness of our approach.

Solving Contextual Stochastic Optimization Problems through Contextual Distribution Estimation

Stochastic optimization models always assume known probability distributions about uncertain parameters. However, it is unrealistic to know the true distributions. In the era of big data, with the knowledge of informative features related to uncertain parameters, this study aims to estimate the conditional distributions of uncertain parameters directly and solve the resulting contextual stochastic optimization problem by using a set of realizations drawn from estimated distributions, which is called the contextual distribution estimation method. We use an energy scheduling problem as the case study and conduct numerical experiments with real-world data. The results demonstrate that the proposed contextual distribution estimation method offers specific benefits in particular scenarios, resulting in improved decisions. This study contributes to the literature on contextual stochastic optimization problems by introducing the contextual distribution estimation method, which holds practical significance for addressing data-driven uncertain decision problems.

Order-Guided Non-Conservative Maximum Flow in Uncertain Network Interdiction Problem with Budget Constraint

Probability theory in decision science fails in the absence of sufficient data. In these situations, uncertainty theory is applied to the problem-solving process, taking into account the opinions of the domain experts. In order to minimize the maximum flow carried by the evader, we describe an interdiction problem in an uncertain network with intermediate storage and resource constraints. Such approaches would help law enforcement combat drug-related and smuggling activities. This work first converts the bi-level deterministic conservative model of the interdictor vs evader problem (IEP) into a non-conservative deterministic IEP. With intermediate storage, a binary interdiction variable, and an interdiction resource constraint, the model is further transformed into an uncertain measure-based model. Then, utilizing uncertainty theory, the uncertain model is again converted into its deterministic equivalent. We have presented two techniques to identify the arc that the interdictor needs to block and to direct the order-guided maximum flow that the evader needs to deliver to the target. The models’ and algorithms’ efficacy is confirmed by an example. Lastly, a graphic representation of the shifting trend of the value of the objective function (VOF) is shown for a range of confidence levels.

An information entropy-based fuzzy stochastic configuration network for robust data modeling

In data-driven modeling, the generalization performance of a neural network based on the minimum mean square error criterion may be affected when the samples contain noise. To handle uncertain data modeling problems, this study contributes a novel robust data modeling method called information entropy-based fuzzy stochastic configuration networks (IEFSCNs), which incorporates the maximum correntropy criterion (MCC) to reflect the squared error of the training sample set and uses the quantized minimum error entropy (QMEE) criterion to mine the distribution structure of the modeling data and suppress outlier data. Fuzzy systems are designed to generate nodes in the fuzzy transformation layer. A nonlinear enhancement layer is established as a hidden layer to enhance the representational capacity of the target system. The fuzzy transformation and nonlinear enhancement layers are fully connected to determine the outputs of the IEFSCNs. In addition, an incremental parameter learning algorithm is developed based on a supervision mechanism for optimizing the cost function, and its convergence property is demonstrated. Owing to the superiorities of the cost function by synthesizing MCC and QMEE, IEFSCNs can improve the modeling accuracy and reduce noise suppression. The performances are evaluated using various regression and classification tasks. Compared with existing methods, including SCNs, RVFL, F-SCNs, RSC-KDE, RSC-MCC, and SM-RSC, the proposed method demonstrates an effective robust modeling performance by reducing network structure redundancy while enhancing its ability to suppress noisy data.

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

Mobility-oriented measurements of people's exposure to outdoor artificial light at night (ALAN) and the uncertain geographic context problem (UGCoP).

Advanced nighttime light (NTL) remote sensing techniques enable the large-scope epidemiological investigations of people's exposure to outdoor artificial light at night (ALAN) and its health effects. However, multiple uncertainties remain in the measurements of people's exposure to outdoor ALAN, including the representations of outdoor ALAN, the contextual settings of exposure measurements, and measurement approaches. Non-exposed but included outdoor ALAN and causally irrelevant outdoor ALAN may manifest as contextual errors, and these uncertain contextual errors may lead to biased measurements and erroneous interpretations when modeling people's health outcomes. In this study, we systematically investigated outdoor ALAN exposure measurements in different geographic contexts using either residence-based or mobility-oriented measurements, different spatial scales, and multiple NTL data sources. Based on the GPS data collected from 208 participants in Hong Kong, outdoor ALAN exposures were measured from NTL imagery at 10 m, 130 m, and 500 m spatial resolutions using in-situ methods or 100 m, 300 m, and 500 m buffer zone averaging. Descriptive analysis, multiple t-tests, and logistic regression were employed to examine the differences between outdoor ALAN exposure measurements using various contextual settings and their effects on modeling people's overall health. Our results confirmed that different contextual settings may lead to significantly different outdoor ALAN exposure measurements. Our results also confirmed that contextual errors may lead to erroneous conclusions when using improper contextual settings to model people's overall health. Consequentially, we suggest measuring people's exposure to outdoor ALAN using the mobility-oriented approach, NTL representation with the high spatial resolution, and a very small buffer zone as a contextual unit to derive outdoor ALAN exposure. This study articulates essential methodological issues induced by uncertainties in outdoor ALAN exposure measurements and can provide essential implications and suggestions for a broad scope of studies that need accurate outdoor ALAN exposure measurements.

Study on the Method of Selecting Sustainable Food Suppliers Considering Interactive Factors

The existing sustainable supplier selection methods are not sufficient to deal with the problem of sustainable food supplier selection with the interaction of criteria under uncertainty. Therefore, this paper proposes a method of sustainable food supplier selection based on an extended decision model. Firstly, a processing method for supplier evaluation information is constructed using the Pythagorean fuzzy set has the function of processing complex uncertain information. Secondly, to obtain the objective weights of decision experts, a Pythagorean fuzzy weighted distance measure model is constructed, and an expert information fusion method based on a weighted power mean operator is proposed to construct the group decision matrix. Then, the decision experiment and evaluation experiment methods are integrated with the traditional MARCOS method, to construct a sustainable food supplier selection method considering the interaction of factors. This method can effectively deal with the complicated and uncertain problem of sustainable food supplier selection with interactive factors. Finally, the feasibility of the proposed method is verified by an example of sustainable food supplier selection. In addition, parameter sensitivity analysis and multi-method comparative analysis verified the rationality of the proposed selection method for sustainable food supplier selection.

A comparative study of fuzzy multi-objective investment project portfolio selection and optimization based on financial return and different risk measurements

Competitiveness in the global market is getting more intense. Due to resource and budget constraints, firms need to achieve their expected goals and satisfy all investment constraints under uncertainty. Selecting the set of projects among other candidates to get the most efficient portfolio requires a lot of attention from the Decision Makers (DMs) as this consideration no longer relies purely on the financial term. This problem becomes a multi-objective problem under uncertainty where the financial return and risk from uncertainty are required into the trading off consideration. Due to the financial uncertainty, the chance-constrained programming has been employed in this study for defuzzifying and solving uncertain optimization problems at a specified confidence level that is defined by the DMs. Then, various kinds of investment or financial risk measures, Lower-Semi Variance Index (LSVI), the absolute deviation with the expected FNPV, and the absolute mean-Conditional Value at Risk (CVaR) gap are provided in the selection of such risk measures to show their differences in characteristics and performances in the obtained results. Since, such problems can consist of many project candidates and complex constraints, which may grow beyond the application of the exact optimization approach, a meta-heuristic method, Genetic Algorithm (GA), is introduced to optimize this problem through designing and constructing a decision support tool for the investment portfolio selection and optimization. The applicability of the proposed comparative approach and the constructed tool are illustrated through examples.

Adaptive weighted total variation expansion and Gaussian curvature guided low-dose CT image denoising network

The denoising task of low-dose CT images is a highly complex and uncertain inverse problem. Previous studies have primarily relied on convolutional neural network to reduce noise by learning the mapping from LDCT images to normal dose CT images. However, simply increasing the network depth alone is not an optimal choice due to the limited performance improvement and significant computational cost. In contrast, integrating prior knowledge of images with a model to assist in image reconstruction is a more efficient approach. This study proposes a new framework for denoising LDCT images, named Noise-Optimized Edge Feature Guided Network (NEFGN). The task of NEFGN is to integrate the noise optimization model of adaptive weighted total variation expansion, the edge detection model guided by Gaussian curvature, and image reconstruction into an end-to-end CNN framework. In order to achieve this goal, the noise optimization model is first constructed by learning the parameters in the adaptive weighted total variation regularization model to approximate the noise level in the NDCT image. The edge detection network is constructed using Gaussian curvature, predicting clear edges directly from the noise image. Finally, under the guidance of the noise optimization model and the edge detail model, NEFGN is more capable of suppressing artifact noise, demonstrating good accuracy and robustness, and can restore finer details. Numerous experimental studies demonstrate that the NEFGN denoising framework effectively restores the structure of LDCT images with limited image details and outperforms other methods in terms of performance.

Slope stability prediction based on GSOEM-SV: A mobile application practicably deploy in engineering verification

Slope stability evaluation is a complex and uncertain system problem, and carrying out slope stability prediction is the prerequisite and foundation for slope disaster prevention. In order to achieve fast and accurate prediction of slope stability, this paper considers height, total slope angle, unit weight, cohesion, internal friction angle, and pore water pressure ratio as input features and proposes an intelligent slope stability prediction method based on grid search optimization ensemble learning model by soft voting (GSOEM-SV). First, 390 sets of on-site data were collected to form a dataset, and analyses including correlation coefficients, density estimates, and box lines were carried out. Then, the grid search optimization algorithm is used to optimize the hyperparameters of five algorithms—Gradient Boosting Decision Trees, Light Gradient Boosting Machine, Categorical Boosting, Support Vector Machine, and Random Forest, and integrates them through soft voting. Furthermore, this paper optimizes the hyperparameters of the above five algorithms based on grid search, particle swarm and simulated annealing algorithms, builds 15 improved models and 2 ensemble models and conducts comparison. The results reveal that the GSOEM-SV has the highest slope stability prediction accuracy, up to 91 %, the area under the curve (AUC) is 0.950, and its F1 score 0.917, which are better than the 15 improved and 2 integrated models. In addition, a set of slope stability prediction app based on uni-app is developed in the paper. It provides a technical foundation and an open and shareable information service platform for slope hazard prediction in geotechnical engineering.

Navigating uncertain distribution problem: a new approach for resolution optimization of transportation with several objectives under uncertainty

Amidst uncertainty, decision-making in manufacturing becomes a central focus due to its complexity. This study explores complex transportation constraints and uses novel ways to guide manufacturers. The Multi-objective Stochastic Linear Fractional Transportation Problem (MOSLFTP) is a crucial tool for managing supply chains, manufacturing operations, energy distribution, emergency routes, healthcare logistics, and other related areas. It adeptly addresses uncertainty, transforming efficiency and effectiveness in several domains. Stochastic programming is the process of converting theoretical probabilities into concrete certainties. The artistic compromise programming technique acts as a proficient mediator, reconciling opposing objectives and enabling equitable decision-making. This novel approach also addresses the Multi-objective Stochastic Linear plus Linear Fractional Transportation Problem (MOSLPLFTP), which involves two interconnected issues. The effectiveness of these principles is clearly shown with the help of the LINGO® 18 optimization solver. This study uses a ranking method to compare the similar methods to solve the current problems. A meticulously designed example acts as a significant achievement, shedding light on our method in a practical setting. It serves as a distinctive instrument, leading manufacturers through the maze of uncertainty and assisting them in determining the most advantageous course of action. This journey involves subtle interactions between complexity and simplicity, uncertainty is overcome by decisiveness, and invention is predominant.

Robust Optimization of Vaccine Distribution Problem with Demand Uncertainty

This study proposes a multi objective optimization model for vaccine distribution problems using the Maximum Covering Location Problem (MCLP) model. The objective function of the MCLP model in this study is to maximize the fulfillment of vaccine demand for each priority group at each demand point. In practice, the MCLP model requires data on the amount of demand at each demand point, which in reality can be influenced by many factors so that the value is uncertain. This problem makes the optimization model to be uncertain linear problem (ULP). The robust optimization approach converts ULP into a single deterministic problem called Robust Counterpart (RC) by assuming the demand quantity parameter in the constraint function is in the set of uncertainty boxes, so that a robust counterpart to the model is obtained. Numerical simulations are carried out using available data. It is found that the optimal value in the robust counterpart model is not better than the deterministic model but is more resistant to changes in parameter values. This causes the robust counterpart model to be more reliable in overcoming uncertain vaccine distribution problems in real life. This research is limited to solving the problem of vaccine distribution at a certain time and only assumes that the uncertainty of the number of requests is within a specified range so that it can be developed by assuming that the number of demand is dynamic.

Rank-1 transition uncertainties in constrained Markov decision processes

We consider an infinite-horizon discounted constrained Markov decision process (CMDP) with uncertain transition probabilities. We assume that the uncertainty in transition probabilities has a rank-1 matrix structure and the underlying uncertain parameters belong to a polytope. We formulate the uncertain CMDP problem using a robust optimization framework. To derive reformulation of the robust CMDP problem, we restrict to the class of stationary policies and show that it is equivalent to a bilinear programming problem. We provide a simple example where a Markov policy performs better than the optimal policy in the class of stationary policies, implying that, unlike in classical CMDP problem, an optimal policy of the robust CMDP problem need not be present in the class of stationary policies. For the case of a single uncertain parameter, we propose sufficient conditions under which an optimal policy of the restricted robust CMDP problem is unaffected by uncertainty. The numerical experiments are performed on randomly generated instances of a machine replacement problem and a well-known class of problems called Garnets.