Uncertain Problem Research Articles

Steepest descent method for uncertain multiobjective optimization problems under finite uncertainty set

In this paper, a steepest descent method is developed for the robust counterpart of uncertain multiobjective optimization problems under finite uncertainty. The robust counterpart under consideration is the minimum of objective wise worst case, which is a nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of the steepest descent method, a subproblem is constructed and solved to find a descent direction. An Armijo-type inexact line search technique is employed to find a suitable step length. With the help of the descent direction and step length, a sequence is generated. The convergence of the proposed method is justified under some common assumptions. Finally, the algorithm is verified and compared with one existing method with the help of some numerical problems.

Disturbance Observer‐Based Neural Adaptive Command Filtered BacksStepping Funnel‐Like Control for the Chaotic PMSM With Asymmetric Prescribed Performance Constraints

ABSTRACTThis paper suggests a neural adaptive command filtered backstepping tracking control strategy for the chaotic permanent magnet synchronous motors with asymmetric prescribed performance constraints. Therefore, enable chaotic permanent magnet synchronous motors (PMSM) to obtain good robustness and better universality in practical industrial environments, and realizes more accurate control effect. The main challenge lies in devising a valid funnel‐like solution within the backstepping frame to handle the asymmetric performance constraints that traditional solutions cannot solve. To achieve this, a novel funnel‐like function is introduced, integrating a performance boundary function independent of initial output error, thereby transforming the system into an unbounded one. Additionally, the “explosion of complexity” with conventional backstepping is mitigated by introducing command filtering and constructing an error compensating system to reduce errors. By combining the theory of Lyapunov function and backstepping technique, the virtual controller and the real controller with adaptive law ensure the stability of the system. The disturbance observer and neural network solve the external disturbance and the uncertain nonlinear problem, respectively. Simulation comparisons confirm the robustness of the proposed control scheme and demonstrate its superiority over existing solutions.

Interval-valued q-rung orthopair fuzzy complex proportional assessment-based approach and its application for evaluating the factors of Blockchain Technology in various domains

Blockchain technology (BT) is a digitally decentralized, distributed and public ledger, which considers a secure and viable solution for storing and accessing the record transactions in a public or private peer-to-peer network and assures a smart world of automation of complex services. This paper aims to evaluate the factors persuading the BT adoption and also to assess the possible application areas for the adoption of BT. Implementation of the BT process considers multiple criteria and alternatives with uncertain information; therefore, it can be considered as an uncertain multi-criteria decision-making problem. In this context, a hybrid approach is proposed based on the criteria interaction through inter-criteria correlation (CRITIC) and the complex proportional assessment (COPRAS) methods with interval-valued q-rung orthopair fuzzy set (IVq-ROFS) named as the “IVq-ROF-CRITIC-COPRAS” framework. In this approach, the significance values of the factors are computed through novel score function-based CRITIC model, whereas the CRITIC-based COPRAS model is employed to rank different domains/application areas for the adoption of BT under IVq-ROFSs environment. In this regard, a novel score function is introduced with its desirable characteristics. Further, the developed model is executed on a case study of BT adoption considering 14 factors, which confirms the efficiency and applicability of introduced approach. Based on the results, the healthcare BT alternative is most appropriate among the others. To evaluate its permanence, sensitivity analysis with regard to various ratings of decision strategic coefficient is presented under IVq-ROFS context. The strength of the developed approach is emphasized by comparing it with some of the former models under the context of IVq-ROFSs. The proposed extension of the COPRAS approach can be utilized to solve other complex group decision-making problems with uncertainties.

Dynamic programming principle for optimal control of uncertain random differential equations and its application to optimal portfolio selection

This study aimed to examine an uncertain stochastic optimal control problem premised on an uncertain stochastic process. The proposed approach is used to solve an optimal portfolio selection problem. This paper’s research is relevant because it outlines the procedure for solving optimal control problems in uncertain random environments. We implement Bellman’s principle of optimality method in dynamic programming to derive the principle of optimality. Then the resulting Hamilton-Jacobi-Bellman equation (the equation of optimality in uncertain stochastic optimal control) is used to solve a proposed portfolio selection problem. The results of this study show that the dynamic programming principle for optimal control of uncertain stochastic differential equations can be applied in optimal portfolio selection. Also, the study results indicate that the optimal fraction of investment is independent of wealth. The main conclusion of this study is that, in Itô-Liu financial markets, the dynamic programming principle for optimal control of uncertain stochastic differential equations can be applied in solving the optimal portfolio selection problem.

Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints Under Data Uncertainty

This article investigates robust optimality conditions and duality results for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (UNMPVC). Mathematical programming problems with vanishing constraints constitute a distinctive class of constrained optimization problems because of the presence of complementarity constraints. Moreover, uncertainties are inherent in various real-life problems. The aim of this article is to identify an optimal solution to an uncertain optimization problem with vanishing constraints that remains feasible in every possible future scenario. Stationary conditions are necessary conditions for optimality in mathematical programming problems with vanishing constraints. These conditions can be derived under various constraint qualifications. Employing the properties of convexificators, we introduce generalized standard Abadie constraint qualification (GS-ACQ) for the considered problem, UNMPVC. We introduce a generalized robust version of nonsmooth stationary conditions, namely a weakly stationary point, a Mordukhovich stationary point, and a strong stationary point (RS-stationary) for UNMPVC. By employing GS-ACQ, we establish the necessary conditions for a local weak Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we derive sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type and Mond–Weir-type robust dual models corresponding to the primal problem, UNMPVC.

Evidence combination with multi-granularity belief structure for pattern classification

Belief function (BF) theory provides a framework for effective modeling, quantifying uncertainty, and combining evidence, rendering it a potent tool for tackling uncertain decision-making problems. However, with the expansion of the frame of discernment, the increasing number of focal elements processed during the fusion procedure leads to a rapid increase in computational complexity, which limits the practical application of BF theory. To overcome this issue, a novel multi-granularity belief structure (MGBS) method was proposed in this study. The construction of MGBS reduced the number of focal elements and preserved crucial information in the basic belief assignment. This effectively reduced the computational complexity of fusion while ensuring the highest possible classification accuracy. We applied the proposed MGBS algorithm to a human activity recognition task and verified its effectiveness using the University of California, Irvine mHealth, PAMAP2, and Smartphone datasets.

Robust joint multiple resources allocation algorithm for cooperative underwater acoustic communication networks

AbstractIn this article, a joint relay selection, power control and time allocation problem is studied to maximize the energy efficiency for the cooperative underwater acoustic communication networks. The joint optimization problem is full of challenges due to the strong coupling of multiple resources and the uncertain characteristics of the underwater acoustic communication scenario. To address this issue, the worst‐case method is employed to transform an original uncertain problem into a deterministic problem. Furthermore, we propose the block coordinate descent‐based method to decouple the strongly coupling multi‐resource allocation problem into three relatively independent sub‐problems. The coupling of multiple resources is completely decoupled, thereby greatly reducing the solving difficulty. In addition, given that the sub‐problems with the fractional objective function are still non‐convex and hard to solve, the Dinkelbach‐based method is proposed to transform the fractional objective function into a subtractive form. At last, the relay selection sub‐problem is transformed into a integer programming problem, and the time allocation sub‐problem is transformed into a linear programming problem, whose optimal solutions can be obtained by some well‐established solution methods. The power allocation problem is transformed into a convex optimization problem, which can be solved by the Lagrangian dual method. Finally, in the proposed iteration structure, the three sub‐problems are alternatingly solved until convergence. Simulation results are presented to demonstrate the efficiency and robustness of the proposed algorithm.

A novel set-induced robust optimization model under correlated uncertainty: a comparative theoretical and computational study

In practical scenarios, optimization problems frequently involve uncertain parameters that exhibit correlated fluctuations. The widely adopted set-induced robust optimization approach is employed to address correlated uncertainty in environments with limited data. This approach focuses on deriving a deterministic reformulation of the original uncertain optimization problem, ensuring that the constructed solution remains feasible for all potential realizations of input parameters within a predefined uncertainty set. However, this approach often yields overly conservative solutions. In this study, an innovative uncertainty set is developed to mitigate the over-conservatism associated with the set-induced robust optimization approach under correlated uncertainty. Moreover, from the proposed description of data uncertainty, a robust linear reformulation of the original uncertain optimization problem is established to strike a balance between conservativeness and optimality. Computational studies exploring production planning optimization programs demonstrate the superior performance of the proposed robust model over other alternatives, considering various levels of correlation among uncertain parameters.

Probabilistic Multi-Robot Task Scheduling for the Antarctic Environments with Crevasses

This paper deals with the problem of multi-robot task scheduling in the Antarctic environments with crevasses. Because the crevasses may cause hazardous situations when robots are operated in the Antarctic environments, robot navigation should be planned to safely avoid the positions of crevasses. However, the positions of the crevasses may be inaccurately measured due to the lack of sensor performance, the asymmetry of sensor data, and the possibility of crevasses drifting irregularly as time passes. To overcome these uncertain and asymmetric problems, this paper proposes a probabilistic multi-robot task scheduling method based on the Nearest Neighbors Test (NNT) algorithm and the probabilistic modeling of the positions of crevasses. The proposed method was tested with a Google map of the Antarctic environments and showed a better performance than the Ant Colony Optimization (ACO) algorithm and the Genetic Algorithm (GA) in the context of total cost and computational time.

An extended goal programming approach with piecewise penalty functions for uncertain supplier-material selection problem in cardboard box manufacturing systems

In this study a real case multi-objective material and supplier selection problem in cardboard box production industries is studied. This problem for the first time optimizes the objective functions such as total wastage amounts remained from all raw sheets, total costs of the system including purchasing cost and transportation cost (including fixed and variable costs) of the raw sheets, and total overplus of produced cardboard boxes. To be closer to the real situations, as a novelty, the problem is formulated in belief-degree-based uncertain environment with normal distribution where this type of uncertainty applies the ideas of experts. A solution approach including two steps is proposed to solve the problem. In the first step, the proposed uncertain formulation is converted to a crisp form using a typical chance constrained programming scheme. In the second step, a new goal programming approach containing a piecewise penalty function is developed in order to solve the obtained multi-objective crisp formulation. In this approach, based on the ideas of experts, multiple goals are considered with different penalty values. A case study from cardboard box industries is considered to evaluate the proposed formulations and solution approach. According to the obtained results, the proposed solution approach is compared to similar approaches of the literature and its efficiency is studied.

Dual Stage Bionic Spatial Convolutional Restoration Model for Image De-noising and De-mosaicking

The first two important steps in the pipeline for processing picture signals are de-noising and de-mosaicking. The joint solution of the highly uncertain inverse problem of de-noising and de-mosaicking has garnered increased attention in research today. It is difficult to restore high-quality images from raw data in low light because of a variety of disturbances brought on by a low photon count and a complex image signal processing scheme. Even if some restoration and improvement techniques have been used, they might not work in harsh situations, including raw data imaging with brief exposure. Therefore, this research focuses on developing a de-mosaicking and de-noising model with effective end to end manner outcomes. Initially, the pre-processing is conducted using Gaussian filtering to eliminate artifacts from the input image, thereby enhancing the image quality. Then, the proposed method incorporates an Enhanced Spatial Convolutional Residual Net (EnConvResNet) for image de-mosaicking and an Adaptive U-net restoration model for image de-noising. An enhanced gazelle optimization (EnGa) algorithm is used to fine-tune the hyper-parameters of the model in order to maximize its performance and improve its generalization capacity. The proposed method accomplished peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) of 46.65 and 98.89, respectively.

Historical Bias in Mortgage Lending, Redlining, and Implications for the Uncertain Geographic Context Problem: A Study of Structural Housing Discrimination in Dallas and Boston.

According to the uncertain geographic context problem, a lack of temporal information can hinder measures of bias in mortgage lending. This study extends previous methods to: (1) measure the persistence of racial bias in mortgage lending for Black Americans by adding temporal trends and credit scores, and (2) evaluate the continuity of bias in discriminatory areas from 1990 to 2020. These additions create an indicator of persistent structural housing discrimination. We studied the Boston-Cambridge-Newton and Dallas-Fort Worth metropolitan statistical areas to examine distinct historical trajectories and urban development. We estimated the odds of mortgage denial for census tracts. Overall, all tracts in Boston-Cambridge-Newton (N = 1003) and Dallas-Fort Worth (N = 1312) displayed significant change, with greater odds of bias over time in Dallas-Fort Worth and lower odds in Boston-Cambridge-Newton. Historically redlined areas displayed the strongest persistence of bias. Results suggest that temporal data can identify persistence and improve sensitivity in measuring neighborhood bias. Understanding the temporality of residential exposure can increase research rigor and inform policy to reduce the health effects of racial bias.

Uncertain Multilevel Programming Based on Hurwicz Criterion with Application to Resource Allocation

A number of uncertain multilevel programming models have been proposed and applied to decentralized decision-making problems. It is assumed that the models of uncertain multilevel problems involve uncertain variables. In these models, the chance constraints are used as constraints, and the objective functions vary according to the requirements of decision-makers. The objective functions in this paper are based on the Hurwicz criterion, which combines optimistic value and pessimistic value to find a balance between optimism and pessimism. To deal with situations in which decision-makers have this type of risk appetite, the uncertain Hurwicz multilevel programming model is proposed based on uncertainty theory and the Hurwicz criterion. Finally, two numerical examples and a case study on resource allocation are given to demonstrate the potential uses of this study.

Intuitionistic fuzzy three-way decision method based on data envelopment analysis

As a powerful mathematical tool for tackling uncertain decision problems, three-way decision has garnered substantial attention since its inception. However, real-world decision problems are inherently complex, and decision-makers often exhibit characteristics of incomplete rationality. Traditional three-way decision models, which rely on functions or relationships, face challenges when confronted with multi-output problems. In response to this challenge, this paper introduces an intuitionistic fuzzy three-way decision model grounded in data envelopment analysis (DEA). Initially, we propose an input–output correlation degree that integrates hesitancy information and serves as a procedural indicator for benefit scores. Subsequently, the traditional DEA is extended to accommodate the intuitionistic fuzzy environment and utilized to construct a comprehensive loss function. Furthermore, a novel intuitionistic fuzzy three-way decision model is developed, incorporating three dimensions: optimism, neutrality, and pessimism, and corresponding decision rules and algorithms are provided. Finally, the effectiveness of the proposed model is rigorously validated through a series of experiments and comparative analyses. The model offers a pioneering approach to address uncertain multi-input–output decision problems, effectively integrating decision-maker’s risk preferences within an intuitionistic fuzzy environment.

Explaining Genetic Programming-Evolved Routing Policies for Uncertain Capacitated Arc Routing Problems

Genetic programming has been successfully used to evolve routing policies that can make real-time routing decisions for uncertain arc routing problems. Although the evolved routing policies are highly effective, they are typically very large and complex, and hard to be understood and trusted by real users. Existing studies have attempted to improve the interpretability by developing new genetic programming approaches to evolve both effective and interpretable (e.g., with smaller program size) routing policies. However, they still have limitations due to the trade-off between effectiveness and interpretability. To address this issue, we propose a new post-hoc explanation approach to explaining the effective but complex routing policies evolved by genetic programming. The new approach includes a local ranking explanation and a global explanation module. The local ranking explanation uses particle swarm optimisation to learn an interpretable linear model that accurately explains the local behaviour of the routing policy for each decision situation. Then, the global explanation module uses a clustering technique to summarise the local explanations into a global explanation. The experimental results and case studies on the benchmark datasets show that the proposed method can obtain accurate and understandable explanations of the routing policies evolved for uncertain arc routing problems. Our explanation approach is not restricted to uncertain arc routing, but has a great potential to be generalised to other optimisation and machine learning problems such as learning classifier systems and reinforcement learning.

Optimizing domestic energy management with a wild Mice colony-inspired algorithm: Enhancing efficiency and coordination in smart grids through dynamic distributed energy storage

Energy management (EM) is a critical strategy that spans the production and consumption of electricity, enhancing the stability of the electricity network. Smart grid technology significantly improves the electrical system's energy efficiency (EE), facilitating a transformation from a conventional power grid (PG) to a smart PG. This paper presents a key strategy for modeling the EE of the smart grid tailored to domestic demand, establishing smart coordination between domestic demand, energy production, and storage to reduce energy waste and costs. Our model integrates various energy sources, including renewable energy (RE), photovoltaic (PV) systems, wind power, and an energy storage system (ESS), interconnected with the PG. The model's structure ensures the coordinated flow of electricity in a residential house through an optimal control method (OCM). To develop a robust closed-loop control model, we employ Demand Response (DR) schemes within the Real-Time Electricity Pricing (RTEP) framework. We construct a dynamic model of the ESS to compute the System Performance Index (SPI), corresponding to energy costs. To enhance our model, we introduce a Dynamic Distributed Energy Storage Strategy (DDESS). Additionally, we introduce a novel optimization algorithm inspired by the behavioral patterns of wild mice, called the Wild Mice Colony (WMC). By analyzing the targeted and advantageous behaviors of wild mice in colonies, we propose that these behaviors can serve as a model for addressing complex, uncertain problems. This strategy is highly advantageous, capable of reducing total energy consumption (EC) from the main grid by over 100 % of the load demand, optimizing the energy system, and ensuring synchronization. The performance of DDESS optimizes energy flow (EF) during the repayment plan, leading to minimized EC costs from the PG.

Uncertain Chinese postman problem with budget constraint: a robust optimization approach

Uncertain Chinese postman problem with budget constraint: a robust optimization approach

Optimal operation of multi-carrier energy systems considering demand response: A hybrid scenario-based/IGDT uncertainty method

The optimal operation of multi-carrier energy systems (MCESs) has opened new horizons for energy network management and the satisfaction of consumers. In this paper, the optimization of the MCES's operation cost is considered by combining several energy hubs (EHs). To make optimal use of thermal and electrical demand response programs (TDRPs and EDRPs), the cost factors are extracted using a new sensitivity analysis (SA) method. Then, taking into account the optimized cost coefficients in EDRP and TDRP, the optimal operation of MCES is investigated in the presence of uncertain parameters. In this paper, a two-stage uncertainty method is used for solving the uncertain problem. First, the uncertainty of wind, photovoltaic (PV), and electrical and thermal loads is modeled with a scenario-based method, in the second step, the price uncertainty of generated electricity is added to the previous model using the information gap decision theory (IGDT). A hybrid scenario-based/IGDT uncertainty has been performed simultaneously at the GAMS platform. The results show the impact of each uncertainty parameter and system resilience due to the optimization done in the problem and the EDRP and TDRP programs. The results show about 135$ difference between the lowest and highest scenarios at a total operation cost.

A modified quasi-Newton method for uncertain multiobjective optimization problems under a finite uncertainty set

ABSTRACT In this article, a modified quasi-Newton method is developed for the robust counterpart (RC) of an uncertain multiobjective optimization problem (UMOP). Specifically, the RC of a UMOP is the minimum of an objective-wise worst-case (OWWC) type RC. To determine the descent direction for the RC, a subproblem using a common Hessian approximation is constructed. An inexact line search technique based on the Armijo technique is employed to find an appropriate step length. Furthermore, a modified version of the Davidon–Fletcher–Powell (DFP) update formula is developed for the RC. A modified quasi-Newton algorithm is built using descent direction step length, and DFP Hessian update formula. Furthermore, the convergence of the modified quasi-Newton algorithm is also discussed. Finally, the modified quasi-Newton algorithm is illustrated with a set of test problems and compared with the weighted sum method. Moreover, it is demonstrated that the algorithm is effective for both convex and non-convex problems.

Pre-disaster evacuation network design with uncertain demand and behavioural choices: A bi-criteria generalized cost perspective

Pre-disaster evacuation network design is critical to improving evacuation efficiency and reducing the loss of life and property caused by disasters. However, evacuation network design is complicated by the uncertainty of pre-disaster evacuation demand and the heterogeneity of evacuees’ route choices when faced with a disaster scenario. Therefore, how to design efficient evacuation networks considering these uncertainties has become an important research topic. In this paper, we study the pre-disaster flood evacuation network design problem, define a bi-criteria generalized cost metric based on Evacuation Travel Time (ETT) and Evacuation Network Congestion Degree (ENCD), and develop a model that considers uncertain demand and evacuation behavioural choices to minimize the generalized cost in the evacuation network. For the uncertain behavioural choice, we propose an Expanded Stochastic User Equilibrium (ESUE) model based on the Random Regret Minimization (RRM) principle and Boundedly Rational User Equilibrium (BRUE) conditions to describe it. For the uncertain demand, we design a Distributionally Robust Optimization (DRO) method based on Mean Absolute Deviation (MAD) to deal with this uncertain model. This paper designs an Improved Method of Successive Averages Combined with Genetic Algorithm (IMSA-GA) to solve the model and uses the Nguyen-Dupuis test network to verify the applicability and feasibility of the model and algorithm. In addition, we also conduct an evacuation network design in the Hawkesbury-Nepean region of Australia. The larger the threshold value based on the regret utility ratio, the smaller the generalized cost value, which indicates the behavioural choices of the evacuees have an impact on the evacuation network design, and the generalized cost decreases by 6.12% when the threshold value is increased from 0.1 to 0.9. In addition, the generalized cost value obtained by IMSA-GA will be 0.0025 lower than Improved Method of Successive Averages Combined with Simulated Annealing (IMSA-SA) and 0.0005 lower than Improved Method of Successive Averages Combined with Taboo Search (IMSA-TS). The theoretical contribution of this paper is to find an approach to the uncertain evacuation network design problem, especially to improve the practicality of the model by fully considering evacuation behaviour. The practical contribution is that our findings can provide insights for government authorities to design efficient and reliable evacuation networks that balance evacuation travel time and evacuation network congestion. In the future, if evacuation behavioural choices can be analysed based on actual surveys, the estimation of behavioural parameters based on survey data will be more instructive for the evacuation process.