Uncertainty Characteristics Research Articles

Methodology for Economic Analysis of Highly Uncertain Innovative Projects of Improbability Type

Modern conditions for real investment are generally associated with increasing uncertainty, which is even more relevant when evaluating innovative projects. Current innovation analysis methods using a linear model are outdated. At the same time, an open interactive model of the innovation process, formed due to digitalization, allows to connect to innovations at almost any stage of their life cycle. The aim of the study is to form a methodology for the economic analysis of innovative projects implemented in the context of an open innovation model. To achieve the goal, the study defines approaches to innovation projects differentiation. The approach to the analysis methods selection is based on the decision matrix. The developed decision matrix allows to determine the location of each project as its element and to select analysis methods, considering the project’s uncertainty characteristics. The logic of the analysis methods transformation under the influence of a changing uncertainty level determines the combination of the fuzzy-set approach and the concept of real options. The implementation of the project analysis algorithm leads to the choice of an appropriate method for evaluating effectiveness and ensures that the flexible risk response concept under conditions of improbable uncertainty is taken into account when implementing the option model.

Multi time scale operation optimization of EHHGS considering equipment uncertainty and response characteristics

The optimal operation of electric hydrogen coupling systems has gradually become a key issue because of the considerable attention being paid to hydrogen energy. Therefore, this study investigates the multi-time scale operation optimization of a rural electricity hydrogen natural gas coupling system（EHHGS）considering equipment uncertainty and response characteristics. First, the framework of an EHHGS in rural areas is designed, and the equipment in the framework is modeled finely. Furthermore, the uncertainty and response characteristics of each link in the EHHGS are analyzed from the source, coupling, and load ends. Thereafter, the multi-time scale operation optimization model of the EHHGS is constructed based on the time resolution optimization model of operation optimization. Finally, a numerical example is analyzed to verify the effectiveness of the uncertainty model of each link and the multi-time scale optimization model.

Two-Stage stochastic optimization for operating a Renewable-Based Microgrid

• A conventional MILP algorithm does not consider the uncertainty in operating a renewable-based Microgrid. • The two-Stage stochastic optimization algorithm takes into consideration the potential future PV profile. • The proposed method improves the Microgrid reliability by a 19.4% decrease in the Energy not supplied. • The proposed method decreases the operation cost by 18.8%. Carbon emissions are increasing as a result of urbanization and population growth all over the world. Scientists agree that these emissions are one of the main causes of climate change and global warming. The power industry is shifting to renewable energy sources (RES) such as solar power (PV) and employing different Energy Storage Systems (ESS) to enable a clean energy future and compensate for the scarcity of fossil fuel. However, the intermittent behaviour of renewable resources causes some obstacles such as power fluctuation, committing extra reserve units, and load shedding. Microgrid (MG) technology is introduced as a promising solution for integrating different RES and loads into the grid. Operating the MG in islanded mode with a limited ESS capacity requires a sophisticated scheduling method. Previous studies on MG addressed the operation issue, neglecting the supply–demand uncertainty or adopting the worst-case scenario. Uncertainty is an inherent characteristic in power systems; on the other hand, considering the worst-case scenario may unnecessarily increase the operation and planning costs. To address the uncertainty and fluctuant characteristics of RES-based MG, this paper proposes a two-stage stochastic optimization integrated with a novel ANN-based prediction model. A new model for PV power prediction is proposed by which the predicted data is in a probability density function (PDF) form. A stochastic optimization (SO) method is proposed to minimize the operation cost and load shedding during the islanding mode. In the proposed SO, the optimal scheduling decision is made in the current moment taking into account the probability of potential supply, load, and ESS capacities in the near future. For this purpose, an ANN-based prediction model is developed to represent the PV output uncertainty in the SO problem. The proposed prediction model proves efficient in the prediction with nRMSE of 9.7% and nMAE of 9.1%. The proposed method is applied to a real Microgrid designed by the Natural Energy Laboratory of Hawaii Authority (NELHA) and compared to a conventional optimization method. The proposed scheduling method reduces both the average Energy Not Supplied (ENS) and operation costs by 19.4% and 18.8%, respectively, with no additional investment cost. A sensitivity study is also conducted to assess the performance of the proposed method in terms of ENS, cost, and simulation time.

A quantitative reliability assessment and risk quantification method for microgrids considering supply and demand uncertainties

Microgrids have received great interest in achieving high renewable energy penetration. However, intermittent renewable generation may cause reliability problem (i.e., power inadequacy), especially for islanded microgrids. A comprehensive quantitative reliability assessment of microgrids considering uncertainties is essential. Current uncertainty-based reliability assessment approaches usually consider the uncertainties on the supply side only or additionally consider the uncertainties on the demand side using a general distribution without considering the uncertainty characteristics of different demands. This may lead to unreliable assessment results. Besides, existing reliability performance indexes cannot measure the probability/risk of power inadequacy under uncertainties. In this study, a novel uncertainty-based reliability assessment approach is therefore developed for microgrids considering uncertainties at both supply and demand sides. A new reliability index is proposed and a risk quantification method is developed to measure the risk/probability of power inadequacy under uncertainties. The uncertainties at both supply and demand sides are detailedly quantified using a bottom-up approach. The proposed reliability assessment and risk quantification method are tested on an islanded hotel microgrid in Hong Kong. The results show that the proposed reliability assessment approach can provide more robust reliability assessment results while the conventional approach has a probability of 8% to underestimate the maximum outage power. The proposed risk quantification method can help to provide more comprehensive reliability assessment results under uncertainties. The risk quantification results indicate that the highest monthly power inadequacy risk of the hotel microgrid appears in August (i.e., 5.8%), while the highest hourly risk appears at 9:00 p.m. (i.e., 4.8%).

Psychosocial support to medical teams in SAMUR-Protection Civile during COVID-19

The COVID-19 pandemic has had an exceptional impact on the health system. The lack of information and resources during the first stage of the outbreak COVID-19 has also meant a change in the way we work and in the way we relate to our relatives, colleagues and, of course, our patients. This traumatic situation, due to its characteristics of total uncertainty, novelty, frequency, and high intensity, made it necessary to develop a new approach to our work, a new psychological approach to the pandemic situation that leads to acute stress, insecurity, unknown consequences, uncertainty about its duration and a desolate future.During the first wave, it was necessary to respond to the new situation. In a first phase, an intervention protocol was created for front-line pre-hospital emergency professionals and a COVID-19 psychological unit was set up in a pandemic hospital in Madrid.In a second phase, emergency actions, their conditioning and possible change due to confinement are analysed; the emotional state of front-line intervention personnel is assessed, comparing the pre- and post-first wave period, and burnout syndrome is studied in the SAMUR-Civil Protection volunteer corps.

Experiment, simulation, optimization design, and damage detection of composite shell of hydrogen storage vessel-A review

The composite shell of composite high pressure hydrogen storage vessel (CHPHSV) is the main structure in bearing inner pressure. Its failure will lead to leakage or burst of CHPHSV, which will cause serious safety problem and economic losses. So the security of CHPHSV has always been a key and difficult problem in academia and industry, which restricts the large-scale application of hydrogen. In this paper, the failures of composite shell of type III, type IV, and type V vessels are reviewed in experiment study, simulation method, optimization design, and damage detection, focusing on the burst modes (safe or unsafe), the influence of hydrogen-thermo-stress field, and the epistemic uncertainty. Firstly, the burst modes, failure behavior, test method, and influencing factors are summarized in the experiment study, and experiment for type V composite pressure vessel is discussed. Secondly, the simulation method is reviewed in the aspect of first ply failure (FPF) analysis and last ply failure (LPF) analysis. The damage evolution of safe burst mode and unsafe burst mode is summarized. Besides, the influence of hydrogen-thermo-stress field and the uncertainty characteristic are also reviewed. Moreover, simulations of micro-crack and permeability for type V composite pressure vessels are summarized. Then, the optimization design methods based on deterministic parameters and uncertain parameters are reviewed. Finally, the damage detection methods of the composite shell of CHPHSV are summarized. The experiment, numerical simulation, and optimization are important for design of the composite vessel, and the damage detection can significantly reduce the degree of uncertainty and maintenance safety. In the future research, precise model considering multiple damage modes, hydrogen-thermo-stress field effect should be established for simulation of safe and unsafe burst mode. Uncertain quantization should be studied for burst pressure with combination of stochastic uncertainty and epistemic uncertainty. Besides, the robust design method based on the reliability of CHPHSV considering the epistemic uncertainty of design parameters should be established for a larger safety margin.

Axiomatic framework of entropy measure for type-2 fuzzy sets with new representation method and its application to product ranking through online reviews

Type-2 fuzzy sets (T2FSs) have the advantage of representing higher-order uncertainty, they have demonstrated superior performance in several applications. In order to fully measure the uncertainty for T2FSs. In this study, several distribution characteristics of uncertainties within T2FSs are analyzed through type-1 fuzzy sets (T1FSs), and the axiomatic framework of fuzzy entropy and overall entropy of T2FSs is established as well. First, a new representation method for T2FSs is given. On this basis, the axiomatic definitions of fuzzy entropy for T1FSs and T2FSs are constructed by analyzing the distribution characteristics of fuzziness, and the construction theorems and basic properties of fuzzy entropy are studied. Further, the overall entropy of T2FSs is given, on this basis, a novel type-2 fuzzy entropy-based decision-making method is proposed, and applied to the selection of cold medicine through online reviews on AliHealth.cn. Finally, the feasibility and effectiveness of the developed definitions and methods are demonstrated by three comparative analyses.

Coordinated Planning of HVDCs and Power-to-Hydrogen Supply Chains for Interregional Renewable Energy Utilization

With the urgent requirement of the utilization of renewable energy (RE) for the decarbonization of energy systems, power transmission via high-voltage direct current (HVDC) lines shows limits in the face of fluctuations of RE generation. This paper addresses the coordinated planning of HVDCs and power-to-hydrogen supply chains (P2HSCs) for RE utilization. First, the lumped cluster model of the large-scale power-to-hydrogen is established based on the derivation of the maximum production points. On this basis, P2HSC is modeled as a constrained power load. Then, a multi-objective multi-stage stochastic planning model of HVDCs and P2HSCs is proposed to fully consider RE fluctuation and uncertainty characteristics. Furthermore, a decomposition algorithm based on the dynamic programming method is designed to solve this problem. Finally, the proposed model and algorithm are applied in real Inner Mongolia-Shandong case studies. The effectiveness and robustness of the proposed model are quantitatively verified. Furthermore, the investment interplay of HVDCs and P2HSCs on the planning timeline and the operational interplay of the two sectors as complementary power loads are verified to create the maximum social benefit in renewable energy systems.

Рекогносцировка профессиональных ресурсов и личностного потенциала педагога в эпоху социальной турбулентности и трансформации образования

Introduction. The article defines the teacher's mission in the era of social turbulence and high uncertainty characteristic of the transition of Russian society to the post-industrial stage of development. The authors focus on training a teacher for the future, determined by social conditions and directions of development of the Russian education system. Relevance. The available scientific ideas about the professional resources and personal potential of the teacher, ways to support his development in modern conditions cannot be recognized as sufficient. This determines the purpose of the study: the definition of professional resources in the context of the development of the personal potential of the teacher, the most demanded in the era of social turbulence and transformation of education. Material and research methods: the work uses theoretical methods (analysis of philosophical, psychological and pedagogical literature), modeling, generalization of the experience of establishing additional pedagogical education; empirical methods (psychological diagnosis of professional resources and personal potential of teachers, readiness of teachers for professional activities in conditions of social turbulence and transformation of education). Study results and discussion. The authors propose a model of professional resources and personal potential of the teacher, indicate diagnostic methods for their research. A description of the possibility of additional pedagogical education is presented as a condition for the development of professional resources and the personal potential of the teacher. It was concluded that it is necessary to improve the advanced training and retraining of teachers in the context of modern requirements for the teacher's activities. The experience of the Ulyanovsk State Pedagogical University named after I. N. Ulyanov in this direction is described. Conclusions. The results of the study can be used in organizing comprehensive support for the development of professional resources and personal potential of teachers in the conditions of further education, managing a teacher's career, developing advanced training and professional retraining programs.

The Comparison between CAPM and FF3 Model: Evidence from America

As the most developed financial market in the world, liquidity in the market remains in a very strong position despite the recent rise in long-end US bond rates. This paper compares the usefulness and characteristics of Capital Asset Pricing Model and Three Factor Model by using the regression model to carry out bigdata analysis from the US market between 2021 and 2022. Based on the analysis, Three Factor Model is better suited to today’s market with the characteristic of variability and uncertainty. However, the concerns raised by previous studies regarding the momentum effect still remain unresolved. In order to enhance the reliability and precision, data spanning a longer period of time should be selected. This paper can be of great help to investors who need to make financial decisions, as it compares the beta of each stock with the beta calculated from two models to find out which model gives a more accurate forecast. Overall, these results shed light on beta evaluation model selection for the state-of-art approaches.

Day-Ahead Optimal Scheduling of Integrated Energy System Based on Type-II Fuzzy Interval Chance-Constrained Programming

Renewable energy sources (RES) generation has huge environmental and social benefits, as a clean energy source with great potential. However, the difference in the uncertainty characteristics of RES and electric–thermal loads poses a significant challenge to the optimal schedule of an integrated energy system (IES). Therefore, for the different characteristics of the multiple uncertainties of IES, this paper proposes a type-II fuzzy interval chance-constrained programming (T2FICCP)-based optimization model to solve the above problem. In this model, type-II fuzzy sets are used to describe the uncertainty of RES in an IES, and interval numbers are used to describe the load uncertainty, thus constructing a T2FICCP-based IES day-ahead economic scheduling model. The model was resolved with a hybrid algorithm based on interval linear programming and T2FICCP. The simulations are conducted for a total of 20 randomly selected days to obtain the advance operation plan of each unit and the operation cost of the system. The research results show that the T2FICCP optimization model has less dependence on RES output power and load forecasting error, so can effectively improve the economy of IES, while ensuring the safe and stable operation of the system.

What we need to know about uncertainty in illness among people with primary malignant brain tumours: A mixed-methods systematic review.

To identify the characteristics of uncertainty in illness (UI) among people with primary malignant brain tumours (PMBT). High recurrence rates and complex symptoms cause uncertainty in people with PMBT. Given the characteristics of PMBT, reviewing UI among people with PMBT will benefit future research and clinical intervention development. A mixed-methods systematic review. We performed a mixed-methods systematic review (PubMed, CINAHL, Embase, PsycINFO, Scopus and Cochrane Library), including studies on UI among people with PMBT, searched from the databases' inception to the search date. The initial search was conducted in July 2021, with an additional search in March 2022. The major search terms were PMBT and UI, and no limitations were placed on the study design. The Cochrane tool was used to evaluate the risk of bias in randomised controlled trials, and JBI checklists were used to evaluate quasi-experimental studies, survey methodology studies and a case study. This review was reported using the PRISMA 2020 checklist. Both quantitative and qualitative research data were extracted, analysed and then integrated in three stages of a mixed-methods systematic review. Eleven studies were included. Due to physical, psychological and social risk factors, the UI progression of people with PMBT was complex and ambiguous, although they adapted to the PMBT diagnosis and treatment process. Subsequently, we proposed a model of UI among people with PMBT. UI has multidimensional characteristics, and healthcare providers need to consider these aspects for people with PMBT. The proposed model provides directions for nursing practice and future research. Nurses caring for people with PMBT should comprehend their UI and intervene accordingly. This review incorporated data including people with PMBT in hospitals and communities. This analysis contributes to the clinical-to-community nursing transition process for people with PMBT.

재생에너지 수용률 확보 조건에서 연 단위의 BESS 경제적 운영전략

The increase in Renewable Energy causes a problem of stability of the power system due to its intermittent characteristics. Renewable Energy depends on natural conditions such as wind speed and solar irradiation, which has characteristics of uncertainty and variability. An ESS(Energy Storage System) is being used as one of the flexible resources to cope with these variables. This paper proposed the economical BESS(Battery Energy Storage System) operation strategy under the precondition of accommodating Renewable Energy maximally, considering both BESS and Renewable Energy. The BESS operation strategy was established from the viewpoint of maximizing efficiency of BESS in consideration of battery degradation conditions and initial SoC(State Of Charge). The operation strategy establishment procedure was conducted in the order of analyzing the actual power demand data, grouping the load characteristics, calculating amount of the Renewable Energy, and deriving BESS charge/discharge scheduling. After removing outliers from the resulting values derived through a series of processes, we finally propose a continuous and consistent annual operation strategy for BESS.

Exploring time evolution characteristics of the collaborative mode in emergency information release of public health emergencies: A network analysis of response to COVID-19 from the central government of China.

Emergency information release during public health emergencies is a governance measure to slow down the spread of the epidemic and guide the public in scientific protection. Because of the uncertainty and life-cycle characteristics of public health emergencies, emergency information release represents the process of time dynamics. At present, it is an inevitable trend to establish a collaborative mechanism for emergency information release of public health emergencies to improve the release efficiency and respond to public demand. To determine time evolution characteristics of organizational collaboration in emergency information release, this study took the response to COVID-19 from the central government of China as an example and conducted research based on social network analysis. Based on information from COVID-19-related press conferences held by China's central government, the emergency information release collaborative networks (EIRCNs), and Emergency Organizations-Emergency Information Release Matters (EOs-EIRMs) 2-mode network were constructed. With the time evolution, the tightness, convergence, stability, and connectivity of EIRCNs in public health emergencies presented the process of lowering and then raising. At different stages, the core emergency organization (EO) nodes in EIRCNs continued to maintain a certain degree of activity. Their dynamic processes showed the characteristics of diversification rather than homogeneity. The time evolution of emergency information release matters (EIRMs) reflected the dynamic adjustment of the government's prevention and control measures and responded to the diversification of the public's understanding and protection needs during different stages of the COVID-19 pandemic. The study further examined the driving factors and implementation mechanism of the time evolution characteristics of the collaborative mode of emergency information release. The implementation of EIRMs at different stages had different resource requirements, which were usually achieved by introducing new EOs (Adding resource increment) or increasing the collaborative frequencies among EOs (Activating resource stock). In addition, further research prospects and feasibility interpretation were proposed.

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional–derivative (PD) type FC with Takagi–Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.

Structural rule-based modeling with granular computing

In order to analyze the dynamic behaviors of complex systems in the era of big data, a new rule-based modeling approach is proposed in this paper. This approach considers structural information mining and granular computing (GrC) in rule-based modeling, it also aims at utilizing granular fuzzy intervals to reflect systems’ behaviors on uncertainty. Major contributions can be summarized as three points. First, using DBSCAN’s advantages in clustering arbitrarily-shaped data, DBSCAN is applied to extract structural information as the basis of rules in complex systems. Second, GrC is leveraged for rule formation and effective rule-based modeling, e.g. granules constructed in input space to refine structural DBSCAN clusters, granular intervals constructed in output space with the principle of justifiable granulating to reflect system dynamic behaviors. Third, experimental analysis based on three different design scenarios was studied on both synthetic data and publicly available datasets. Through comparative discussion, the proposed approach can outperform the conventional rule-based models, specifically having an improvement ratio of 0.18% to 1.48% on the proposed comprehensive indicator. Therefore, it can be concluded that the proposed approach has the feasibility and advantages of reflecting the structural and uncertainty characteristics of system dynamic analysis.

A Novel Hybrid Method to Predict PM2.5 Concentration Based on the SWT-QPSO-LSTM Hybrid Model

PM2.5 concentration is an important indicator to measure air quality. Its value is affected by meteorological factors and air pollutants, so it has the characteristics of nonlinearity, irregularity, and uncertainty. To accurately predict PM2.5 concentration, this paper proposes a hybrid prediction system based on the Synchrosqueezing Wavelet Transform (SWT) method, Quantum Particle Swarm Optimization (QPSO) algorithm, and Long Short-Term Memory (LSTM) model. First, the original data are denoised by the SWT method and taken as the input of the prediction model. Then, the main parameters of the LSTM model are optimized by global search based on the QPSO algorithm, which solves the problems of slow convergence and local extremum of traditional parameter training algorithms. Finally, the PM2.5 daily concentration data of Chengdu, Shijiazhuang, Shenyang, and Wuhan are predicted by the proposed SWT-QPSO-LSTM model, and the prediction results are compared with those of single prediction models and hybrid prediction models. The experimental results show that the proposed model achieves higher prediction precision and lower prediction error than other models.

A Simple Statistical Model of the Uncertainty Distribution for Daily Gridded Precipitation Multi-Platform Satellite Products

Multi-platform satellite-based precipitation gridded estimates are becoming widely available in support of climate monitoring and climate science. The characterization of the performances of these emerging Level-4 products is an active field of research. This study introduced a simple Gaussian mixture model (GMM) to characterize the distribution of uncertainty in these satellite products. The following three types of uncertainty were analyzed: constellation changes-induced uncertainties, sampling uncertainties and comparison with rain-gauges. The GMM was systematically compared with a single Gaussian approach and shown to perform well for the variety of uncertainties under consideration regardless of the precipitation levels. Additionally, GMM has also been demonstrated to be effective in evaluating the impact of Level-2 PMW rain estimates’ detection threshold definition on the constellation changes-induced uncertainty characteristics at Level-4. This simple additive perspective opens future avenues for better understanding error propagation from Level-2 to Level-4.

Understanding Errors in Cloud Liquid Water Path Retrievals Derived from CloudSat Path-Integrated Attenuation

Abstract An algorithm that derives the nonprecipitating cloud liquid water path Wcld from CloudSat using a surface reference technique (SRT) is presented. The uncertainty characteristics of the SRT are evaluated. It is demonstrated that an accurate analytical formulation for the pixel-scale precision can be derived. The average precision of the SRT is estimated to be 34 g m−2 at the individual pixel scale; however, precision systematically decreases from around 30 to 40 g m−2 as cloud fraction varies from 0% to 100%. The retrievals of clear-sky Wcld have a mean bias of 0.9 g m−2. Output from a large-eddy simulation coupled to a radar simulator shows that an additional bias of −8% may result from nonuniformity within the footprint of cloudy pixels. The retrieval yield for the SRT, measured relative to all warm clouds over ocean between 60°N and 60°S latitude is 43%. The SRT Wcld is compared with one estimate of Wcld from the Moderate Resolution Imaging Spectroradiometer (MODIS) using an adiabatic cloud profile and an effective radius derived from 3.7-μm reflectance. A strong correlation between the mean MODIS Wcld and SRT Wcld is found across diverse cloud regimes, but with biases in the mean Wcld that are cloud-regime dependent. Overall, the mean bias of the SRT relative to MODIS is −13.1 g m−2. Systematic underestimates of Wcld by the SRT resulting from nonuniform beamfilling cannot be ruled out as an explanation for the retrieval bias.

Robust Multiobjective Optimization for Vehicle Routing Problem With Time Windows.

In this article, we focus on the vehicle routing problem (VRP) with time windows under uncertainty. To capture the uncertainty characteristics in a real-life scenario, we design a new form of disturbance on travel time and construct robust multiobjective VRP with the time window, where the perturbation range of travel time is determined by the maximum disturbance degree. Two conflicting objectives include: 1)the minimization of both the total distance and: 2)the number of vehicles. A robust multiobjective particle swarms optimization approach is developed by incorporating an advanced encoding and decoding scheme, a robustness measurement metric, as well as the local search strategy. First, through particle flying in the decision space, the problem space characteristic under deterministic environment is fully exploited to provide guidance for robust optimization. Then, a designed metric is adopted to measure the robustness of solutions and help to search for the robust optimal solutions during the particle flying process. In addition to the updating process of particle, two local search strategies, problem-based local search and route-based local search, are developed for further improving the performance of solutions. For comparison, we develop several robust optimization problems by adding disturbances on selected benchmark problems. The experimental results validate our proposed algorithm has a distinguished ability to generate enough robust solutions and ensure the optimality of these solutions.