An integrated bi-level optimization model for air quality management of Beijing's energy system under uncertainty

A bi-level multi-objective programming model for water resources management under compound uncertainties in Dongjiang River Basin, Greater Bay Area of China

To facilitate regional water resources allocation, an integrated bi-level multi-objective programming (IBMP) model with dual random fuzzy variables was developed in this research The proposed model was derived through incorporating dual random fuzzy variables, multi-objective programming, and interval parameter programming within a bi-level optimization framework. This approach improved upon the previous bi-level programming methods and had two advantages. Firstly, it was capable of reflecting tradeoffs among multiple conflict preferences for water related bi-level hierarchical decision-making processes. Secondly, random fuzzy variables were used to tackle the dual uncertainties in both sides of the constraints, which were characterize as probability density functions and discrete intervals. Then, a real-world water resources planning problem was employed for illustrating feasibility of the application of IBMP model in Dongjiang river watershed of south China. Results reflected the alternative decisions for water allocation schemes under a set of probability levels and fuzzy α - cut levels, which can support in-depth analysis of tradeoffs among multiple levels and objective values. Moreover, modeling comparison analysis was undertaken to illustrate the performances of the proposed model.

A dual-randomness bi-level interval multi-objective programming model for regional water resources management

In this research, a dual-randomness bi-level interval multi-objective programming (DR-BIMP) model was developed for supporting water resources management among multiple water sectors under complexities and uncertainties. Techniques of bi-level multi-objective programming (BMOP), double-sided stochastic chance-constrained programming (DSCCP), and interval parameter programming (IPP) were incorporated into an integrated modeling framework to achieve comprehensive consideration of the complexities and uncertainties of water resources management systems. The DR-BIMP model can not only effectively deal with the interactive effects between multiple decision-makers in complex water management systems through the bi-level hierarchical strategies, but also can characterize the multiple uncertainties information expressed as interval format and probability density functions. It could thus improve upon the existing bi-level multi-objective programming through addressing discrete interval parameters and dual-randomness problems in optimization processes simultaneously. Then, the developed model was applied to a real-world case to optimally allocate water resources among three different water sectors in five sub-regions in the Dongjiang River basin, south China. The results of the model include determining values, interval values, and stochastic distribution information, which can assist bi-level decision-makers to plan future resources effectively to some extent. After comparing the variations of results, it is found that an increasing probability level can lead to higher system benefits, which is increased from [20,786.00, 26,425.92] × 10⁸ CNY to [22,290.84, 27,492.57] × 10⁸ CNY, while the Gini value is reduced from [0.365, 0.446] to [0.345, 0.405]. A set of increased probability levels gives rise to the lower-level objectives. Furthermore, the advantages of the DR-BIMP model were highlighted by comparing with the other models originated from the developed model. The comparison results indicated that the DR-BIMP model was a valuable tool for generating a range of decision alternatives and thus assists the bi-level decision-makers to identify the desired water resources allocation schemes under multiple scenarios.

A bi-level multiobjective stochastic approach for supporting environment-friendly agricultural planting strategy formulation

In this study, integration of analytic hierarchy process method and entropy method (AHP-EW) for quantifying the knowledge and experience accumulated by regional managers as well as the socioeconomic situation, the partial least squares regression (PLS) for reflecting the relationship between irrigation water use efficiency and agronomic inputs, and the ecosystem service value for measuring environmental impacts of changing crop planting area were considered in one framework simultaneously. With help of these efforts, a bi-level multiobjective stochastic approach to improve irrigation water use efficiency and decrease the pollution production of agronomic measures in the process of agricultural production. The proposed framework integrate bi-level multiobjective programming and stochastic expectation programming to not only make tradeoffs among multiple concerns from two-level decision makers, but also deal with the randomness of runoff. Then, the proposed approach was applied to a real-world case in the middle reaches of the Heihe River basin, northwest China. Results show that the developed approach can improve irrigation water use efficiency, reduce CO₂ emission, expand ecosystem service values, and provide more profitable and environment-friendly agricultural planting strategies to decision makers, which can further contribute to the sustainable development of agriculture. Furthermore, by comparing the bi-level multiobjective stochastic programming (BMSP) model with the other six models originated from developed model, it can be found that 1) the single objective model can obtain the best value of that objective, but cannot readily consider other important aspects; 2) the multiobjective models can make tradeoffs among multiple objectives; 3) the BMSP model can reflect the leader-follower relationship in the optimization process. The approach is applicable for arid and semiarid regions that face similar problems to determine agricultural planting strategies.

A simulation-based bi-level multi-objective programming model for watershed water quality management under interval and stochastic uncertainties

A simulation-based interval stochastic bi-level multi-objective programming (SISBLMOP) model was proposed in this research, through integrating the global nutrient export from watersheds model, interval parameter programming and stochastic chance-constrained programming into a general bi-level multi-objective programming framework. The SISBLMOP model can handle multiple uncertainties expressed as discrete intervals and probability density functions in both the simulation and optimization processes. System complexities, including the hierarchy structure of upper- and lower-level decision makers, can also be addressed in the model. The proposed model is applied to a real-world case study of the Xinfengjiang Reservoir Watershed in South China to identify the satisfactory implementation levels of multiple best management practices (BMPs). The model results show that multiple BMP schemes for water quality management can be obtained under different upper- and lower-level decision-making and risk-violation scenarios, reflecting the cooperation and gaming results of the two-level decision makers. Consequently, the corresponding BMP implementation costs are acceptable to both the upper- and lower-level decision makers. The model is widely applicable and can be effectively used for water quality management under multiple uncertainties and complexities.

An Optimization-Evaluation Agricultural Water Planning Approach Based on Interval Linear Fractional Bi-Level Programming and IAHP-TOPSIS

In this study, an interval linear fractional bi-level programming (ILFBP) model was developed for managing irrigation-water resources under uncertainty. The ILFBP can fully address system fairness, uncertainties, and the leader–follower relationship of decision makers in the optimization process, which can better reflect the complexity of real decision-making process and help formulate reasonable water policies. An interactive fuzzy coordination algorithm based on satisfaction degree was introduced to solve the ILFBP model. In order to evaluate the applicability of optimization schemes, the interval analytic hierarchy process (IAHP) and the interval technique for order preference by similarity to an ideal solution (TOPSIS) method were integrated as IAHP-TOPSIS. To verify its validity, the developed optimization-evaluation framework was applied to an irrigation water management case study in the middle reaches of the Shiyang River Basin, located in the northwest China. The ILFBP model results show that the total water allocation is [6.73, 7.37] × 108 m3, saving nearly 0.9 × 108 m3 more than the current situation. The benefit per unit of water is [2.38, 2.95] yuan/m3, nearly 0.4 yuan/m3 more than the status quo, and the Gini coefficient is within a reasonable range of [0.35, 0.38]. The ILFBP model can well balance economic benefits and system fairness. Through the evaluation bases on IAHP-TOPSIS, the results of ILFBP show better water allocation effects and applicability than the other two models in this study area. Furthermore, due to various characteristics such as geographical location, population and area, there are three irrigation districts, Xiying, Donghe, and Qinghe, showing higher importance than others when considering regional water allocation. These findings can provide useful information for limited water resource managers and help decision makers determine effective alternatives of water resource planning under uncertainty.

Microstructure and Corrosion Resistance of PEO Coatings Formed on KBM10 Mg Alloy Pretreated with Nd(NO₃)₃

Plasma electrolytic oxidation (PEO) technique is one of the important methods used in the surface modification of magnesium alloys. In this paper, the ceramic coatings on pretreated KBM10 magnesium alloy with Nd(NO₃)₃ solution were prepared by PEO. The effects of Nd(NO₃)₃ solution concentration on the microstructure and corrosion resistance of PEO coatings on magnesium alloys were investigated by means of scanning electron microscopy (SEM), X-ray diffractometer (XRD), and electrochemical workstation. It was found that the surface of the coatings was porous after PEO, and element Nd could be deposited on the surface of the coatings by pretreatment and existed in the PEO coatings. The coating formed at Nd(NO₃)₃ solution concentration of 0.06 mol/L exhibited the best corrosion resistance among all the as-prepared coatings.