Multistage scenario-based interval-stochastic programming for planning water resources allocation

In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit

Shades of Grey: A Critical Review of Grey-Number Optimization

A grey number is an uncertain number with fixed lower and upper bounds but unknown distribution. Grey numbers find use in optimization to systematically and proactively incorporate uncertainties expressed as intervals plus communicate resulting stable, feasible ranges for the objective function and decision variables. This article critically reviews their use in linear and stochastic programs with recourse. It summarizes grey model formulation and solution algorithms. It advances multiple counter-examples that yield risk-prone grey solutions that perform worse than a worst-case analysis and do not span the stable feasible range of the decision space. The article suggests reasons for the poor performance and identifies conditions for which it typically occurs. It also identifies a fundamental shortcoming of grey stochastic programming with recourse and suggests new solution algorithms that give more risk-adverse solutions. The review also helps clarify the important advantages, disadvantages, and distinctions between risk-prone and risk-adverse grey-programming and best/worst case analysis

An Inexact System Programming for Agricultural Land Utilization Based on Control of Non-point Source Pollution in Wuchuan Catchment

以福建省九龙江西溪五川流域为例,借助区间数系统优化模型和AGNPS模拟模型,对现有农业生产土地利用方式和管理措施性土地利用方式进行了系统分析,探讨通过土地利用的调整,实现低成本控制农业面源污染的最佳途径。结果表明,五川流域目前的土地利用模式不能满足面源污染控制和经济效益最大化的共同要求,其农业生产习惯和面源污染控制措施也需要适当调整。总体上现有土地利用的经济收益低于最佳土地利用优化的下限收益,环境效益一般的坡草地、香蕉地、果园、菜地和村庄用地所占比例过多。农业面源污染控制性措施的用地规划不够,应加大保护性耕作和建立多水塘系统等措施的用地量。An interval numbers optimization model and AGNPS model(Agricultural Non-point Source Model 5.0)were adopted to study the relationship between land use and agricultural nutrient pollution control with the minial cost in Wuchuan Catchment of upstream Xixi River in Jiulong River Watershed,Fujian Province.Both land utilization pattern of agricultural processes and land use pattern of pollution control practices implemented were analyzed systematically.Results indicated that the current land utilization patterns of the catchment needed to be improved,and that the situation of farming habits and management practices should be ameliorated too.The total profit on the basis of the current land use patterns was less than the optimal lower value of system interval.The field scale occupied by pollution control practices with poor environmental effectiveness was too much,such as sloping grassland,banana field,orchard,vegetable and residence.The village should promote the land use with pollution control practices.The area of conservation tillage and multi-pond system are encouraged to increase for their high environmental and economical effectiveness.To achieve a reasonable and applicable program,the decision maker can integrate the solutions of the model with his or her experience and other updated information jointly.福建省“十五”重大科技攻关项目(2002H009);; 福建省发展与改革委员会项目(ZB2003JWKJ001

Applying an Extended Fuzzy Parametric Approach to the Problem of Water Allocations

An extended fuzzy parametric programming (EFPP) model was proposed for supporting water resources allocation problems under uncertainty. EFPP deals with flexible constraints (i.e., fuzzy relationships) by allowing violation of constraints at certain satisfaction degrees (i.e., α levels) and employs fuzzy ranking method to handle trapezoidal-shaped fuzzy coefficients. The objective function is defuzzified by using β cuts and weighting factors. The applicability of EFPP was demonstrated by a numerical example and a water resources allocation case. A series of decision alternatives at various satisfaction degrees were obtained. Generally, the higher the α level, the lower the system benefit. In comparison, the β level in the objective function posed less sensitive impacts on both objective function and model solutions. The reliability of EFPP was tested by comparing its solutions with those from fuzzy chance constrained programming (FCCP). The results indicated that EFPP performed equally well with FCCP in addressing parameter uncertainties, but it demonstrated a wider applicability due to its extended capacity of handling fuzzy relationships in the model constraints

A generalized fuzzy chance-constrained energy systems planning model for Guangzhou, China

National Key Research and Development Plan (2016YFC0502800), the Natural Sciences Foundation (51520105013, 51679087), the 111 Program (B14008) and the Natural Science and Engineering Research Council of Canada

A factorial inexact copula stochastic programming (FICSP) approach for water-energy- food nexus system management

Data Availability: Data will be made available on request.Copyright © 2022 The Authors. In this study, a factorial inexact copula stochastic programming (FICSP) method is developed for planning the regional-scale water-energy-food nexus (WEFN) system. The FICSP cannot only deal with uncertainties expressed as interval and random parameters, but also handle the interdependence among correlated random variables. Moreover, the multilevel factorial analysis embedded in FICSP is able to reflect the main and interactive effects among uncertain parameters. The IFCCP approach was then applied to planning the WEFN system for the City of Jinan, Shandong Province, China. A FICSP-WEFN model has been established under consideration of various restrictions related to water and land availability, food and vegetable demands and other environmental constraints. The obtained results indicated that the surface water and groundwater availabilities would be highly correlated with their marginals fitted through the Gaussian distribution and their dependence described by the Gaussian copula. Under limited water resources, the corn cultivation would be prioritized but the increase of water resources tends to increase the wheat cultivation and reduce corn planting. Under the advantageous conditions where sufficient water resources are available, the additional water resources tend to be allocated to wheat and vegetables whilst corn cultivation would not be changed. Moreover, the surface and recycled water would be first utilized for crop production, with the remaining water requirements satisfied by groundwater. The results from factorial analysis indicated that the system benefits would be increased under the demanding conditions through increasing the joint risk level and also the violation risk for surface water availability or decreasing the violation risk of groundwater availability. Nevertheless, the increase in the violation risks under the advantageous conditions would not necessarily lead to increased system benefit, implying that the crop cultivation patterns may be influenced by other restrictions rather than the water availability. In general, the developed FICSP method cannot only generate desired management strategies for WEFN system under consideration of joint risks, but also help track the factors that make dominant impacts on the WEFN management practices.National Natural Science Foundation of China (62073134)

Optimal design and operation of energy polygeneration systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 301-319).Polygeneration is a concept where multiple energy products are generated in a single plant by tightly integrating multiple processes into one system. Compared to conventional single-product systems, polygeneration systems have many economic advantages, such as potentially high profitability and high viability when exposed to market fluctuations. The optimal design of an energy polygeneration system that converts coal and biomass to electricity, liquid fuels (naphtha and diesel) and chemical products (methanol) with carbon dioxide (CO²) capture under different economic scenarios is investigated. In this system, syngas is produced by gasification of coal and/or biomass; purified by a cleaning process to remove particles, mercury, sulfur and CO²; and then split to different downstream sections such as the gas turbine, FT process and the methanol process. In this thesis, the optimal design with the highest net present value (NPV) is determined by optimizing equipment capacities, stream flow rates and stream split fractions. The case study results for static polygeneration systems reveal that the optimal design of polygeneration systems is strongly influenced by economic conditions such as feedstock prices, product prices, and potential emissions penalties for CO². Over the range of economic scenarios considered, it can be optimal to produce a mixture of electricity, liquid fuels, and methanol; only one each; or mixtures in-between. The optimal biomass/coal feed ratio significantly increases when the carbon tax increases or the biomass price decreases. An economic analysis of the optimal static polygeneration designs yielded a slightly higher NPV than comparable single-product plants. The flexible operation is then considered for the energy polygeneration system. In real applications, product prices can fluctuate significantly seasonally or even daily. The profitability of the polygeneration system can potentially be increased if some operational flexibility is introduced, such as adjusting the product mix in response to changing market prices. The major challenge of this flexible design is the determination of the optimal trade-off between flexibility and capital cost because higher flexibility typically implies both higher product revenues and larger equipment sizes. A two-stage optimization formulation for is used for the optimal design and operation of flexible energy polygeneration systems, which simultaneously optimizes design decision variables (e.g., equipment sizes) and operational decision variables (e.g., production rate schedules) in several different market scenarios to achieve the best expected economic performance. Case study results for flexible polygeneration systems show that for most of market scenarios, flexible polygeneration systems achieved higher expected NPVs than static polygeneration systems. Furthermore, even higher expected NPVs could be obtained with increases in flexibility. The flexible polygeneration optimization problem is a potentially large-scale nonconvex mixed-integer nonlinear program (MINLP) and cannot be solved to global optimality by state-of-the-art global optimization solvers, such as BARON, within a reasonable time. The nonconvex generalized Benders decomposition (NGBD) method can exploit the special structure of this mathematical programming problem and enable faster solution. In this method, the nonconvex MINLP is relaxed into a convex lower bounding problem which can be further reformulated into a relaxed master problem according to the principles of projection, dualization and relaxation. The relaxed master problem yields an nondecreasing sequence of lower bounds for the original problem. And an nonincreasing sequence of upper bounds is obtained by solving primal problems, which are generated by fixing the integer variables in the original problem. A global optimal objective is obtained when the lower and upper bounds coincide. The decomposition algorithm guarantees to find an E-optimal solution in a finite number of iterations. In this thesis, several enhanced decomposition methods with improved relaxed master problems are developed, including enhanced NGBD with primal dual information (NGBD-D), piecewise convex relaxation (NGBD-PCR) and lift-and-project cuts (NGBD-LAP). In NGBD-D, additional dual information is introduced into the relaxed master problem by solving the relaxed dual of primal problem. The soobtained primal dual cuts can significantly improve the convergence rate of the algorithm. In NGBD-PCR, the piecewise McCormick relaxation technique is integrated into the NGBD algorithm to reduce the gap between the original problem and its convex relaxation. The domains of variables in bilinear functions can be uniformly partitioned before solution or dynamically partitioned in the algorithm by using the intermediate solution information. In NGBD-LAP, lift-and-project cuts are employed for solving the piecewise lower bounding problem. In all three enhanced decomposition algorithms, there is a trade-off between tighter relaxations and more solution times for subproblems. The computational advantages of the enhanced decomposition methods are demonstrated via case studies on the flexible polygeneration problems. The computational results show that, while NGBD can solve problems that are intractable for a state-ofthe- art global optimization solver (BARON), the enhanced NGBD algorithms help to reduce the solution time by up to an order of magnitude compared to NGBD. And enhanced NGBD algorithms solved the large-scale nonconvex MINLPs to [epsilon]-optimality in practical times (e.g., a problem with 70 binary variables and 44136 continuous variables was solved within 19 hours).by Yang Chen.Ph.D

Spatial Energy System Modelling under Uncertainty with application to Thailand

The current awareness of the depletion in the fossil fuels reserves and the effect of green house gases (GHG) toward global warming has motivated many researchers in the area of energy system modelling. This thesis presents mathematical models to aid decision makers in determining the optimal spatially aggregated energy supply chain network to satisfy the future energy demand at the national level. Firstly, the energy planning problem using Thailand’s energy system as the case study is addressed by the development of a multi-period environmentally conscious deterministic energy system optimisation model. The model is formulated as a linear programming (LP) model that can address decision-making of the optimal future energy supply chain network at the national level with consideration of the scale of GHG emissions of the network. The determination of data required for the development of the proposed model is also tackled. Secondly, the reformulation of the multi-period deterministic model as a three-staged stochastic energy system optimisation model that can support decision-making under uncertainty in energy demand is addressed. Further extensions to the deterministic model include its reformulation to take into account the geographical location of an energy system. The linear programming model is reformulated as a mixed integer linear programming model (MILP) that can incorporated the spatial nature of the energy system as part of the decision-making process. The decisions to be determined include: (1) scale, type and location of energy production facility, (2) scale and type of resource usage in each location, (3) flow of resources and energy between grids to satisfy the energy demand throughout the planning horizon. Next, the Biomass-to-Energy supply chain network over long-term planning with application to Thailand is focused, based on the spatial MILP formulation. A higher complexity of geographical location is addressed as well as increases in types of biomass and biomass thermal conversion technologies. The objective function is modified to maximise the total network profit rather than minimising the total network costs. Finally, the long-term planning of a Waste-to Energy supply chain network with application to Thailand is investigated. The Waste-to-Energy system is addressed in view of investors as decision-makers as the objective function is also to maximise the total profit of the network. Different network structures of converting waste into energy are applied. The problem is also formulated as a MILP problem. This thesis reveals that, based on the model assumptions, the optimal environmentally conscious energy supply chain networks rely heavily on the utilisation of renewable resources throughout the country. With the abundant amount of biomass and waste resources available in Thailand, Biomass and Waste-to-Energy projects have a high potential in diversifying the use of fossil fuels as primary energy sources in Thailand

Managing uncertainty in modelling of wicked problems: theory and application to Sustainable Aquifer Yield

This thesis presents two approaches to help manage uncertainty in modelling for the resolution of wicked problems , which have no clear problem definition, solution or measure of success. It focuses on Sustainable Aquifer Yield (SAY) as an example. SAY is defined as the pumping volume obtained by a management plan that is expected to satisfy objectives under future conditions within a groundwater system. Integrated modelling can help express, systematise and use knowledge of relevant behaviour of the system, while engaging diverse stakeholders and addressing their interests. Uncertainty is however a key and multifaceted issue when dealing with wicked problems. While many modelling methods exist to help address this uncertainty, there is a need for modellers to be able to integrate these methods purposefully for an applied problem. The research presented involved iteratively proposing two approaches to manage uncertainties in integrated modelling that supports decision making, and exploring the value of each approach by applying it to case studies. For each approach, the applications specifically a) address a technical problem, b) push boundaries on how the problem is viewed, specifically identifying hitherto neglected aspects, and c) address a context where accounting for contested views and surprise is imperative. This research process is described in terms of Critical Systems Practice and resulted in a compilation of linked publications. The first approach proposed is an Uncertainty Management Framework that can be used to help audit the treatment of uncertainty in a step-wise description of an analysis (e.g. evaluating a management plan). The framework provides a formal structure for managing uncertainty by incorporating an uncertainty typology and a set of fundamental uncertainty management actions, but may be too restrictive and demanding for some contexts. To address these limitations, a complementary second approach, designated Iterative Closed Question Modelling, addresses uncertainty by constructing models to test whether each possible answer to a closed question is plausible. The question, assumptions about plausibility and the process of constructing models are all considered uncertain and therefore themselves iteratively critiqued. This approach is formalised in terms of Boundary Critique such that it provides a philosophical foundation justifying the use of a broad range of methods to manage uncertainty in predictive modelling. The thesis concludes that uncertainty needs to be embraced as a natural part of researchers, policy makers and community coming to grips with an evolving situation, rather than being an obstacle to be eliminated. Training of modellers to manage uncertainty needs to specifically address: identification of model scenarios that contradict dominant conclusions; critique of model assumptions and questions from multiple stakeholders’ points of view; and negotiation of the modeller’s role in anticipating surprise (e.g. through understanding consequences of error, design of monitoring, contingency planning and adaptive management). The resulting emphasis on critical thinking about alternative models helps to remind the user that modelling is not a magic trick for seeing the future, but a structured way to reason about both what we do and do not know