A Robust Optimization Model for an Invasive Species Management Problem

Invasive species pose a significant threat to global biodiversity. Managing invasive species often involves modeling the species’ spread pattern, estimating control costs and damage costs due to the invasion, designing control efforts, and accounting for uncertainties in model parameters. Dealing with uncertainty is arguably the most important part of the process, since biological, environmental, and economic factors can cause parameter values to vary greatly. Managers need decision tools that are robust to such limited or variable information. Here, we present a robust spatial optimization model to select treatment sites in a way that maximally reduces the size of an invasive population, given a constraint on financial resources. We develop an integer programming model that includes population dynamics and management costs over space and time. The model incorporates uncertainty in the available budget and the invasive spread rate as sets of discrete scenarios to determine a robust, cost-effective management plan in a novel way.     

Robust Energy Portfolios Under Climate Policy and Socioeconomic Uncertainty

Concerning the stabilization of greenhouse gases, the UNFCCC prescribes measures to anticipate, prevent, or minimize the causes of climate change and mitigate their adverse effects. Such measures should be cost-effective and scientific uncertainty should not be used as a reason for postponing them. However, in the light of uncertainty about climate sensitivity and other underlying parameters, it is difficult to assess the importance of different technologies in achieving robust long-term climate risk mitigation. One example currently debated in this context is biomass energy, which can be used to produce both carbon-neutral energy carriers, e.g., electricity, and at the same time offer a permanent CO₂ sink by capturing carbon from the biomass at the conversion facility and permanently storing it. We use the GGI Scenario Database IIASA [3] as a point of departure for deriving optimal technology portfolios across different socioeconomic scenarios for a range of stabilization targets, focusing, in particular, on new, low-emission scenarios. More precisely, the dynamics underlying technology adoption and operational decisions are analyzed in a real options model, the output of which then informs the portfolio optimization. In this way, we determine the importance of different energy technologies in meeting specific stabilization targets under different circumstances (i.e., under different socioeconomic scenarios), providing valuable insight to policymakers about the incentive mechanisms needed to achieve robust long-term climate risk mitigation.     

A method for monitoring ground water quality near waste storage facilities

A practical optimization approach developed in this paper derives effective monitoring configurations for detecting contaminants in ground water. The approach integrates numerical simulation of contaminant transport and mathematical programming. Well sites identified by the methodology can be monitored to establish the occurrence of a contaminant release before a plume migrates to a regulatory compliance boundary. Monitoring sites are established along several horizons located between the downgradient margin of a contaminant source and a compliance boundary. A horizon can form an effective line of defense against contaminant migration to the compliance boundary if it is spanned (covered) by a sufficient number of sites to yield a well spacing that is equal to or less than a maximum value established by numerical modeling. The objective function of the integer programming model formulation expresses the goals of: (1) covering a maximum number of siting horizons, and (2) allocating wells to the single most effective horizon. The latter is determined from well spacing requirements and the width of the zone of potential contaminant migration traversed by the horizon. The methodology employs a highly tractable linear programming model formulation, and the user is not required to predefine a set of potential well sites. These attributes can facilitate its implementation in practice.     

NEMS and MARKAL-MACRO Models for Energy-Environmental-Economic Analysis: A Comparison of the Electricity and Carbon Reduction Projections

The Annual Energy Outlook forecasts published by the United States Energy Information Administration (EIA) of the Department of Energy are based on results from the National Energy Modeling system (NEMS). This paper compares NEMS, which is used only in the U.S., with the U.S. version of MARKAL-MACRO (USMM) model, which is used in more than thirty-five countries. The two models predict similar results for the base 1999 US Annual Energy Outlook (AEO), but their results with carbon constraints are quite different. The differences of the models and those of their predictions are explained. USMM can be used to provide an alternative and complementary approach to projections of renewable technologies penetration and their potential in reducing carbon dioxide emissions in the USA.     

An Interval-Parameter Fuzzy-Stochastic Programming Approach for Municipal Solid Waste Management and Planning

In this study, an integrated fuzzy-stochastic linear programming model is developed and applied to municipal solid waste management. Methods of chance-constrained programming and fuzzy linear programming are incorporated within a general interval-parameter mixed-integer linear programming framework. It improves upon the existing optimization methods with advantages in uncertainty reflection, data availability, and computational requirement. The model can be used for answering questions related to types, times and sites of solid waste management practices, with the objective of minimizing system costs over the planning horizon. The model can effectively reflect dynamic, interactive, and uncertain characteristics of municipal waste management systems. In its solution process, the model is transformed into two deterministic submodels, corresponding to upper and lower bounds of the desired objective function values under a given significance level, based on an interactive algorithm. Results of the method's application to a hypothetical case indicate that reasonable outputs have been obtained. It demonstrates the practical applicability of the proposed methodology.     

Interval-parameter Fuzzy-stochastic Semi-infinite Mixed-integer Linear Programming for Waste Management under Uncertainty

An interval-parameter fuzzy-stochastic semi-infinite mixed-integer linear programming (IFSSIP) method is developed for waste management under uncertainties. The IFSSIP method integrates the fuzzy programming, chance-constrained programming, integer programming and interval semi-infinite programming within a general optimization framework. The model is applied to a waste management system with three disposal facilities, three municipalities, and three periods. Compared with the previous methods, IFSSIP have two major advantages. One is that it can help generate solutions for the stable ranges of the decision variables and objective function value under fuzzy satisfaction degree and different levels of probability of violating constraints, which are informative and flexible for solution users to interpret/justify. The other is that IFSSIP can not only handle uncertainties through constructing fuzzy and random parameter, but also reflect dynamic features of the system conditions through interval function of time over the planning horizon. By comparing IFSSIP with interval-parameter mixed-integer linear semi-infinite programming and parametric programming, the IFSSIP method is more reasonable than others.     

Marginal Abatement Cost Curves: Combining Energy System Modelling and Decomposition Analysis

Marginal abatement cost (MAC) curves are a useful policy tool to communicate findings on the technological structure and the economics of CO₂ emissions reduction. However, existing ways of generating MAC curves do not display consistent technological detail and do not consider system-wide interactions and uncertainty in a structured manner. This paper details a new approach to overcome the present shortcomings by using an energy system model, UK MARKAL, in combination with index decomposition analysis. In addition, this approach allows different forms of uncertainty analysis to be used in order to test the robustness of the MAC curve. For illustration purposes, a sensitivity analysis concerning fossil fuel prices is applied to the transport sector of the UK. The resulting MAC curves are found to be relatively robust to different fuel costs at higher CO₂ tax levels. The new systems-based approach improves MAC curves through the avoidance of an inconsistent emissions baseline, the incorporation of system-wide interactions and the price responsiveness of demand.     

Designing a conservation reserve network with minimal fragmentation: A linear integer programming approach

In the biological conservation literature, the optimum reserve site selection problem has often been addressed by using the prototype set covering and maximal covering formulations, assuming that representation of species is the only criterion in site selection. This approach usually results in a small but highly fragmented reserve, which is not useful for practical conservation planning. To improve the chances of species' persistence, it may be desirable to reduce habitat fragmentation. This paper presents a linear integer programming formulation to minimize spatial gaps between selected sites in a reserve network, which is applied to a data set on breeding birds. The authors express their willingness to share the database used in this study. Those readers who wish to have access to the data may contact Robert A. Briers at r.briers@napier.ac.uk.     

IFTCIP: An Integrated Optimization Model for Environmental Management under Uncertainty

In this study, an interval-fuzzy two-stage chance-constrained integer programming (IFTCIP) method is developed for supporting environmental management under uncertainty. The IFTCIP improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within a general mixed integer linear programming framework. It has advantages in uncertainty reflection, policy investigation, risk assessment, and capacity-expansion analysis in comparison to the other optimization methods. Moreover, it can help examine the risk of violating system constraints and the associated consequences. The developed method is applied to the planning for facility expansion and waste-flow allocation within a municipal solid waste management system. Violations of capacity constraints are allowed under a range of significance levels, which reflects tradeoffs between the system cost and the constraint-violation risk. The results indicate that reasonable solutions for both binary and continuous variables have been generated under different risk levels. They are useful for generating desired decision alternatives with minimized system cost and constraint-violation risk under various environmental, economic, and system-reliability conditions. Generally, willingness to take a higher risk of constraint violation will guarantee a lower system cost; a strong desire to acquire a lower risk will run into a higher system cost.     

Robust Regression with Data-Dependent Regularization Parameters and Autoregressive Temporal Correlations

We introduce robust procedures for analyzing water quality data collected over time. One challenging task in analyzing such data is how to achieve robustness in presence of outliers while maintaining high estimation efficiency so that we can draw valid conclusions and provide useful advices in water management. The robust approach requires specification of a loss function such as the Huber, Tukey’s bisquare and the exponential loss function, and an associated tuning parameter determining the extent of robustness needed. High robustness is at the cost of efficiency loss in parameter loss. To this end, we propose a data-driven method which leads to more efficient parameter estimation. This data-dependent approach allows us to choose a regularization (tuning) parameter that depends on the proportion of “outliers” in the data so that estimation efficiency is maximized. We illustrate the proposed methods using a study on ammonium nitrogen concentrations from two sites in the Huaihe River in China, where the interest is in quantifying the trend in the most recent years while accounting for possible temporal correlations and “irregular” observations in earlier years.     

An Inexact Fuzzy-robust Two-stage Programming Model for Managing Sulfur Dioxide Abatement Under Uncertainty

In this study, an inexact fuzzy-robust two-stage programming (IFRTSP) method is developed for tackling multiple forms of uncertainties that can be expressed as discrete intervals, probabilistic distributions and/or fuzzy membership functions. The model can reflect economic penalties of corrective measures against any infeasibilities arising due to a particular realization of system uncertainties. Moreover, the fuzzy decision space can be delimited into a more robust one with the uncertainties being specified through dimensional enlargement of the original fuzzy constraints. A management problem in terms of regional air pollution control has been studied to illustrate the applicability of the proposed approach. Results indicate that useful solutions for planning the air quality management practices have been generated. They can help decision makers identify desired pollution-abatement strategy with minimized system cost and maximized environmental efficiency.     

实验室间比对能力验证中的两种稳健统计技术探讨

对环境监测实验室能力验证中两种稳健数据统计技术以及z比分数评价准则进行了探讨,并介绍了如何使用Excel电子表格软件实现数据的统计处理。四分位数法和迭代法均可作为实验室比对能力验证的数据处理技术,相对于四分位数稳健统计方法,迭代法是一种更加温和且可靠的稳健统计方法,但不适用于分割水平设计的能力验证计划。     

Application of Sensitivity and Flux Analyses for the Reduction of Model Predicting the Photooxidative Degradation of an Azo Dye in Aqueous Media

The prediction of the system behavior is of significant interest when evaluating appropriate technologies for wastewater treatment. The robust prediction could be achieved by empirical mathematical modeling techniques, but they do not include steps in degradation of organic pollutants. Mechanistic models (MM) include chemical/physical phenomena, but may also include numerous reactions resulting with the complicated kinetic expressions with large number of parameters. This modeling approach can be challenging for complex system such as advanced oxidation processes. With the goal to reduce the number of reactions involved in developed MM, keeping the high prediction power, sensitivity, and flux analyses was employed. The results showed that MM describing the degradation of organic dye in water matrix by photooxidation processes can be significantly simplified, by reducing the number of reactions included without affecting the predictive power. The calculated root mean square deviation values between data predicted by MM and reduced MM_R differ insignificantly (≤1.4 %).     

用稳健统计法处理方法标准验证实验中方法检出限数据

方法检出限是分析方法基本性能参数之一。根据《环境监测分析方法标准制修订技术导则》(HJ 168—2010)的要求,此参数需要6家以上实验室基于特定样品测试数据的标准偏差得到。目前,标准文本大多采用各家实验室方法检出限中最大值。研究提出用稳健统计法处理方法验证数据,无需识别和删去离群值,可将离群值的影响降到最小。基于4组公开发表数据和2组实测数据,比较了不同方法计算结果。结果表明:参与统计的3组数据29个检测项目中,常规方法确认的方法检出限被判为离群值占27.6%。取最大值存在数值偏高的风险。提出了用曼德尔k检验法识别1组方法检出限数据中的离群值,该方法同样可以用于实验室数据与标准文本中方法检出限符合性判断。     

Representing uncertainty in climate change scenarios: a Monte-Carlo approach

Climate change impact assessment is subject to a range of uncertainties due to both incomplete and unknowable knowledge. This paper presents an approach to quantifying some of these uncertainties within a probabilistic framework. A hierarchical impact model is developed that addresses uncertainty about future greenhouse gas emissions, the climate sensitivity, and limitations and unpredictability in general circulation models. The hierarchical model is used in Bayesian Monte-Carlo simulations to define posterior probability distributions for changes in seasonal-mean temperature and precipitation over the United Kingdom that are conditional on prior distributions for the model parameters. The application of this approach to an impact model is demonstrated using a hydrological example. This revised version was published online in July 2006 with corrections to the Cover Date.     

Combinatorial optimization of elk habitat effectiveness and timber harvest volume

Forest resource planning processes in the western United States have been placing an increasing emphasis on wildlife and fish habitat goals. With this in mind, we developed a method that incorporates a Habitat Effectiveness Index (HEI) for Roosevelt elk (Cervus elaphus roosevelti) into the objective function of a mathematical forest planning model. In addition, a commodity production goal is proposed (maximum timber production), and the habitat and commodity production goals are allowed to act as goals in a multi-objective goal programming planning problem. A heuristic programming technique (tabu search) is used to develop feasible solutions to the resulting non-linear, integer programming problem. Using a hypothetical example, we illustrate results of five scenarios, where the emphasis of the achievement of one or both goals is altered. The main contribution of this approach is the ability to measure and evaluate the trade-offs among achieving a certain level of a complex wildlife goal and achieving commodity production goals. These trade-offs are measured using a flexible model, allowing planners to formulate non-linear spatial goals as objectives of a problem, rather than forcing them to rely on posterior evaluations of the suitability of management plans to goals such as elk HEI.     

Integral transform solutions for atmospheric pollutant dispersion

A transient two-dimensional advection–diffusion model describing the turbulent dispersion of pollutants in the atmosphere has been solved via the Generalized Integral Transform Technique (GITT), by two different schemes. The first approach performs numerical integration of the transformed system using available routines for initial value problems with automatic error control. In spite of the time-consuming character of such a scheme, its flexibility allows the handling of problems involving time-dependent meteorological parameters such as wind speed and eddy diffusivities. The second approach works fully analytically being thus intrinsically more robust and economic, although not directly applicable in dealing with time-dependent parameters. For the test problem used in this work, both methods agree very well with each other, as well as with a known analytical solution for a simpler formulation used as benchmark. The impact of the longitudinal diffusivity on the stiffness of the ordinary differential equation (ODE) system arising from the integral transformation has been assessed through the processing time demanded to solve it when the numerical approach is used. The observed CPU times show that the analytical approach is clearly preferable unless the problem involves time-dependent parameters.     

A rapid approach to rational water pollution control strategies

The formulation of rational wastewater control strategies is becoming increasingly important in many countries where, exploding urbanization, industrialization and/or tourism, often combined with improved standards of living and better awareness of the environmental problems, are resulting in enlarged pollution problems, but also in the availability of expanding financial resources for environmental protection. However, more often than one tends to believe, lack of planning, or planning with limited understanding of the principles involved, has resulted in solutions that are both expensive and incapable of addressing the key problems.As rigorous planning is extremely resource intensive, and for this reason impractical for most study areas, the development of a much simplified analysis procedure, capable of generating rational, near-optimum, strategies and detailed action programs, is required, if proper environmental management is to be widely practiced.In an effort to achieve the above objectives, a systems analysis approach is selected as the most suitable at rationalizing the allocation of available resources and at producing detailed action programs that promote implementation. In the context of this approach, new, easy to use models have been developed, while others, have been selected, adapted and streamlined in their use. The entire problem analysis and strategy synthesis procedures have thus been simplified and defined to a degree appropriate for widespread use, and the resultant procedure is actively promoted by WHO and UNEP.     

应用稳健马氏距离评价实验室间比对能力考核

基于稳健马氏距离的多元统计算法，综合评价了全国环境监测系统96个实验室4种有机氯农药监测能力考核的结果，从中筛选出25个考核结果存在异常的实验室。将多元统计结果与稳健Z比分数结果进行比较，发现基于稳健马氏距离筛选出的异常实验室其稳健Z比分数结果也存在一定的问题。同时简单介绍了稳健马氏距离及其相关的异常值筛选的算法原理，并详细介绍了其基于R语言的实现过程。     

应用稳健统计方法对环境空气臭氧自动监测现场比对核查结果的分析研究

根据2015年9个城市53台现场臭氧分析仪的现场比对核查结果,比较研究了稳健统计方法和一般统计方法在评价国控网臭氧自动监测数据准确性和精密性上的应用。研究表明:稳健统计能够在不剔除异常数据的前提下降低异常值对正确评价臭氧自动监测数据质量的影响,适合评价现场比对核查结果;采用Hubers方法进行稳健统计,2015年国控网臭氧日常浓度点相对偏差的95%置信区间约为-0.1%至4.5%,95%预测区间为-14.0%~18.3%,变异系数约为9.5%,数据质量仍有提升空间。