A COMPARISON OF TWO METHODS FOR MULTIOBJECTIVE OPTIMIZATION FOR RESERVOIR OPERATION1

ABSTRACT: Two major objectives in operating the multireservoir system of the Upper Colorado River basin are maximization of hydroelectric power production and maximization of the reliability of annual water supply. These two objectives conflict. Optimal operation of the reservoir system to achieve both is unattainable. This paper seeks the best compromise solution for an aggregated reservoir as a surrogate of the multireservoir system by using two methods: the constraint method and the method of combined stochastic and deterministic modeling. Both methods are used to derive the stationary optimal operating policy for the aggregated reservoir by using stochastic dynamic programming but with different objective functions and minimum monthly release constraints. The resulting operating policies are then used in simulated operation of the reservoir with historical inflow records to evaluate their relative effectiveness. The results show that the policy obtained from the combination method would yield more hydropower production and higher reliability of annual water supply than that from the constraint-method policy.     

SPATIALLY OPTIMIZING FOREST MANAGEMENT SCHEDULES TO MEET STORMFLOW CONSTRAINTS1

ABSTRACT: A spatial optimization model is developed and used to limit cumulative effects resulting from storm events by strategically arranging and scheduling forest treatments to meet peak storm-flow constraints. A mixed integer forest management scheduling formulation is used to select the location and timing of forest treatments. The approach includes simulated spatial routing of storm-flows imbedded as hydrologic process constraints (in a nested schedule) within longer-term forest management planning periods in the mathematical programming model. Although difficult to solve, the model shows promise for further research.     

基于AHP LP法的南水北调中线水资源优化配置

水资源是不可替代的重要自然资源和战略性经济资源，水资源优化配置是解决水资源问题的重要手段。为促进区域水资源供需状况相对平衡，按可持续发展的要求，根据区域水资源优化配置的含义和南水北调河北省受水区的具体情况，以有限水资源综合效益最大为目标，考虑水源可供水量、用户需水量和水环境与经济系统协调发展等约束，采用层次分析法与线性规划法相结合的方法，建立了水资源优化配置模型，并对模型的目标函数、约束条件和主要参数确定进行了初步探讨。最后用该模型进行了南水北调河北省受水区2005年和2010年95%保证率下的水资源优化配置研究，并对求解结果进行了分析、评价及展望。结果表明，南水北调工程实施后，能够解决河北省受水区严重缺水的状况。     

Convexity in projection matrices: Projection to a calibration problem

Convexity, as a fundamental property of sets and functions defined on convex sets, plays an important role in many mathematical and applied disciplines, including extremal and optimal-control problems. We prove the set of all feasible projection matrices in a general class of matrix models for stage-structured population dynamics to be convex and the dominant eigenvalue (λ₁) of any projection 2 × 2 matrix to be either a convex, or a concave function on a simplex of the matrix first-row entries (i.e., stage-specific reproduction rates). The latter is also conjectured for the general n × n case. Though looking far from practical needs of matrix population models, this mathematical result has appeared to be quite useful in solving a practical problem to calibrate the projection matrix, i.e., to estimate all the stage-specific vital rates, from empirical data. The data from monitoring of individual life histories of marked plants on permanent sample plots during successive years enable direct calculation of the stage-specific survival and ontogenetic transition rates, but the rates of reproduction do remain uncertain as far as the parent plants can hardly be determined for the (not yet marked!) recruitment.     

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION1

ABSTRACT: Operation of a storage‐based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long‐term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent.     

An integrated optimization and simulation approach for air pollution control under uncertainty in open-pit metal mine

Air Pollution Control model is developed for open-pit metal mines. Model will aid decision makers to select a cost-effective solution. Open-pit metal mines contribute toward air pollution and without effective control techniques manifests the risk of violation of environmental guidelines. This paper establishes a stochastic approach to conceptualize the air pollution control model to attain a sustainable solution. The model is formulated for decision makers to select the least costly treatment method using linear programming with a defined objective function and multi-constraints. Furthermore, an integrated fuzzy based risk assessment approach is applied to examine uncertainties and evaluate an ambient air quality systematically. The applicability of the optimized model is explored through an open-pit metal mine case study, in North America. This method also incorporates the meteorological data as input to accommodate the local conditions. The uncertainties in the inputs, and predicted concentration are accomplished by probabilistic analysis using Monte Carlo simulation method. The output results are obtained to select the cost-effective pollution control technologies for PM_2.5, PM₁₀, NO_x, SO₂ and greenhouse gases. The risk level is divided into three types (loose, medium and strict) using a triangular fuzzy membership approach based on different environmental guidelines. Fuzzy logic is then used to identify environmental risk through stochastic simulated cumulative distribution functions of pollutant concentration. Thus, an integrated modeling approach can be used as a decision tool for decision makers to select the cost-effective technology to control air pollution.     

Wildlife corridors as a connected subgraph problem

Wildlife corridors connect areas of biological significance to mitigate the negative ecological impacts of habitat fragmentation. In this article we formalize the optimal corridor design as a connected subgraph problem, which maximizes the amount of suitable habitat in a fully connected parcel network linking core habitat areas, subject to a constraint on the funds available for land acquisition. To solve this challenging computational problem, we propose a hybrid approach that combines graph algorithms with Mixed Integer Programming-based optimization. We apply this technique to the design of corridors for grizzly bears in the U.S. Northern Rockies, illustrating the underlying computational complexities by varying the granularity of the parcels available for acquisition. The approach that is introduced is general and can be applied to other species or other similar problems, such as those occurring in social networks.     

规划岸线影响下的电厂冷却水数值模拟

随着深圳南山区规划岸线的实施,将影响该海区潮流流态,给前湾燃机电厂的循环冷却水工程造成影响.针对这种情况,利用数值模拟对现状海域流场进行了验证计算,对规划岸线下的流场变化情况及电厂温排水的水力热力特性进行了模拟.在考虑取水温度、经济性、环保性的基础上,为环境评价提供了科学依据.     

基于不确定性的水资源优化配置模型及其实证研究

针对城市水资源系统中存在的不确定性,将可信性模糊机会约束规划模型与区间规划相结合,提出了不确定环境下的可信性模糊-区间线性规划(FILP)模型,将其应用于某城市水资源优化配置与科学管理中,构建了城市水资源优化配置FILP模型.该模型以城市的经济、社会与环境的可持续发展为目标,以供需水量等为不确定性约束,以各水源在各子区不同部门间的分配为决策变量,利用改进的风险显性区间规划算法进行求解得到一定置信度和意愿水平下的水资源优化配置风险-收益权衡方案.实证研究表明,该模型反映了不确定性因素对水资源系统收益的影响,能够为实际的优化决策提供方法支持.     

Beijing's coordinated development of population,resources, environment,and economy

Since the Olympic Games will be held in Beijing at 2008, the urban development plan of Beijing deserves special attention. The essence of regional sustainable development is that population (P), resources (R), environment (E) and economy (E) could develop with sustenance, order and coordination during a certain period, which forms a complex system called the PREE complex system. For this system, a multi-objective integrated model is formulated and solved by a nonlinear goal programming technique. Beijing's PREE complex system is then used as an empirical study. Twelve interesting goals are carefully selected, the parameters of each goal function were estimated by using Beijing's 50-year (1949–1999) statistical data, and their ideal goal limits for 2000 and 2005 are chosen according to the 9th and 10th Five-Year Economic Development Plans of Beijing. The results showed that population size is the most sensitive element in Beijing's PREE complex system. Furthermore, some suggestions related to public policies about the urban development of Beijing are proposed.