Mashor Housh

Limited multi-stage stochastic programming for managing water supply systems

Decision-making processes often involve uncertainty. A common approach for modeling uncertain scenario-based decision-making progressions is through multi-stage stochastic programming. The size of optimization problems derived from multi-stage stochastic programs is frequently too large to be addressed by a direct solution technique. This is due to the size of the optimization problems, which grows exponentially as the number of scenarios and stages increases. To cope up with this computational difficulty, solution schemes turn to decomposition methods for defining smaller and easier to solve equivalent sub-problems, or through using scenario-reduction techniques. In our study a new methodology is proposed, titled Limited Multi-stage Stochastic Programming (LMSP), in which the number of decision variables at each stage remains constant and thus the total number of decision variables increases only linearly as the number of scenarios and stages grows. The LMSP employs a decision-clustering framework, which utilizes the optimal decisions obtained by solving a set of deterministic optimization problems to identify decision nodes, which have similar decisions. These nodes are clustered into a preselected number of clusters, where decisions are made for each cluster instead of for each individual decision node. The methodology is demonstrated on a multi-stage water supply system operation problem, which is optimized for flow and salinity decisions. LMSP performance is compared to that of classical multi-stage stochastic programming (MSP) method.

Robust stochastic optimization for reservoir operation

Optimal reservoir operation under uncertainty is a challenging engineering problem. Application of classic stochastic optimization methods to large-scale problems is limited due to computational difficulty. Moreover, classic stochastic methods assume that the estimated distribution function or the sample inflow data accurately represents the true probability distribution, which may be invalid and the performance of the algorithms may be undermined. In this study, we introduce a robust optimization (RO) approach, Iterative Linear Decision Rule (ILDR), so as to provide a tractable approximation for a multiperiod hydropower generation problem. The proposed approach extends the existing LDR method by accommodating nonlinear objective functions. It also provides users with the flexibility of choosing the accuracy of ILDR approximations by assigning a desired number of piecewise linear segments to each uncertainty. The performance of the ILDR is compared with benchmark policies including the sampling stochastic dynamic programming (SSDP) policy derived from historical data. The ILDR solves both the single and multireservoir systems efficiently. The single reservoir case study results show that the RO method is as good as SSDP when implemented on the original historical inflows and it outperforms SSDP policy when tested on generated inflows with the same mean and covariance matrix as those in history. For the multireservoir case study, which considers water supply in addition to power generation, numerical results show that the proposed approach performs as well as in the single reservoir case study in terms of optimal value and distributional robustness.

System of Systems Model for Analysis of Biofuel Development

AbstractThis paper presents a system of systems (SoS) Biofuel model considering the interdependency among the systems involved in biofuel development, including biofuel refinery location, transportation infrastructure, agricultural production and markets, environment, and social communities. The model provides the optimal infrastructure development and land-use allocation for biofuel production in a region considering socio-economic and water quality and quantity effects. The optimal development plan quantifies economic and hydrologic outputs and specifies biofuel refinery locations and capacities, refinery operations, land allocation between biofuel and food crops, optimal shipments of products and feedstock, and transportation infrastructure. The model is formulated as a mixed integer linear program (MILP) and is solved by an algorithm developed specifically to cope with the large size of the optimization problem. In addition to the development of the SoS-Biofuel model, this paper demonstrates the funct...

An integrated logit model for contamination event detection in water distribution systems.

The problem of contamination event detection in water distribution systems has become one of the most challenging research topics in water distribution systems analysis. Current attempts for event detection utilize a variety of approaches including statistical, heuristics, machine learning, and optimization methods. Several existing event detection systems share a common feature in which alarms are obtained separately for each of the water quality indicators. Unifying those single alarms from different indicators is usually performed by means of simple heuristics. A salient feature of the current developed approach is using a statistically oriented model for discrete choice prediction which is estimated using the maximum likelihood method for integrating the single alarms. The discrete choice model is jointly calibrated with other components of the event detection system framework in a training data set using genetic algorithms. The fusing process of each indicator probabilities, which is left out of focus in many existing event detection system models, is confirmed to be a crucial part of the system which could be modelled by exploiting a discrete choice model for improving its performance. The developed methodology is tested on real water quality data, showing improved performances in decreasing the number of false positive alarms and in its ability to detect events with higher probabilities, compared to previous studies.

Managing Multiple Mandates: A System of Systems Model to Analyze Strategies for Producing Cellulosic Ethanol and Reducing Riverine Nitrate Loads in the Upper Mississippi River Basin

Implementing public policies often involves navigating an array of choices that have economic and environmental consequences that are difficult to quantify due to the complexity of multiple system interactions. Implementing the mandate for cellulosic biofuel production in the Renewable Fuel Standard (RFS) and reducing hypoxia in the northern Gulf of Mexico by reducing riverine nitrate-N loads represent two such cases that overlap in the Mississippi River Basin. To quantify the consequences of these interactions, a system of systems (SoS) model was developed that incorporates interdependencies among the various subsystems, including biofuel refineries, transportation, agriculture, water resources and crop/ethanol markets. The model allows examination of the impact of imposing riverine nitrate-N load limits on the biofuel production system as a whole, including land use change and infrastructure needs. The synergies of crop choice (first versus second generation biofuel crops), infrastructure development, and environmental impacts (streamflow and nitrate-N load) were analyzed to determine the complementarities and trade-offs between environmental protection and biofuel development objectives. For example, the results show that meeting the cellulosic biofuel target in the RFS using Miscanthus x giganteus reduces system profits by 8% and reduces nitrate-N loads by 12% compared to the scenario without a mandate. However, greater water consumption by Miscanthus is likely to reduce streamflow with potentially adverse environmental consequences that need to be considered in future decision making.

Implicit Mean-Variance Approach for Optimal Management of a Water Supply System under Uncertainty

AbstractThis study addresses the management of a water supply system under uncertainty. Water is taken from sources that include aquifers and desalination plants and conveyed through a distribution system to consumers under constraints of quantity and quality. The replenishment into the aquifers is stochastic, whereas the desalination plants can produce a large and reliable amount, but at a higher cost. The cost is stochastic because it depends on the realization of the replenishment into the aquifer. A new implicit mean-variance approach is developed and applied. It utilizes the advantages of implicit stochastic programming to formulate a small size and easy to solve convex external optimization problem (quadratic objective and linear constraints) that generates the mean-variance tradeoff without the need to solve a large-scale problem. The results are presented as a tradeoff between the expected value versus the standard deviation. At one end of the tradeoff curve, dependence on the aquifer results in l...

Least-Cost Robust Design Optimization of Water Distribution Systems under Multiple Loading

AbstractLeast-cost design of water distribution system is a well-known problem in the literature. The formulation of the least-cost design problem started by deterministic modeling and later by more sophisticated stochastic models that incorporate uncertainties related to the problem’s parameters. Recently, a new nonprobabilistic modeling, titled the robust counterpart (RC) approach, has been developed for the least-cost design problem to incorporate the uncertainty without the need for full stochastic information. These nonprobabilistic methods, developed in the field of robust optimization, were shown to be advantageous over classical stochastic methods in the following aspects: tractability and computation time, nonnecessity of full probabilistic information, and the ability to integrate correlation of uncertain parameters aspects without adding complexity. Former studies have considered the RC approach for a special case of the least-cost problem with a single load demand uncertainty, and single gravi...

Seasonal multi-year optimal management of quantities and salinities in regional water supply systems

A seasonal multi-year model for management of water quantities and salinities in regional water supply systems (WSS) was developed and implemented. Water is taken from sources which include aquifers, reservoirs, and desalination plants, and conveyed through a distribution system to consumers who require quantities of water under salinity constraints. The year is partitioned into seasons, and the operation is subject to technological, administrative, and environmental constraints such as water levels and salinities in the aquifers, capacities of the pumping, distribution system, and the desalination plants, and the desalination plants maximum removal ratios. The objective is to operate the system at minimum total cost. The objective function and some of the constraints are nonlinear, leading to a nonlinear optimization problem. The nonlinear optimization problem is solved efficiently by adapting (1) a set of manipulations that reduce the problem size and (2) a novel finite difference scheme for calculating the derivatives required by the optimization solver, entitled the Time-Chained-Method (TCM). The model is demonstrated on a small illustrative example and on a real sized regional water supply system in Israel.

Modelling infrastructure interdependencies, resiliency and sustainability

The three key concepts of interdependency, resiliency and sustainability of a complex system have appeared in a number of studies and in various contexts. Nevertheless, little has been done to define and analyse them, especially the latter two, in a unified quantitative framework for engineering infrastructures. In this paper, we propose overarching mathematical modelling frameworks to quantify these three key concepts in the context of complex infrastructure systems with multiple interdependent subsystems (i.e., the system of systems). We show how interdependencies between subsystems can affect the resiliency and sustainability of the entire system. We provide a case study in the context of biofuel development and use different dynamical models to demonstrate these concepts.

Mix of First- and Second-Generation Biofuels to Meet Multiple Environmental Objectives: Implications for Policy at a Watershed Scale

Biofuel mandates are being widely used by countries to achieve multiple objectives of energy security and climate change mitigation. The Renewable Fuel Standard (RFS) in the US specifies arbitrarily chosen volumetric targets for different types of biofuels in the US based on their greenhouse gas intensity only. Cellulosic biofuels from high yielding energy crops like miscanthus have the potential to co-generate multiple environmental impacts, including reducing nitrate runoff, being a sink for Greenhouse Gas (GHG) emissions and providing a given volume of biofuel with less diversion of land from food crop production than corn ethanol, but at a significantly higher cost. This paper quantifies the tradeoffs between profitability, food and fuel production, GHG emissions and nitrate runoff reduction with different types of biofuels in the Sangamon watershed in Illinois and analyzes the optimal mix of biofuels as well as the policies that should supplement the mandate to achieve multiple environmental outcomes. We find that a two-thirds share of cellulosic biofuel in the mandated level could reduce nitrate run-off by 20% while reducing GHG emissions by 88–100% but would reduce profits by 15–27% depending on whether a GHG policy or a Nitrate policy is used relative to the case where the mandate is met by corn ethanol alone. Additionally, the ratio of corn stover to miscanthus used to produce cellulosic biofuels is higher under a GHG policy compared to a Nitrate policy that achieves the same level of nitrate reduction. Our results show that the optimal mix of different types of biofuels and the policy to induce it depend on the environmental objectives and the tradeoffs that society is willing to make between low cost energy security, food production and various environmental benefits.