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Barrera, J., Homem-De-Mello, T., Moreno, E., Pagnoncelli, B. K., & Canessa, G. (2016). Chance-constrained problems and rare events: an importance sampling approach. Math. Program., 157(1), 153–189.
Abstract: We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAA-IS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study; in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.
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Chadwick, C., Babonneau, F., Homem-de-Mello, T., & Letelier, A. (2024). Synthetic Simulation of Spatially-Correlated Streamflows: Weighted-Modified Fractional Gaussian Noise. Water Resour. Res., 60(2), e2023WR035371.
Abstract: Stochastic methods have been typically used for the design and operations of hydraulic infrastructure. They allow decision makers to evaluate existing or new infrastructure under different possible scenarios, giving them the flexibility and tools needed in decision making. In this paper, we present a novel stochastic streamflow simulation approach able to replicate both temporal and spatial dependencies from the original data in a multi-site basin context. The proposed model is a multi-site extension of the modified Fractional Gaussian Noise (mFGN) model which is well-known to be efficient to maintain periodic correlation for several time lags, but presents shortcomings in preserving the spatial correlation. Our method, called Weighted-mFGN (WmFGN), incorporates spatial dependency into streamflows simulated with mFGN by relying on the Cholesky decomposition of the spatial correlation matrix of the historical streamflow records. As the order in which the decomposition steps are performed (temporal then spatial, or vice-versa) affects the performance in terms of preserving the temporal and spatial correlation, our method searches for an optimal convex combination of the resulting correlation matrices. The result is a Pareto-curve that indicates the optimal weights of the convex combination depending on the importance given by the user to spatial and temporal correlations. The model is applied to a number of river basins in Chile, where the results show that the WmFGN approach maintains the qualities of the single-site mFGN, while significantly improving spatial correlation.
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Ferrada, F., Babonneau, F., Homem-de-Mello, T., & Jalil-Vega, F. (2022). Energy planning policies for residential and commercial sectors under ambitious global and local emissions objectives: A Chilean case study. J. Clean. Prod., 350, 131299.
Abstract: Chile is currently engaged in an energy transition process to meet ambitious greenhouse gas reductions and improved air quality indices. In this paper, we apply a long-term energy planning model, with the objective of finding the set of technologies that meet strong reductions of CO2 emissions and of local PM2.5 concentrations. For this purpose, we use the existing ETEM-Chile (Energy-Technology-Environment-Model) model which considers a simplified version of the Chilean electricity sector that we extend to the residential and commercial sectors and to local concentration considerations. We propose an original approach to integrate in the same framework local and global emission constraints. Results show that to meet the goal of zero emissions by 2050, electrification of end-use demands increases up to 49.2% with a strong growth of the CO2 marginal cost. It should be noted that this electrification rate is much lower than government projections and those usually found in the literature, in certain geographic areas in southern Chile with a wide availability of firewood for residential heating. Regarding local PM2.5 concentrations, our analysis shows that even without a specific emission reduction target, acceptable PM2.5 concentrations are achieved by 2045, due to first the emergence of more efficient, cleaner and cost-effective end-use technologies, in particular, residential firewood heaters, and second the use of drier and therefore less contaminating firewood. Achieving acceptable air quality as early as 2030 is also possible but comes with a high marginal cost of PM2.5 concentration. Our results illustrate the need for implementing effective public policies to (i) regulate the firewood heating market to increase its production and improve its environmental quality and (ii) incentivize the installation of efficient firewood heaters in the residential sector.
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Ferrada, F., Babonneau, F., Homem-de-Mello, T., & Jalil-Vega, F. (2023). The role of hydrogen for deep decarbonization of energy systems: A Chilean case study. Energy Policy, 177, 113536.
Abstract: In this paper we implement a long-term multi-sectoral energy planning model to evaluate the role of green hydrogen in the energy mix of Chile, a country with a high renewable potential, under stringent emission reduction objectives in 2050. Our results show that green hydrogen is a cost-effective and environmentally friendly route especially for hard-to-abate sectors, such as interprovincial and freight transport. They also suggest a strong synergy of hydrogen with electricity generation from renewable sources. Our numerical simulations show that Chile should (i) start immediately to develop hydrogen production through electrolyzers all along the country, (ii) keep investing in wind and solar generation capacities ensuring a low cost hydrogen production and reinforce the power transmission grid to allow nodal hydrogen production, (iii) foster the use of electric mobility for cars and local buses and of hydrogen for long-haul trucks and interprovincial buses and, (iv) develop seasonal hydrogen storage and hydrogen cells to be exploited for electricity supply, especially for the most stringent emission reduction objectives.
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Guevara, E., Babonneau, F., Homem-de-Mello, T., & Moret, S. (2020). A machine learning and distributionally robust optimization framework for strategic energy planning under uncertainty. Appl. Energy, 271, 18 pp.
Abstract: This paper investigates how the choice of stochastic approaches and distribution assumptions impacts strategic investment decisions in energy planning problems. We formulate a two-stage stochastic programming model assuming different distributions for the input parameters and show that there is significant discrepancy among the associated stochastic solutions and other robust solutions published in the literature. To remedy this sensitivity issue, we propose a combined machine learning and distributionally robust optimization (DRO) approach which produces more robust and stable strategic investment decisions with respect to uncertainty assumptions. DRO is applied to deal with ambiguous probability distributions and Machine Learning is used to restrict the DRO model to a subset of important uncertain parameters ensuring computational tractability. Finally, we perform an out-of-sample simulation process to evaluate solutions performances. The Swiss energy system is used as a case study all along the paper to validate the approach.
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Homem-de-Mello, T., Kong, Q. X., & Godoy-Barba, R. (2022). A Simulation Optimization Approach for the Appointment Scheduling Problem with Decision-Dependent Uncertainties. INFORMS J. Comput., Early Access.
Abstract: The appointment scheduling problem (ASP) studies how to manage patient arrivals to a healthcare system to improve system performance. An important challenge occurs when some patients may not show up for an appointment. Although the ASP is well studied in the literature, the vast majority of the existing work does not consider the well-observed phenomenon that patient no-show is influenced by the appointment time, the usual decision variable in the ASP. This paper studies the ASP with random service time (exogenous uncertainty) with known distribution and patient decision-dependent no-show behavior (endogenous uncertainty). This problem belongs to the class of stochastic optimization with decision-dependent uncertainties. Such problems are notoriously difficult as they are typically nonconvex. We propose a stochastic projected gradient path (SPGP) method to solve the problem, which requires the development of a gradient estimator of the objective function-a nontrivial task, as the literature on gradient-based optimization algorithms for problems with decision-dependent uncertainty is very scarce and unsuitable for our model. Our method can solve the ASP problem under arbitrarily smooth show-up probability functions. We present solutions under different patterns of no-show behavior and demonstrate that breaking the assumption of constant show-up probability substantially changes the scheduling solutions. We conduct numerical experiments in a variety of settings to compare our results with those obtained with a distributionally robust optimization method developed in the literature. The cost reduction obtained with our method, which we call the value of distribution information, can be interpreted as how much the system performance can be improved by knowing the distribution of the service times, compared to not knowing it. We observe that the value of distribution information is up to 31% of the baseline cost, and that such value is higher when the system is crowded or/and the waiting time cost is relatively high.
Summary of Contribution: This paper studies an appointment scheduling problem under time-dependent patient no-show behavior, a situation commonly observed in practice. The problem belongs to the class of stochastic optimization problems with decision-dependent uncertainties in the operations research literature. Such problems are notoriously difficult to solve as a result of the lack of convexity, and the present case requires different techniques because of the presence of continuous distributions for the service times. A stochastic projected gradient path method, which includes the development of specialized techniques to estimate the gradient of the objective function, is proposed to solve the problem. For problems with a similar structure, the algorithm can be applied once the gradient estimator of the objective function is obtained. Extensive numerical studies are presented to demonstrate the quality of the solutions, the importance of modeling time-dependent no-shows in appointment scheduling, and the value of using distribution information about the service times.
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Lagos, T., Armstrong, M., Homem-de-Mello, T., Lagos, G., & Saure, D. (2021). A framework for adaptive open-pit mining planning under geological uncertainty. Optim. Eng., 72, 102086.
Abstract: Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity-the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard-practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for large mines. Additionally, any comprehensive approach to mine planning ought to consider the underlying geostatistical uncertainty as only limited information obtained from drill hole samples of the mineral is initially available. In this regard, as blocks are extracted sequentially, information about the ore grades of blocks yet to be extracted changes based on the blocks that have already been mined. Thus, the problem lies in the class of multi-period large scale stochastic optimization problems with decision-dependent information uncertainty. Such problems are exceedingly hard to solve, so approximations are required. This paper presents an adaptive optimization scheme for multi-period production scheduling in open-pit mining under geological uncertainty that allows us to solve practical instances of the problem. Our approach is based on a rolling-horizon adaptive optimization framework that learns from new information that becomes available as blocks are mined. By considering the evolution of geostatistical uncertainty, the proposed optimization framework produces an operational policy that reduces the risk of the production schedule. Our numerical tests with mines of moderate sizes show that our rolling horizon adaptive policy gives consistently better results than a non-adaptive stochastic optimization formulation, for a range of realistic problem instances.
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Zavala, C., Babonneau, F., & Homem-de-Mello, T. (2023). Measuring the impact of regional climate change on heating and cooling demand for the Chilean energy transition. J. Clean. Prod., 428, 139390.
Abstract: The regional impact of climate change on heating and cooling demand is important to consider when designing optimal long-term energy policies. Several studies have addressed this issue, but either at a very aggregated level or without optimizing the whole energy system. The aims of this paper are to fill this gap in a generic way and to assess the impact of climate change on heating and cooling energy demands for residential and commercial sectors at the regional and nodal levels in the context of Chile's energy transition. We propose a methodology based on high resolution climate simulations for the Representative Concentration Pathways (RCP) RCP 2.6 and RCP 8.5 scenarios. First, a statistical analysis is performed to estimate the long-term trends of so-called heating and cooling degree-days and their impact on final regional energy demands. Then, demand pathways in the energy transition are assessed using a multi-sectoral energy planning model. Numerical experiments using data from Chile show an overall positive economic impact of climate change (limited to heating and cooling demands) for the energy system, with a significant decrease in heating demand compared to a limited increase in cooling requirements. For the RCP 8.5 scenario, cost reductions reach 2.1% of the total discounted system cost on the 2020-2050 period mainly due to a significant decrease of gas consumption for heating. This research highlights the importance for policymakers to consider climate change in efficient energy policies.
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