Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the bl...
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Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the block separable structure of multi-horizon stochastic linear programming, and establish that it can be decomposed by Benders decomposition and Lagrangean decomposition. In addition, we propose parallel Lagrangean decomposition with primal reduction that, (1) solves the scenario subproblems in parallel, (2) reduces the primal problem by keeping one copy for each scenario group at each stage, and (3) solves the reduced primal problem in parallel. We apply the parallel Lagrangean decomposition with primal reduction, Lagrangean decomposition and Benders decomposition to solve a stochastic energy system investment planning problem. The computational results show that: (a) the Lagrangean type decomposition algorithms have better convergence at the first iterations to Benders decomposition, and (b) parallel Lagrangean decomposition with primal reduction is very efficient for solving multi-horizon stochastic programming problems. Based on the computational results, the choice of algorithms for multi-horizon stochastic programming is discussed.
We study the problem of determining the target inventory level of stations in a bike-sharing system, when bikes can be rebalanced later during the day. We propose a two-stage stochastic programming formulation, where ...
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We study the problem of determining the target inventory level of stations in a bike-sharing system, when bikes can be rebalanced later during the day. We propose a two-stage stochastic programming formulation, where the target inventory decisions are made at the first stage, while the recourse decisions, related to rebalancing, are made at the second stage. In the literature, the problem of determining the target inventory levels is solved without taking into account the rebalancing problem, or these two problems are solved sequentially. We prove that more efficient bike-sharing systems can be obtained by integrating these two problems. Moreover, we show that our methodology provides better results than the deterministic formulation, and consider an effective matheuristic, based on the solution of the deterministic problem, to solve the stochastic program. Finally, we compare the solutions obtained by our approach with the actual allocation of bikes in the real bike-sharing system of the city of San Francisco. The results show the effectiveness of our approach also in a realistic setting.
stochastic programming problems with continuous parameter are considered. The empirical function is constructed by the observations of random processes. Stationary and no stationary observations are investigated. Larg...
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This study proposes an approximate stochastic programming approach for solving the service scheduling problem under uncertain demands. Neural networks are introduced as the universal approximator for the analytically ...
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This article presents a model for maximizing the profit of a commercial virtual power plant (VPP) comprised of heterogeneous distributed energy resources (DERs) considering the failure or power outage of its intermitt...
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This article presents a model for maximizing the profit of a commercial virtual power plant (VPP) comprised of heterogeneous distributed energy resources (DERs) considering the failure or power outage of its intermittent units. The failures are taken into account through scenarios of failure happening in different parts of the units with different probabilities. The VPP has access to the future market, the day-ahead (DA) market, and bilateral contracts for trading. Since some of the parameters such as the DA market prices are volatile and uncertain, a two-stage stochastic programming approach is developed to simulate the uncertainty effectively. The VPP makes decisions regarding the future market and signing bilateral contracts in the first stage, then, decisions regarding trading in the DA market and the operation of the VPP's DERs are taken in the second stage. Using the conditional value at risk (CVaR) approach, the behavior of the risk-neutral VPP is compared to the risk-averse VPP. It is shown that considering the failure of intermittent generation units of the VPP leads to more sensitivity of its profit toward pool prices for both risk-neutral and risk-averse VPPs. It also leads to at least 3.4% of VPP's profit lost in the specific designed case study.
In recent years, introducing electric vehicle (EV) buses, their charging equipment and infrastructures has become an urgent issue. The purpose of this study is to propose a scheduling model that minimizes the total ch...
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The design-operation optimization problem for an electricity retailer involves decisions about i) sizes of the energy conversion units and ii) operation in the Day-Ahead market (DA) and Balancing Market (BM), under un...
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Scenario-based stochastic programming is a widely used method for optimization under uncertainty. The solution quality of this approach is dependent on the approximation of the underlying uncertainty distribution. The...
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Scenario-based stochastic programming is a widely used method for optimization under uncertainty. The solution quality of this approach is dependent on the approximation of the underlying uncertainty distribution. Therefore, the optimal generation of scenarios (or scenario trees) is a pertinent research objective in stochastic programming. In this work, we approach the scenario reduction and scenario tree generation problem through the perspective of optimal transport, specifically entropy-regularized optimal transport. The availability of an iterative procedure to compute the optimal entropy-regularized transport plan between support sets, using the Sinkhorn-Knopp algorithm in lieu of conventional linear programming-based optimal transport, is found to decrease solution time appreciably, with a decrease in memory burden as well. We present algorithms for optimal scenario reduction and multistage scenario tree generation, and illustrate their use through two case studies. We show that the proposed approach generates high-quality scenarios whose use in stochastic programming offers solutions with good accuracy.
This work presents a risk-averse stochastic programming model for the optimal planning of hybrid electrical energy systems (HEES), considering the regulatory policy applied to distribution systems in Brazil. Uncertain...
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This work presents a risk-averse stochastic programming model for the optimal planning of hybrid electrical energy systems (HEES), considering the regulatory policy applied to distribution systems in Brazil. Uncertainties associated with variables related to photovoltaic (PV) generation, load demand, fuel price for diesel generation and electricity tariff are considered, through the definition of scenarios. The conditional value-at-risk (CVaR) metric is used in the optimization problem to consider the consumer's risk propensity. The model determines the number and type of PV panels, diesel generation, and battery storage capacities, in which the objective is to minimize investment and operating costs over the planning horizon. Case studies involving a large commercial consumer are carried out to evaluate the proposed model. Results showed that under normal conditions only the PV system is viable. The PV/diesel system tends to be viable in adverse hydrological conditions for risk-averse consumers. Under this condition, the PV/battery system is viable for a reduction of 87% in the battery investment cost. An important conclusion is that the risk analysis tool is essential to assist consumers in the decision-making process of investing in HEES.
In the context of optimization under uncertainty, we consider various combinations of distribution estimation and resampling (bootstrap and bagging) for obtaining samples used to estimate a confidence interval for an ...
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In the context of optimization under uncertainty, we consider various combinations of distribution estimation and resampling (bootstrap and bagging) for obtaining samples used to estimate a confidence interval for an optimality gap. This paper makes three experimental contributions to on-going research in data driven stochastic programming: (a) most of the combinations of distribution estimation and resampling result in algorithms that have not been published before, (b) within the algorithms, we describe innovations that improve performance, and (c) we provide open-source software implementations of the algorithms. Among others, three important conclusions can be drawn: using a smoothed point estimate for the optimality gap for the center of the confidence interval is preferable to a purely empirical estimate, bagging often performs better than bootstrap, and smoothed bagging sometimes performs better than bagging based directly on the data.
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