Disaster management is a complex problem demanding sophisticated modeling approaches. We propose utilizing a hybrid method involving inverse optimization to parameterize the cost functions for a road network’s traffi...
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Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable tec...
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Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies has motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the dispatch is adapted to the uncertainty, whereas in multi-stage models the generation schedule is also allowed to dynamically adapt to the uncertainty realization. Multi-stage models provide more flexibility in the generation schedule;however, they require significantly higher computational effort than two-stage models. To justify this additional computational effort, we provide theoretical and empirical analyses of the value of multi-stage solution for risk-averse multi-stage stochastic unit commitment models. The value of multi-stage solution measures the relative advantage of multi-stage solutions over their two-stage counterparts. Our results indicate that, for unit commitment models, the value of multi-stage solution increases with the level of uncertainty and number of periods, and decreases with the degree of risk aversion of the decision maker.
Advantages of combined heat and power system such as high efficiency, low environmental pollution, reliability and controllable output result in its widely application in commercial and residential buildings. Finding ...
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Advantages of combined heat and power system such as high efficiency, low environmental pollution, reliability and controllable output result in its widely application in commercial and residential buildings. Finding the optimal number and capacity of combined heat and power (CHP) units in commercial buildings is a challengeable issue. In this paper, an optimization method based on constrained index of reliability is used for optimal allocation of these systems. Hence, the value of lost load is considered as the reliability index. The random prediction errors of load and energy in CHP systems are modelled as a scenario based on Monte Carlo sampling procedure. Optimization is formulated by using a two-stage stochastic integer linear programming. To reduce the computation time, the number of scenarios has been reduced. Finally, the proposed model is used in a commercial building as a case study.
A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on clas...
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A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on classical interior ballistics, projectile initial disturbance calculation model, exterior ballistics and firing dispersion calculation model. Secondly, the random characteristics of uncertainties are simulated using a hybrid probabilistic and interval model. Then, a nonlinear stochastic programming method is put forward by integrating a back-propagation neural network with the Monte Carlo method. Thus, the uncertain optimization problem is transformed into a deterministic multi-objective optimization problem by employing the mean value, the standard deviation, the probability and the expected loss function, and then the sorting and optimizing of design vectors are realized by the non-dominated sorting genetic algorithm-II. Finally, two numerical examples in practical engineering are presented to demonstrate the effectiveness and robustness of the proposed method.
Solid waste management poses a rich variety of interesting and challenging optimization problems. Waste managers are required to take short-, medium-, and long-term planning decisions, while taking into account the ar...
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Solid waste management poses a rich variety of interesting and challenging optimization problems. Waste managers are required to take short-, medium-, and long-term planning decisions, while taking into account the articulated multi-echelon supply chain of waste generation, treatment and disposal. In all such situations, neglecting the uncertainty of the waste generation rates can lead to unreliable decision plans. In this paper, we address a tactical problem of waste flow allocation from a waste operator point of view with the aim of minimizing the total management cost, net of possible profits obtained by special subproducts. We propose a two-stage multi-period stochastic programming formulation. The first-stage decisions take into account the facility activation and a pre-allocation of waste flow, while the recourse action considers the excess waste. We then benchmark the formulation by solving an instance derived from historical data provided by a large Italian waste treatment company. Scenario trees are generated from predictive models of unsorted waste. Finally, the impact of the stochastic waste generation on the problem solution is examined, showing the benefit of the stochastic methodology when compared with the deterministic formulation. (C) 2018 Elsevier B.V. All rights reserved.
We consider a linear stochastic programming problem with a deterministic objective function and individual probabilistic constraints. Each probabilistic constraint is a lower bound on the probability function equal to...
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We consider a linear stochastic programming problem with a deterministic objective function and individual probabilistic constraints. Each probabilistic constraint is a lower bound on the probability function equal to the probability of the fulfillment of a certain linear inequality. We propose to first represent probabilistic constraints in the form of equivalent inequalities for the quantile functions. After that, each quantile function is approximated using the confidence method. The main analytic tool is based on polyhedral approximation of the p-kernel for the multidimensional probability distribution. For the case when probability functions are defined by linear inequalities, constraints on quantile functions are with arbitrary accuracy approximated by systems of deterministic linear inequalities. As a result, the original problem is approximated by a linear programming problem.
Robust stochastic optimization provides a worst-case decision-making scheme under uncertain probability distributions, but the results could be too conservative and pessimistic. This paper establishes a class of adjus...
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The randomness introduced by reactants is an issue when processing renewable bioresources. In this paper, we apply tools from dynamic stochastic programming theory to the biochemical process. Instead of introducing ex...
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The randomness introduced by reactants is an issue when processing renewable bioresources. In this paper, we apply tools from dynamic stochastic programming theory to the biochemical process. Instead of introducing extra preprocessing units, we consider the inherent randomness of the process and optimize in expectation the performance of the system. In a general setting, this is a multistage stochastic optimization problem and we investigate its approximate solution via two approaches, namely stochastic dual dynamic programming (SDDP) and the finite state, finite action Markov decision process (MDP) framework. These two methods are implemented to a case study of lignin valorization that is crucial to a cost-effective biorefinery process using biomass as the feedstock.
We propose a multistage stochastic programming model to optimally allocate cargo to the passengers network in order to maximize profit, taking into account incomes, costs and penalties for not delivering cargo that wa...
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We propose a multistage stochastic programming model to optimally allocate cargo to the passengers network in order to maximize profit, taking into account incomes, costs and penalties for not delivering cargo that was previously accepted. Flights have a discrete number of possible capacity outcomes, with known probabilities, and uncertainty is represented by a scenario tree. The resulting problem is a large-scale linear program, and we use decomposition techniques to solve it, leveraging on the problem structure in order to be able to find good quality solutions. Our numerical experiments are based on a real network of a major commercial airline.
With the growing global energy demand and worsening ecological environment, coal-abundant countries are actively developing the technologies which could convert coal to liquid fuels, so called coal-to liquids (CTL), t...
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With the growing global energy demand and worsening ecological environment, coal-abundant countries are actively developing the technologies which could convert coal to liquid fuels, so called coal-to liquids (CTL), to adjust and optimize energy structure, guarantee energy security, and reduce environmental pollution. For the optimal planning of a CTL supply chain, a two-stage stochastic programming model is established to maximize the profit of the CTL supply chain under the products demand uncertainty. Various technical and operational constraints involving the infrastructure construction, CTL plants production, products and coal transport as well as the influence of products oversupply, are considered in the model. Based on the sample average approximation method, a number of finite scenarios for the uncertain parameters are generated, the established stochastic model is converted into an equivalent deterministic model and then solved. Finally, the model was successfully applied to a real world CTL supply chain in Sinkiang, China. The applicability of the proposed model was testified. Also, comparative studies were carried out to illustrate the influence of the uncertainty on the CTL supply chain. (C) 2019 Elsevier Ltd. All rights reserved.
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