Benders decomposition with adaptive oracles was proposed to solve large-scale optimisation problems with a column bounded block-diagonal structure, where subproblems differ on the right-hand side and cost coefficients...
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With the large-scale integration of the uncertain and renewable power sources, more attention has been paid to stochastic optimization based methods for security constrained unit commitment（SCUC） problems in recent ...
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With the large-scale integration of the uncertain and renewable power sources, more attention has been paid to stochastic optimization based methods for security constrained unit commitment（SCUC） problems in recent years. In this paper, several representative formulations and methods are reviewed and compared qualitatively including deterministic method with increased system reserves, two-stage/multi-stage stochastic programming, two-stage/multi-stage robust optimization, interval optimization, and all-scenario-feasible formulation. The methods are mainly compared on four aspects: uncertainty representation, solution’s nonanticipativity, solution’s all-scenario-feasibility, complexity of formulations and solution methods. Several simple while important examples are given in the paper to get a better understanding of the methods. It is concluded from the comparison that nonanticipativity is a crucial requirement in problem formulation and in real world application and has to be carefully addressed. Possible extensions of future research are also discussed in this paper.
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these con...
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We consider stochastic motion planning in single-source single-destination robotic relay networks, under a cooperative beam-forming framework. Assuming that the communication medium constitutes a spatiotemporal stocha...
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ISBN:
(纸本)9781479999897
We consider stochastic motion planning in single-source single-destination robotic relay networks, under a cooperative beam-forming framework. Assuming that the communication medium constitutes a spatiotemporal stochastic field, we propose a 2-stage stochastic programming formulation of the problem of specifying the positions of the relays, such that the expected reciprocal of their total beamforming power is maximized. stochastic decision making is made on the basis of random causal CSI. Recognizing the intractability of the original problem, we propose a lower bound relaxation, resulting to a nontrivial optimization problem with respect to the relay locations, which is equivalent to a small set of simple, tractable subproblems. Our formulation results in spatial controllers with a predictive character;at each time slot, the new relay positions should be such that the expected power reciprocal at the next time slot is maximized. Quite remarkably, the optimal control policy to the relaxed problem is purely selective;under a certain sense, only the best relay should move.
This paper studies the online stochastic resource allocation problem (RAP) with chance constraints. The online RAP is a 0-1 integer linear programming problem where the resource consumption coefficients are revealed c...
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Assemble-to-order approaches deal with randomness in demand for end items by producing components under uncertainty, but assembling them only after demand is observed. Such planning problems can be tackled by stochast...
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The pumped hydro energy storage (PHES) systems can be installed in various configurations depending on the specific geographical and hydrological conditions. The closed-loop PHES systems are off-stream and have no nat...
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We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite...
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We consider Benders decomposition for solving two-stage stochastic programs with complete recourse and finite samples of uncertain parameters. We define the Benders cuts binding at the final optimal solution or the on...
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stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piece...
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