In this paper, we propose a framework for selecting a high quality global optimal solution for discrete stochastic optimization problems with a predetermined confidence level using general random search methods. This ...
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In this paper, we propose a framework for selecting a high quality global optimal solution for discrete stochastic optimization problems with a predetermined confidence level using general random search methods. This procedure is based on performing the random search algorithm several replications to get estimate of the error gap between the estimated optimal value and the actual optimal value. A confidence set that contains the optimal solution is then constructed and methods of the indifference zone approach are used to select the optimal solution with high probability. The proposed procedure is applied on a simulated annealing algorithm for solving a particular discrete stochastic optimization problem involving queuing models. The numerical results indicate that the proposed technique indeed locate a high quality optimal solution. (c) 2004 Published by Elsevier B.V. on behalf of IMACS.
This paper describes the implementation of a new solution approach - Fletcher-Ponnambalam model (FP) - for risk management in hydropower system under deregulated electricity market. The FP model is an explicit method ...
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This paper describes the implementation of a new solution approach - Fletcher-Ponnambalam model (FP) - for risk management in hydropower system under deregulated electricity market. The FP model is an explicit method developed for the first and second moments of the storage state distributions in terms of moments of the inflow distributions. This method provides statistical information on the nature of random behaviour of the system state variables without any discretization and hence suitable for multi-reservoir problems. Also avoiding a scenario-based optimization makes it computationally inexpensive, as there is little growth to the size of the original problem. In this paper, the price uncertainty was introduced into the FP model in addition to the inflow uncertainty. Lake Nipigon reservoir system is chosen as the case study and FP results are compared with the stochastic dual dynamic programming (SDDP). Our studies indicate that the method could achieve optimum operations, considering risk minimization as one of the objectives in optimization.
We consider an optimization problem in which some uncertain parameters are replaced by random variables. The minimax approach to stochastic programming concerns the problem of minimizing the worst expected value of th...
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We consider an optimization problem in which some uncertain parameters are replaced by random variables. The minimax approach to stochastic programming concerns the problem of minimizing the worst expected value of the objective function with respect to the set of probability measures that are consistent with the available information on the random data. Only very few practicable solution procedures have been proposed for this problem and the existing ones rely on simplifying assumptions. In this paper, we establish a number of stability results for the minimax stochastic program, justifying in particular the approach of restricting attention to probability measures with support in some known finite set. Following this approach, we elaborate solution procedures for the minimax problem in the setting of two-stage stochastic recourse models, considering the linear recourse case as well as the integer recourse case. Since the solution procedures are modifications of well-known algorithms, their efficacy is immediate from the computational testing of these procedures and we do not report results of any computational experiments. (c) 2004 Elsevier B.V. All rights reserved.
This paper develops trading strategies for liquidation of a financial security, which maximize the expected return. The problem is formulated as a stochastic programming problem that utilizes the scenario representati...
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This paper develops trading strategies for liquidation of a financial security, which maximize the expected return. The problem is formulated as a stochastic programming problem that utilizes the scenario representation of possible returns. Two cases are considered, a case with no constraint on risk and a case when the risk of losses associated with trading strategy is constrained by Conditional Value-at-Risk (CVaR) measure. In the first case, two algorithms are proposed;one is based on linear programming techniques, and the other uses dynamic programming to solve the formulated stochastic program. The third proposed algorithm is obtained by adding the risk constraints to the linear program. The algorithms provide path-dependent strategies, i.e., the fraction of security sold depends upon price sample-path of the security up to the current moment. The performance of the considered approaches is tested using a set of historical sample-paths of prices.
This paper considers a profit-maximizing thermal producer that participates in a sequence of spot markets, namely, day-ahead, automatic generation control (AGC), and balancing markets. The producer behaves as a price-...
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This paper considers a profit-maximizing thermal producer that participates in a sequence of spot markets, namely, day-ahead, automatic generation control (AGC), and balancing markets. The producer behaves as a price-taker in both the day-ahead market and the AGC market but as a potential price-maker in the volatile balancing market. The paper provides a stochastic programming methodology to determine the optimal bidding strategies for the day-ahead market. Uncertainty sources include prices for the day-ahead and AGC markets and balancing market linear price variations with the production of the thermal producer. Results from a realistic case study are reported and analyzed. Conclusions are duly drawn.
The paper deals with the minimization of an integral functional over an L-p space subject to various types of constraints. For such optimization problems, new necessary optimality conditions are derived, based on seve...
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The paper deals with the minimization of an integral functional over an L-p space subject to various types of constraints. For such optimization problems, new necessary optimality conditions are derived, based on several concepts of nonsmooth analysis. In particular, we employ the generalized differential calculus of Mordukhovich and the fuzzy calculus of proximal subgradients. The results are specialized to nonsmooth two-stage and multistage stochastic programs.
Project scheduling problem is to determine the schedule of allocating resources so as to balance the total cost and the completion time. This paper considers project scheduling problem with stochastic activity duratio...
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Project scheduling problem is to determine the schedule of allocating resources so as to balance the total cost and the completion time. This paper considers project scheduling problem with stochastic activity duration times, which has the objective of minimizing the total cost under some completion time limits. Three types of stochastic models will be built to solve the problem according to different management requirements. Moreover, stochastic simulation and genetic algorithm will be integrated to design a hybrid intelligent algorithm to solve the above models. Finally, some numerical examples are illustrated to show the effectiveness of the algorithm. (c) 2004 Elsevier Inc. All rights reserved.
The first of this two-paper series formulates a stochastic security-constrained multi-period electricity marketclearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set o...
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The first of this two-paper series formulates a stochastic security-constrained multi-period electricity marketclearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies. This stochastic programming formulation is solved in the second companion paper using mixedinteger linear programming methods. Two cases are presented: a small transmission-constrained three-bus network scheduled over a horizon of four hours and the IEEE Reliability Test System scheduled over 24 h. The impact on the resulting generation and reserve schedules of transmission constraints and generation ramp limits, of demand-side reserve, of the value of load not served, and of the constitution of the pre-selected set of contingencies are assessed.
This paper proposes a Beam Search heuristic strategy to solve stochastic integer programming problems under probabilistic constraints. Beam Search is an adaptation of the classical Branch and Bound method in which at ...
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This paper proposes a Beam Search heuristic strategy to solve stochastic integer programming problems under probabilistic constraints. Beam Search is an adaptation of the classical Branch and Bound method in which at any level of the search tree only the most promising nodes are kept for further exploration, whereas the remaining are pruned out permanently. The proposed algorithm has been compared with the Branch and Bound method. The numerical results collected on the probabilistic set covering problem show that the Beam Search technique is very efficient and appears to be a promising tool to solve difficult stochastic integer problems under probabilistic constraints. (c) 2004 Elsevier B.V. All rights reserved.
We describe the application of a decomposition based solution method to a class of network interdiction problems. The problem of maximizing the probability of sufficient disruption of the flow of information or goods ...
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We describe the application of a decomposition based solution method to a class of network interdiction problems. The problem of maximizing the probability of sufficient disruption of the flow of information or goods in a network whose characteristics are not certain is shown to be solved effectively by applying a scenario decomposition method developed by Riis and Schultz [Comput Optim Appl 24 (2003), 267-287]. Computational results demonstrate the effectiveness of the algorithm and design decisions that result in speed improvements. (c) 2005 Wiley Periodicals, Inc.
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