We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks Subject to multiple scenarios of externally caused damage. We present computation with netw...
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We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks Subject to multiple scenarios of externally caused damage. We present computation with networks with up to 600 nodes and 827 edges, and many thousands of damage scenarios. (c) 2006 Elsevier B.V. All rights reserved.
As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction...
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As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.
作者：
Ketkov, Sergey S.HSE Univ
Lab Algorithms & Technol Networks Anal Rodionova St 136 Nizhnii Novgorod 603093 Russia Univ Zurich
Dept Business Adm CH-8032 Zurich Switzerland
This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability dis...
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This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.
The unit restriction model and the area restriction model are the two main approaches to dealing with adjacency in forest harvest planning. In this paper, we present a new mixed-integer programming (MIP) formulation t...
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The unit restriction model and the area restriction model are the two main approaches to dealing with adjacency in forest harvest planning. In this paper, we present a new mixed-integer programming (MIP) formulation that can be classified as both a unit restriction approach and an area restriction approach. Weneed to generate a feasible cluster to formulate the model. However, unlike other approaches, there is no need to generate specific model constraints representing computationally burdensome clusters for large cases. We describe and analyze our approach by comparing it with the most efficient approaches presented in the literature. Comparisons are made from modeling and computational points of view. Results showed that the proposed model was competitive with regard to modeling complexity and size of formulation. Furthermore, it is easy to implement in standard modeling software.
The climate change emergency calls for a reduction in energy consumption in all human activities and production processes. The radio broadcasting industry is no exception. However, reducing energy requirements by unif...
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The climate change emergency calls for a reduction in energy consumption in all human activities and production processes. The radio broadcasting industry is no exception. However, reducing energy requirements by uniformly cutting the radiated power at every transmitter can potentially impair the quality of service. A careful evaluation and optimization study are in order. In this paper, by analyzing the Italian frequency modulation analog broadcasting service, we show that it is indeed possible to significantly reduce the energy consumption of the broadcasters without sacrificing the quality of the service, rather, even getting improvements.
Cloud manufacturing is an emerging service-oriented manufacturing paradigm that integrates and manages distributed manufacturing resources through which complex manufacturing demands with a high degree of customizatio...
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Cloud manufacturing is an emerging service-oriented manufacturing paradigm that integrates and manages distributed manufacturing resources through which complex manufacturing demands with a high degree of customization can be fulfilled. The process of service selection optimization and scheduling (SSOS) is an important issue for practical implementation of cloud manufacturing. In this paper, we propose new mixed-integer programming (MIP) models for solving the SSOS problem with basic composition structures (i.e., sequential, parallel, loop, and selective). Through incorporation of the proposed MIP models, the SSOS with a mixed composition structure can be tackled. As transportation is indispensable in cloud manufacturing environment, the models also optimize routing decisions within a given hybrid hub-and-spoke transportation network in which the central decision is to optimally determine whether a shipment between a pair of distributed manufacturing resources is routed directly or using hub facilities. Unlike the majority of previous research undertaken in cloud manufacturing, it is assumed that manufacturing resources are not continuously available for processing but the start time and end time of their occupancy interval are known in advance. The performance of the proposed models is evaluated through solving different scenarios in the SSOS. Moreover, in order to examine the robustness of the results, a series of sensitivity analysis are conducted on key parameters. The outcomes of this study demonstrate that the consideration of transportation and availability not only can change the results of the SSOS significantly, but also is necessary for obtaining more realistic solutions. The results also show that routing within a hybrid hub-and-spoke transportation network, compared with a pure hub-and-spoke network or a pure direct network, leads to more flexibility and has advantage of cost and time saving. The level of saving depends on the value of discount factor f
The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the ...
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The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the liquid natural gas supply chain, supply requirements and problem specific network constraints require a unique optimization model. We develop a large-scale, discrete time, path-based integer-programming model which solves optimally with CPLEX. Computational results implementing a rolling horizon structure and testing based on historical data are presented. A detailed sensitivity analysis demonstrates the effective use of our model, testing a variety of realistic parameter settings for the liquid helium supply chain.
Rapid population growth, industrialization, and lifestyle modernization all increase water demand. However, water supplies are dramatically decreasing due to declining and irregular precipitation and the excessive use...
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Rapid population growth, industrialization, and lifestyle modernization all increase water demand. However, water supplies are dramatically decreasing due to declining and irregular precipitation and the excessive use and deterioration of existing resources. This situation places tremendous pressure on decision-makers, who must implement plans to create new water supplies in regions likely to experience water shortages in the future. Deciding which projects to implement among various alternatives is challenging with a limited budget. This study aims to create a feasible strategic plan to select the most suitable alternative projects by proposing a multi-objective mixed-integer programming approach to the water supply problem. Considering several criteria, including chance of success, ease of application, nature-friendliness, and project prestige level, the proposed model is integrated using the analytical hierarchical process technique. Decision-makers' views of the project alternatives are reflected by weights in the model. Also, interval numbers represent the costs of alternatives to handle the problem more realistically. A real-life situation is simulated under various scenarios to test the proposed model. The results show that the proposed integrated model generates more applicable solutions than a classic multi-objective optimization model.
The natural gas supply chain involves three main agents: producers, transportation companies, and local distribution companies (LDCs). We present a MIP model that is the basis for a decision support system developed f...
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The natural gas supply chain involves three main agents: producers, transportation companies, and local distribution companies (LDCs). We present a MIP model that is the basis for a decision support system developed for a Chilean LDC. This model takes into account many of the complexities of the purchasing and transportation contracts to help optimize daily purchase and transportation decisions in the absence of local storage facilities. The model was solved to optimality within a reasonable time. We show how the model handles several contractual issues and give some insights for the case when demand scenarios are used to deal with uncertainty.
The branch-and-bound optimization algorithm for mixed-integer model predictive control (MI-MPC) solves several convex quadratic program relaxations, but often the solutions are discarded based on already known integer...
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The branch-and-bound optimization algorithm for mixed-integer model predictive control (MI-MPC) solves several convex quadratic program relaxations, but often the solutions are discarded based on already known integer feasible solutions. This letter presents a projection and early termination strategy for infeasible interior point methods to reduce the computational effort of finding a globally optimal solution for MI-MPC. The method is shown to be also effective for infeasibility detection of the convex relaxations. We present numerical simulation results with a reduction of the total number of solver iterations by 42% for an MI-MPC example of decision making for automated driving with obstacle avoidance constraints.
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