The aim of the present paper is to provide (n-1)-reliability to a power grid, guaranteeing nominal operation after the failure of any one out of n present grid components. Building on previous work (Fliscounakis et al...
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ISBN:
(纸本)9781910963104
The aim of the present paper is to provide (n-1)-reliability to a power grid, guaranteeing nominal operation after the failure of any one out of n present grid components. Building on previous work (Fliscounakis et al., IEEE Transactions on Power Systems, 2013), a hierarchical programming problem is proposed to characterize the worst-case behavior of a power grid under a given contingency. The formulation is a mixed integer linear generalized semi-infinite program with a max-min program embedded. The different levels correspond to the choice of preventive actions, realization of uncertainties in the power supply and demand, and the choice of corrective actions. In order to model active components of the grid, models are proposed for load balancing and the behavior of phase-shifting transformers. Since no rigorous solution approaches are published for the problem at hand, the possibility of extending generalized semi infinite programming approaches to the present problem is discussed.
We address the minimization of an objective function over the solution set of a (non-parametric) lower-level variational inequality. This problem is a special instance of semi-infinite programs and encompasses, as par...
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We address the minimization of an objective function over the solution set of a (non-parametric) lower-level variational inequality. This problem is a special instance of semi-infinite programs and encompasses, as particular cases, simple (smooth) bilevel and equilibrium selection problems. We resort to a suitable approximated version of the hierarchical problem. We show that this, on the one hand, does not perturb the original (exact) program 'too much', on the other hand, allows one to rely on some suitable exact penalty approaches whose convergence properties are established.
Approximately twenty years ago the modern interest for hierarchical programming was initiated by J. Bracken and J.M. McGill [9], [10]. The activities in the field have ever grown lively, both in terms of theoretical d...
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Approximately twenty years ago the modern interest for hierarchical programming was initiated by J. Bracken and J.M. McGill [9], [10]. The activities in the field have ever grown lively, both in terms of theoretical developments and terms of the diversity of the applications. The collection of seven papers in this issue covers a diverse number of topics and provides a good picture of recent research activities in the field of bilevel and hierarchical programming. The papers can be roughly divided into three categories;Linear bilevel programming is addressed in the first two papers by Gendreau et al and Moshirvaziri et al;The following three papers by Nicholls, Loridan & Morgan, and Kalashnikov & Kalashnikova are concerned with nonlinear bilevel programming;and, finally, Wen & Lin and Nagase & Aiyoshi address hierarchical decision making issues relating to both biobjective and bilevel programming.
Motivated by the increasing need to hedge against load and generation uncertainty in the operation of power grids, we propose flexibility maximization during operation. We consider flexibility explicitly as the amount...
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Motivated by the increasing need to hedge against load and generation uncertainty in the operation of power grids, we propose flexibility maximization during operation. We consider flexibility explicitly as the amount of uncertainty that can be handled while still ensuring nominal grid operation in the worst case. We apply the proposed flexibility optimization in the context of a DC flow approximation. By using a corresponding parameterization, we can find the maximal range of uncertainty and a range for the manageable power transfer between two parts of a network subject to uncertainty. We formulate the corresponding optimization problem as an (existence-constrained) semi-infinite optimization problem and specialize an existing algorithm for its solution.
We consider a generalized Nash equilibrium problem whose joint feasible region is implicitly defined as the solution set of another Nash game. This structure arises, e.g., in multiportfolio selection contexts, wheneve...
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We consider a generalized Nash equilibrium problem whose joint feasible region is implicitly defined as the solution set of another Nash game. This structure arises, e.g., in multiportfolio selection contexts, whenever agents interact at different hierarchical levels. We consider nonsmooth terms in all players' objectives, to promote, for example, sparsity in the solution. Under standard assumptions, we show that the equilibrium problems we deal with have a nonempty solution set and turn out to be jointly convex. To compute variational equilibria, we devise different first-order projection Tikhonov-like methods whose convergence properties are studied. We provide complexity bounds and equip our analysis with numerical tests using real-world financial datasets.
The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathema...
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The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, quantile minimization, and a"" (0) minimization, the LPCC provides a gateway to a mathematical program with equilibrium constraints, which itself is an important class of constrained optimization problems that has broad applications. We describe several approaches for the global resolution of the LPCC, including a logical Benders approach that can be applied to problems that may be infeasible or unbounded.
This paper examines the problem of scheduling of inbound trucks to the inbound doors at a cross-docking facility. The authors optimize for two conflicting objectives: minimize the total service time for all the inboun...
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This paper examines the problem of scheduling of inbound trucks to the inbound doors at a cross-docking facility. The authors optimize for two conflicting objectives: minimize the total service time for all the inbound trucks and minimize the delayed completion of service for a subset of the inbound trucks, which are considered as preferential customers. The problem is formulated as a bi-objective and as a bi-level mixed integer problem. Due to the nature of the former and the complexity of the latter formulation, a genetic algorithm and a k-th best based algorithm are proposed as the solution approaches. Computational examples are used to discuss the advantages and drawbacks of each formulation.
In this paper, cooperative problem-solving in Distributed Artificial Intelligent System is analyzed. A formal model for Multi-Node Cooperative Processing is proposed. programming for multi—intelligent—node cooperati...
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In this paper, cooperative problem-solving in Distributed Artificial Intelligent System is analyzed. A formal model for Multi-Node Cooperative Processing is proposed. programming for multi—intelligent—node cooperative solving of well-structured problem is studied. An hierarchical programming approach of multi—intelligent—node cooperative solving is put forward. A processing model is built up. And finally, cooperative solving process and steps are given.
The programming language MODULA is extended to permit the formal specification of the structure and functional capabilities of modules. This makes true hierarchical programming possible in MODULA by allowing programme...
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This paper presents how the hierarchical decision structure can be effectively used for modeling and solving an environmental-economic thermal power generation and dispatch problems in a fuzzy decision environment. In...
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ISBN:
(纸本)9788132222507;9788132222491
This paper presents how the hierarchical decision structure can be effectively used for modeling and solving an environmental-economic thermal power generation and dispatch problems in a fuzzy decision environment. In the proposed approach, minimization of the functions of fuel-cost, environmental-emission and transmission-loss are considered at the three hierarchical levels to solve the problem within a power plant operational system. In the model formulation, a priority based linear fuzzy goal programming (LFGP) method is employed to achieve the highest membership value (unity) of the defined fuzzy goals to the extent possible on the basis of priorities in the decision making horizon. To illustrate the effective use of the approach, the problem of standard IEEE 6-Generator 30-Bus System is considered.
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