The purpose of this paper is to consider a class of nonsmooth minimax fractional semi-infinite programming problem. Based on the concept of H - tangent derivative, a new generalization of convexity, namely generalized...
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This article offers a spreadsheet/integer programming approach for teachinglot-sizing decisions. Unlike the W-W approach, this spreadsheet method allows students to readilyunderstand the concept of the mixed-integer p...
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This article offers a spreadsheet/integer programming approach for teachinglot-sizing decisions. Unlike the W-W approach, this spreadsheet method allows students to readilyunderstand the concept of the mixed-integer programming. One of the strengths of this method is toimmediately solve the lot-sizing problems without introducing complicated mathematical *** order to clarify the effectiveness of our spreadsheet approach, we compared ours with othermethods. It is shown that among the lot-sizing methods considered, the spreadsheet integerprogramming yields the least sum of total carrying and ordering costs. Conclusively, the spreadsheetformulation approach provides three major advantages for POM classes: (1) the output of thespreadsheet formulation guarantees optimal results, (2) the spreadsheet is user-friendly, and (3)the spreadsheet program (e.g., Excel Solver) is readily available for use. Given these advantages,the use of the spreadsheet can play a vital role in solving the problems related to MRP lot-sizingdecisions and in achieving POM pedagogical concepts.
Optimal experiment design is usually performed as a search over a finitely-parameterized shape that (over-) approximates the confidence region of parameters of a model. In general, there exists no such shape to exactl...
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Optimal experiment design is usually performed as a search over a finitely-parameterized shape that (over-) approximates the confidence region of parameters of a model. In general, there exists no such shape to exactly enclose the confidence region of a nonlinear parameter estimation problem. Due to this fact, the design-of-experiment techniques are not well established for this problem and approximate designs are conducted. In this contribution, assuming Gaussian (normally distributed) noise, we propose and study (a) two schemes to over-approximate the confidence region of parameters using an ellipsoid and an orthotope and (b) a framework for optimal experiment design. We formulate the over-approximation of the confidence region as an optimization problem. The optimal experiment design is then proposed as a bi-level optimization problem. In line with the existing optimal experiment design methodology for a linear parameter estimation problem, we also propose several design criteria that optimize some measure of the over-approximated confidence region for the nonlinear case. The proposed bi-level optimization problem is solved (i) as a nonlinear programming problem using the necessary conditions for optimality or (ii) as a nested problem with globally optimized inner-level problem. We illustrate the proposed schemes on a benchmark test case. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
In this paper we study cascading blackouts in power transmission networks due to spatially localized load anomalies. The term "spatially localized load anomalies" means that the overloaded nodes in the graph...
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ISBN:
(纸本)9783642035517
In this paper we study cascading blackouts in power transmission networks due to spatially localized load anomalies. The term "spatially localized load anomalies" means that the overloaded nodes in the graph representing the power transmission network are concentrated in a small zone of the graph. Typically these anomalies are caused by extreme weather conditions localized in some parts of the region served by the power transmission network. We generalize a mathematical formulation of the cascading blackout problem introduced in [1] and later developed in [2]. This mathematical formulation of the blackout problem when the load of the network is perturbed randomly allows the study of the probability density functions of the measure of the size of the blackout generated and of the occupation of the network lines. The analysis presented shows that spatially localized load anomalies of a given "magnitude" can generate blackouts of larger size than the blackouts generated by a load anomaly of the same magnitude distributed proportionally oil the entire network. Load anomalies of this last type have been studied in [1], [2]. The previous results are obtained studying the behaviour of the Italian high voltage power transmission network through some numerical experiments.
In this paper, a new meta-heuristic method of finding roots and poles of a complex function of a complex variable is presented. The algorithm combines an efficient space exploration provided by the particle swarm opti...
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ISBN:
(纸本)9788394942175
In this paper, a new meta-heuristic method of finding roots and poles of a complex function of a complex variable is presented. The algorithm combines an efficient space exploration provided by the particle swarm optimization (PSO) and the classification of root and pole occurrences based on the phase analysis of the complex function. The method initially generates two uniformly distributed populations of particles on the complex plane and extracts the function phase in a position of each particle. By collecting phase samples, the candidate regions of root and pole occurrences are selected. Then, the second population, by iteratively converging towards candidate regions, thoroughly explores an area outside candidate regions and reduces the possibility of root or pole omission. The subsequent swarms are generated locally to explore candidate regions and decrease their size. The algorithm is verified in electromagnetic benchmark that solves the equation determining surface waves on a microstrip antenna. The numerical results show that the algorithm is able to solve multimodal problems quickly even with a small initial population and a small number of generated swarms.
A function with one integer variable is defined to be integer convex by Fox [3] and Denardo [1] if its second forward differences are positive. In this paper, condense discrete convexity of nonlinear discrete multivar...
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ISBN:
(纸本)9783642206610
A function with one integer variable is defined to be integer convex by Fox [3] and Denardo [1] if its second forward differences are positive. In this paper, condense discrete convexity of nonlinear discrete multivariable functions with their corresponding Hessian matrices is introduced which is a generalization of the integer convexity definition of Fox [3] and Denardo [1] to higher din-tensional space Z(n). In addition, optimization results are proven for C-1 condense discrete convex functions assuming that the given condense discrete convex function is C-1. Yuceer [17] proves convexity results for a certain class of discrete convex functions and shows that the restriction of the adaptation of Rosenbrook's function from real variables to discrete variables does not yield a discretely convex function. Here it is shown that the adaptation of Rosenbrook's function considered in [17] is a condense discrete convex function where the set of local minimums is also the the set of global minimums.
In 1994 Herbelin started and partially achieved the programme of showing that, for intuitionistic implicational logic, there is a Curry-Howard interpretation of sequent calculus into a variant of the lambda-calculus, ...
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ISBN:
(纸本)9783540732273
In 1994 Herbelin started and partially achieved the programme of showing that, for intuitionistic implicational logic, there is a Curry-Howard interpretation of sequent calculus into a variant of the lambda-calculus, specifically a variant which manipulates formally "applicative contexts" and inverts the associativity of "applicative terms". Herbelin worked with a fragment of sequent calculus with constraints on left introduction. In this paper we complete Herbelin's programme for full sequent calculus, that is, sequent calculus without the mentioned constraints, but where permutative conversions necessarily show up. This requires the introduction of a lambda-like calculus for full sequent calculus and an extension of natural deduction that gives meaning to "applicative contexts" and "applicative terms". Such extension is a calculus with modus ponens and primitive substitution that refines von Plato's natural deduction;it is also a "coercion calculus", in the sense of Cervesato and Pfenning. The proof-theoretical outcome is noteworthy: the puzzling relationship between cut and substitution is settled;and cut-elimination in sequent calculus is proven isomorphic to normalisation in the proposed natural deduction system. The isomorphism is the mapping that inverts the associativity of applicative terms.
Day-ahead scheduling of hybrid power plants with renewable energy resources is inherently associated with uncertainties. We therefore show how to formulate the problem as a two-stage stochastic optimization. To hedge ...
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ISBN:
(纸本)9781538645055
Day-ahead scheduling of hybrid power plants with renewable energy resources is inherently associated with uncertainties. We therefore show how to formulate the problem as a two-stage stochastic optimization. To hedge against low profits or even losses, risk averse scheduling is achieved by including risk measures like the (conditional) value at risk into the objective. However, a standard formulation of this approach entails multiple drawbacks, e.g., large sample sizes are required to correctly capture the tails of the profit distribution. To overcome these deficiencies we propose two new methods based on the principles of the recently introduced Robust Common Rank Approximation. The methods are based on efficient scenario reduction with the aid of a simplified, quickly computable proxy model of the full system. We demonstrate dramatically reduced computation times at similar or even superior solution quality with simulations of a hybrid power plant located at the French Antilles.
This is an investigation into how optimal production rates and optimal price levels react to the introduction of an environmental tax on emissions. While, in the case of perfect competition, a linear tax has no effect...
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Maintenance of the power generating facilities in due time is essential for economical and reliable operation of the power system. Economical aspects, which bring revenue, and technical aspects, which keep the power s...
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ISBN:
(纸本)9781424417636
Maintenance of the power generating facilities in due time is essential for economical and reliable operation of the power system. Economical aspects, which bring revenue, and technical aspects, which keep the power system above the desired level of reliability, have to be confronted and the cheapest solution, which complies with the strict technical limitations, has to be obtained. This paper addresses the problem of obtaining the optimal maintenance schedule for generating units. For this purpose, this paper discusses the mathematical programming method Benders decomposition. After the brief description, an application of the Benders decomposition on the three Croatian hydroelectric power plants in a row on the river Drava is carried Out.
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