Considering the constrain on VaR, laws, regulations and operation, using combination profits maximum of bank as objective function, applying the backward induction idea of multi - period assets allocation and linear p...
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Considering the constrain on VaR, laws, regulations and operation, using combination profits maximum of bank as objective function, applying the backward induction idea of multi - period assets allocation and linearprogramming method, the dynamic optimization model of bank asset combination is set up. There are some characteristics and innovations in this paper. The characteristics lie on four aspects. Firstly, by using backward induction method, the combination of this period is set up based on the combination of the next period. And then such problems as the neglect or lack consideration of the interaction of each period can be solved. Secondly, it is taken into account that the earning rate of this period will be affected by loan credit migration of the former period. Then in this study the earning rates of different levels and the probability of risk migration for one year are used to obtain the earning rates of every corporation each year and mean square deviations. It can objectively reflect the actual combination and risk. As a result, the neglect of the earning rates is avoided. Finally, the combination risk of multi-period loan is controlled by the introduction of VaR constrain. Then the lack consideration of the bank's risk tolerance ability and the demand of capital intendance in present multi-period study are avoided.
This paper provides a new methodology to solve bilinear, non-convex mathematical programming problems by a suitable transformation of variables. Schur's decomposition and special ordered sets (SOS) type 2 constrai...
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This paper provides a new methodology to solve bilinear, non-convex mathematical programming problems by a suitable transformation of variables. Schur's decomposition and special ordered sets (SOS) type 2 constraints are used resulting in a mixed integer linear or quadratic program in the two applications shown. While Beale, Tomlin and others developed the use of SOS type 2 variables to handle non-convexities, our approach is novel in two aspects. First, the use of Schur's decomposition as an integral part of the approximation step is new and leads to a numerically viable method to separate the variables. Second, the combination of our approach for handling bilinear side constraints in a complementarity or equilibrium problem setting is also new and opens the way to many interesting and realistic modi. cations to such models. We contrast our approach with other methods for solving bilinear problems also known as indefinite quadratic programs. From a practical point of view our methodology is helpful since no specialized procedures need to be created so that existing solvers can be used. The approach is illustrated with two engineering examples and the mathematical analysis appears in the Appendices. Journal of the Operational Research Society (2006) 57, 995-1004.
In this formulation, the objective function and operating constraints include the corona power-loss term. The objective function consists of three terms: cost of investment of new transmission lines, ohmic power loss ...
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In this formulation, the objective function and operating constraints include the corona power-loss term. The objective function consists of three terms: cost of investment of new transmission lines, ohmic power loss of new and existing lines, and corona-power loss of new lines. This combination of terms results in a non-linear objective function. The non-linear programming or the non-convex optimization technique is used to solve such large-scale practical problem. The new formulation has been applied to the 28-bus Jordanian high-voltage transmission network in order to test and justify its applicability. (C) 2003 Elsevier Ltd. All rights reserved.
We discuss computational enhancements for the low-rank semidefinite programming algorithm, including the extension to block semidefinite programs (SDPs), an exact linesearch procedure, and a dynamic rank reduction sch...
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We discuss computational enhancements for the low-rank semidefinite programming algorithm, including the extension to block semidefinite programs (SDPs), an exact linesearch procedure, and a dynamic rank reduction scheme. A truncated-Newton method is also introduced, and several preconditioning strategies are proposed. Numerical experiments illustrating these enhancements are provided on a wide class of test problems. In particular, the truncated-Newton variant is able to achieve high accuracy in modest amounts of time on maximum-cut-type SDPs.
This paper addresses classes of assembled printed circuit boards, which faces certain kinds of errors during its process of manufacturing. Occurrence of errors may lead the manufacturer to be in loss. The encountered ...
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This paper addresses classes of assembled printed circuit boards, which faces certain kinds of errors during its process of manufacturing. Occurrence of errors may lead the manufacturer to be in loss. The encountered problem has two objective functions, one is fractional and the other is a non-linear objective. The manufacturers are confined to maximize the fractional objective and to minimize the non-linear objective subject to stochastic and non-stochastic environment. This problem is decomposed into two problems. A solution approach to this model has been developed in this paper. Results of some test problems are provided.
One of the first multiple objective versions of the tabu search (TS) algorithm is proposed by the author. The idea of applying TS to multiple objective optimization is inspired from its solution structure. TS works wi...
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One of the first multiple objective versions of the tabu search (TS) algorithm is proposed by the author. The idea of applying TS to multiple objective optimization is inspired from its solution structure. TS works with more than one solution (neighbourhood solutions) at a time and this situation gives the opportunity to evaluate multiple objectives simultaneously in one run. The selection and updating stages are modified to enable the original TS algorithm to work with more than one objective. In this paper, the multiple objective tabu search (MOTS) algorithm is applied to multiple objective non-linear optimization problems with continuous variables using a simple neighbourhood strategy. The algorithm is applied to four mechanical components design problems. The results are compared with several other solution techniques including multiple objective genetic algorithms. It is observed that MOTS is able to find better and much wider spread of solutions than the reported ones. Copyright (c) 2005 John Wiley & Sons, Ltd.
The perturbed and constrained fuel-optimal impulsive rendezvous problem is formulated, developed, and solved. A non-linear programming model is established for the general perturbed fuel-optimal multiple-impulse time-...
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The perturbed and constrained fuel-optimal impulsive rendezvous problem is formulated, developed, and solved. A non-linear programming model is established for the general perturbed fuel-optimal multiple-impulse time-fixed rendezvous with path constraints, and a hybrid approach is proposed as a global and efficient optimization tool. A floating-coded genetic algorithm is employed in this hybrid approach to locate an initial reference solution for sequential quadratic programming (SQP) using a simplified analytical propagator. Subsequently, SQP is used to locate the accurate solution using numerical integration of the high-fidelity trajectory dynamic equations. The hybrid approach is evaluated in three test cases: (i) Holman rendezvous and Lambert rendezvous, (ii) a three-impulse homing rendezvous with and without communication window constraints, and (iii) a four- and five-impulse non-coplanar multi-revolution rendezvous. The results show that the hybrid approach is effective and efficient in optimizing the perturbed and constrained fuel-optimal multiple-impulse rendezvous.
We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-...
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We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters. (c) 2005 Elsevier B.V. All rights reserved.
In this paper, a heuristic algorithm, different from the Frank-Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, ...
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In this paper, a heuristic algorithm, different from the Frank-Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, the new method need not enumerate initially all feasible paths for all origin/destination (O/D) pairs, but can give all paths used between each O/D pair and the path flows accordingly while the new algorithm obtains an optimal traffic assignment. Some convergence issues of the new method is discussed in this paper. Numerical experiments show that the new method is efficient and robust. (c) 2005 Elsevier Inc. All rights reserved.
We have developed a sequential set of computational screens that may prove useful for evaluating analyte sets for their ability to accurately report on metabolic fluxes. The methodology is problem-centric in that the ...
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We have developed a sequential set of computational screens that may prove useful for evaluating analyte sets for their ability to accurately report on metabolic fluxes. The methodology is problem-centric in that the screens are used in the context of a particular metabolic engineering problem. That is, flux bounds and alternative flux routings are first identified for a particular problem, and then the information is used to inform the design of nuclear magnetic resonance (NMR) experiments. After obtaining the flux bounds via MILP, analytes are first screened for whether the predicted NMR spectra associated with various analytes can differentiate between different extreme point (or linear combinations of extreme point) flux solutions. The second screen entails determining whether the analytes provide unique flux values or multiple flux solutions. Finally, the economics associated with using different analytes is considered in order to further refine the analyte selection process in terms of an overall utility index, where the index summarizes the cost-benefit attributes by quantifying benefit (contrast power) per cost (e.g., NMR instrument time required). We also demonstrate the use of an alternative strategy, the Analytical Hierarchy Process, for ranking analytes based on the individual experimentalist's-generated weights assigned for the relative value of flux scenario contrast, unique inversion of NMR data to fluxes, etc. (C) 2006 Elsevier Inc. All rights reserved.
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