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  • Articles: DFG German National Licenses  (26)
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  • Articles  (26)
  • Other Sources
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  • Articles: DFG German National Licenses  (26)
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  • Springer  (26)
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  • 1995-1999
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  • 1
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    Mathematical programming 53 (1992), S. 323-338 
    ISSN: 1436-4646
    Keywords: Random search ; Monte Carlo optimization ; global optimization ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space. That is, at any iteration, the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence. The complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution. We show that for global mathematical programs satisfying the Lipschitz condition, its complexity increases at mostlinearly in the dimension of the problem.
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  • 2
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    Mathematical programming 56 (1992), S. 51-64 
    ISSN: 1436-4646
    Keywords: Non-convex quadratic programming problem ; global optimization ; parametric simplex algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An algorithm for solving a linear multiplicative programming problem (referred to as LMP) is proposed. LMP minimizes the product of two linear functions subject to general linear constraints. The product of two linear functions is a typical non-convex function, so that it can have multiple local minima. It is shown, however, that LMP can be solved efficiently by the combination of the parametric simplex method and any standard convex minimization procedure. The computational results indicate that the amount of computation is not much different from that of solving linear programs of the same size. In addition, the method proposed for LMP can be extended to a convex multiplicative programming problem (CMP), which minimizes the product of two convex functions under convex constraints.
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  • 3
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    Mathematical programming 57 (1992), S. 203-214 
    ISSN: 1436-4646
    Keywords: 90C30 ; 68Q15 ; 90C20 ; 90C25 ; 52A25 ; global optimization ; quadratic programming ; unique optimum ; polytope ; parallelotope ; norm ; NP-hardness ; diameter ; width ; inradius ; circumradius
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract NP-hardness is established for the problem whose instance is a system of linear inequalities defining a polytopeP, and whose question is whether, onP, the global maximum of the Euclidean norm is attained at more than one vertex ofP. The NP-hardness persists even for the restricted problem in whichP is a full-dimensional parallelotope with one vertex at the origin. This makes it possible to establish NP-hardness for other uniqueness problems, including some from pseudoboolean programming and computational convexity.
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  • 4
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    Journal of intelligent manufacturing 3 (1992), S. 43-57 
    ISSN: 1572-8145
    Keywords: Machine learning ; simulation ; flexible manufacturing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper describes a synergistic approach that is applicable to a wide variety of system control problems. The approach utilizes a machine learning technique, goal-directed conceptual aggregation (GDCA), to facilitate dynamic decision-making. The application domain employed is Flexible Manufacturing System (FMS) scheduling and control. Simulation is used for the dual purpose of providing a realistic depiction of FMSs, and serves as an engine for demonstrating the viability of a synergistic system involving incremental learning. The paper briefly describes prior approaches to FMS scheduling and control, and machine learning. It outlines the GDCA approach, provides a generalized architecture for dynamic control problems, and describes the implementation of the system as applied to FMS scheduling and control. The paper concludes with a discussion of the general applicability of this approach.
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  • 5
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    Journal of intelligent manufacturing 3 (1992), S. 193-204 
    ISSN: 1572-8145
    Keywords: Neural networks ; simulation ; continuous improvement systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The use of a neural network embedded in a larger general-purpose simulation system (GPSS) simulation used to model continuous improvement systems (CIS) policies in a factory setting is described. The neural network is used to accelerate the identification of an effective CIS policy by providing a more realistic simulation framework. The interface between general simulation theory and neural network simulation is examined. Neural networks, when embedded in larger general-purpose simulations, are found to offer the potential for improving on the capabilities of those simulations, in particular manufacturing simulations for continuous improvement of production processes.
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  • 6
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    Journal of intelligent manufacturing 3 (1992), S. 263-276 
    ISSN: 1572-8145
    Keywords: parallel distributed ; processing ; simulation ; object-oriented programming systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The field of neural networks is being investigated by many researchers in order to provide solutions to difficult problems in the area of manufacturing systems. Computer simulation of neural networks is an important part of this investigation. This paper applies concepts from an important trend in software engineering research, namely object-oriented programming, to model neural networks. The design and implementation of a software object library is crucial to obtaining the full benefits of object-oriented programming. In this paper we discuss the design and implementation of a foundation library of software objects for the purpose of simulating and validating different network architectures and learning rules. The library contains objects that implement various types of nodes and learning rules. We discuss the results of our experiments to illustrate the benefits of using an object-oriented approach to modeling neural networks.
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  • 7
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    Annals of operations research 39 (1992), S. 157-172 
    ISSN: 1572-9338
    Keywords: Score function method ; likelihood ratio ; sensitivity analysis ; simulation ; Monte Carlo methods ; conditioning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider first a discrete event static system that is to be simulated at values of a parameter or vector of parametersθ. The system is assumed driven by an inputX, where typicallyX is a vector of variables whose densityf θ (x) depends on the parameterθ. For the purpose of optimizing, finding roots, or graphing the expected performanceE θ L(X) for performance measureL, it is useful to estimate not only the expected value but also its gradient. An unbiased estimator for the latter is the score function estimator $$L(X)S(\theta ) = L(X)\frac{\partial }{{\partial \theta }}\ln f_\theta (x).$$ This estimator and likelihood ratio analogues typically require variance reduction, and we consider conditioning on the value of the score function for this purpose. The efficiency gains due to performing the Monte Carlo conditionally can be very large. Extension to discrete event dynamic systems such as theM/G/1 queue and other more complicated systems is considered.
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  • 8
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    International journal of flexible manufacturing systems 4 (1992), S. 113-127 
    ISSN: 1572-9370
    Keywords: Flexible manufacturing ; simulation ; rules ; heuristics ; fuzzy logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This article reports an investigation into part-input methods for an implemented flexible flow system (FFS). Two new dynamic methods—look-ahead simulation and a fuzzy heuristic rule base—are compared to three simple myopic static sequencing rules and one dynamic rule. It is shown using simulation that for the existing system, the best sequence generated from the minimum production set performs very well, but the dynamic methods outperform the sequence when the system is modified and the sequence is unaltered. It is concluded that for a stable FFS, the static determination of the best input sequence is appropriate, but that a rapidly changing FFS—due to machine breakdown, changes in production requirements, etc.—may benefit from a dynamic part-input method. The look-ahead simulation outperforms the fuzzy rule base, and appears to be a more promising dynamic method. Suggestions for future research and evaluation are given.
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  • 9
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    Annals of operations research 39 (1992), S. 1-39 
    ISSN: 1572-9338
    Keywords: Stochastic programming ; stochastic quasigradient methods ; discrete event systems ; simulation ; concurrent approximation and optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported.
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  • 10
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    Mathematical programming 53 (1992), S. 339-359 
    ISSN: 1436-4646
    Keywords: Concave cost ; hierarchical structure ; uncapacitated network ; nonconvex decomposition ; pricing mechanism ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we develop a decomposition method using a pricing mechanism which has been widely applied to linear and convex programs for a class of nonconvex optimization problems that are min concave cost flow problems under directed, uncapacitated networks with a hierarchical structure.
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  • 11
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    Journal of intelligent and robotic systems 5 (1992), S. 49-62 
    ISSN: 1573-0409
    Keywords: Off-line programming ; robot programming ; simulation ; computer graphics ; sensor programming ; sensor modeling ; robotics ; world modeling ; calibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The programming of robots is slowly evolving from traditional teach pendant methods to graphical Off-Line Programming (OLP) methods. Graphical simulation tools, such as OLP, are very useful for developing and testing robot programs before they are run on real industrial equipment. OLP systems are also used to develop task level programs. Traditional OLP systems, however, suffer from the limitations of using only position control which does not account for inherent robot inaccuracies and dynamic environments. This paper describes our work on improving and supplementing traditional position control programming methods. A baseline OLP system was implemented at NIST's Automated Manufacturing Research Facility (AMRF). Experience gained in implementing this system showed that an effective OLP system must accurately simulate the real world and must support sensor programming to compensate for real-world changes that cannot be simulated. The developed OLP geometric world model is calibrated using robot mounted ultrasound ranging sensors. This measurement capability produces a baseline geometric model of relatively good static accuracy for off-line programming. The graphical environment must also provide representations of sensor features. For this specific application, force is simulated in order to include force based commands in our robot programs. These sensor based programs are able to run reliably and safely in an unpredictable industrial environment. The last portion of this paper extends OLP and describes the functionality of a complete system for programming complex robot tasks.
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  • 12
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    Mathematical geology 3 (1971), S. 281-295 
    ISSN: 1573-8868
    Keywords: analysis of variance ; autocorrelation ; simulation ; trend analysis ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is proposed that the variance in mapped geologic data should be formally considered to be composed of three components which arise on different geographic scales. The three components (regional, local, and residual) should be defined solely in terms of the parameters of the sample data set. A two-step analysis is required to separate three components. Applying autocorrelation criteria, trend-surface analysis has been used, in the first step, to remove the residual component and, in the second step, to separate regional and local components from the resulting noise-free data. This procedure has made it possible to quantify local components in stratigraphic thickness data from the East Midlands coalfield (central England) which can be identified in terms of the known geology.
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  • 13
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    Mathematical geology 3 (1971), S. 239-263 
    ISSN: 1573-8868
    Keywords: simulation ; hydrology ; petroleum ; sedimentology ; high fluid pressures ; compaction ; primary migration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A mathematical model of sedimentation and compaction of fine-grained rocks such as shale has been constructed. Water is considered to flow upward or downward out of a compacting rock according to Darcy's law until the pore-water pressure within the rock is normal for the depth in question. The porosity decreases during compaction until a minimum porosity, determined by the difference between total vertical stress (overburden pressure) and pore-water pressure, is obtained. The model takes into account the dependence of permeability on porosity for a given rock type, and the dependence of water viscosity on salinity, temperature, and pressure. The derived equations have been computer programmed to obtain the time dependence of porosity, pressure, water velocity, permeability, and other factors within a compacting shale during (a) shale sedimentation, (b) a time lapse following shale deposition, (c) the deposition of normally pressured sediments over the shale, and (d) a second time lapse following deposition of the normally pressured unit. Solutions to these problems are given for the situation when the unit underlying the shale is normally pressured, and for the situation when the underlying unit is impermeable. The calculations show that a portion of a thick shale adjacent to a normally pressured unit may have a considerably reduced porosity and permeability, and act as a seal for the remainder of the shale. High fluid pressures may persist for many millions of years in thick shales with low permeability. The computations can be extended to cover more complicated cases of interbedded shales, sands, and other lithologies.
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  • 14
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    Mathematical geology 3 (1971), S. 265-279 
    ISSN: 1573-8868
    Keywords: simulation ; mathematical models ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract To study sedimentary phenomena, we introduce random-genetic models in which genetic hypotheses and structural random elements occur for the main part. Starting from geologic hypotheses we choose principal factors which may be random functions or random variables. These factors are: depth, nature of the facies, sedimentation rate, and subsidence. Equations of evolution link the factors. Depth is a Markov process, but generally the resultant sequence does not make a Markov chain or Markov process. Three examples of such models are given with the results of simulations.
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  • 15
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    Mathematical geology 24 (1992), S. 99-128 
    ISSN: 1573-8868
    Keywords: correlation ; fractal functions ; fractional Brownian bridges ; hydrology ; expert input ; mining ; Monte Carlo ; nonstationary ; probability ; random walk ; reservoir engineering ; risk analysis ; sampling ; simulation ; stochastic process ; trajectory ; waste cleanup
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper describes a new method of analyzing the risk incurred when the outcome of a decision depends on interpolated values, for example, on the flow through an aquifer sparsely sampled for permeability or on the ratio of waste to ore in a mineral deposit sparsely sampled for grade. The method uses large families of interpolations constructed between sample values using adaptations of the well-known midpoint displacement method for generating pseudo-fractional Brownian motion trajectories. The parameters defining each family are chosen interactively by specialists to incorporate their expert knowledge. Each family, or ensemble, then defines a population of values for any global characteristic (functional) such as flow rate or waste ratio. The probabilities of various outcomes are estimated by counting them and calculating their ratios. For example, if 900 out of 1000 are acceptable the chance of success is estimated to be 90%.
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  • 16
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    Journal of global optimization 2 (1992), S. 41-60 
    ISSN: 1573-2916
    Keywords: Quadratic program ; bilinear program ; global optimization ; reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Indefinite quadratic programs with quadratic constraints can be reduced to bilinear programs with bilinear constraints by duplication of variables. Such reductions are studied in which: (i) the number of additional variables is minimum or (ii) the number of complicating variables, i.e., variables to be fixed in order to obtain a linear program, in the resulting bilinear program is minimum. These two problems are shown to be equivalent to a maximum bipartite subgraph and a maximum stable set problem respectively in a graph associated with the quadratic program. Non-polynomial but practically efficient algorithms for both reductions are thus obtaine.d Reduction of more general global optimization problems than quadratic programs to bilinear programs is also briefly discussed.
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  • 17
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    Mathematical methods of operations research 36 (1992), S. 477-495 
    ISSN: 1432-5217
    Keywords: Cost-oriented assembly line balancing ; heuristic algorithms ; worst-case analysis ; simulation ; NP-completeness ; time complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Two new heuristic algorithms for solving cost-oriented assembly line balancing problems -the Wage-Rate-Method (WR) and the Wage-Rate-Smoothing-Method (WRS) — are presented and compared with two known heuristics — the Positional-Weight-Method (PW) and the Positional-Weight-Wage-Rate-Difference-Method (PWWD) with respect to their solution qualities. Firstly, the heuristics are outlined and their computational effort is stated. Then, a theoretical worst-case bound for the solution quality is given and the results of an extensive performance study are reported. In the study the heuristics were investigated with respect to their solution quality by solving randomly generated line balancing problems and problems from literature. It can be concluded that PWWD and WRS are generally superior to PW and WR.
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  • 18
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    Journal of optimization theory and applications 73 (1992), S. 47-64 
    ISSN: 1573-2878
    Keywords: Multiple-criteria decision making ; extreme-point search ; global optimization ; efficient set ; nonconvex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem (P) of optimizing a linear function over the efficient set of a multiple-objective linear program serves many useful purposes in multiple-criteria decision making. Mathematically, problem (P) can be classified as a global optimization problem. Such problems are much more difficult to solve than convex programming problems. In this paper, a nonadjacent extreme-point search algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact extreme-point optimal solution for the problem after a finite number of iterations. It can be implemented using only linear programming methods. Convergence of the algorithm is proven, and a discussion is included of its main advantages and disadvantages.
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  • 19
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    Journal of global optimization 2 (1992), S. 259-280 
    ISSN: 1573-2916
    Keywords: Primary: 65K10 ; Secondary: 65G10 ; Nonlinear algebraic systems ; Newton's method ; interval arithmetic ; Gauss-Seidel method ; global optimization ; singularities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose modifications to a prototypical branch and bound algorithm for nonlinear optimization so that the algorithm efficiently handles constrained problems with constant bound constraints. The modifications involve treating subregions of the boundary identically to interior regions during the branch and bound process, but using reduced gradients for the interval Newton method. The modifications also involve preconditioners for the interval Gauss-Seidel method which are optimal in the sense that their application selectively gives a coordinate bound of minimum width, a coordinate bound whose left endpoint is as large as possible, or a coordinate bound whose right endpoint is as small as possible. We give experimental results on a selection of problems with different properties.
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  • 20
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    Journal of optimization theory and applications 73 (1992), S. 547-562 
    ISSN: 1573-2878
    Keywords: Nonlinear optimal control ; nonlinear programming ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract To determine the optimum in nonlinear optimal control problems, it is proposed to convert the continuous problems into a form suitable for nonlinear programming (NLP). Since the resulting finite-dimensional NLP problems can present multiple local optima, a global optimization approach is developed where random starting conditions are improved by using special line searches. The efficiency, speed, and reliability of the proposed approach is examined by using two examples.
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  • 21
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    Journal of optimization theory and applications 75 (1992), S. 423-432 
    ISSN: 1573-2878
    Keywords: Multilevel methods ; global optimization ; Monte Carlo methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach to the global optimization of functions with extremely rugged graphs is introduced. This multilevel search method is both an algorithm and a meta-algorithm, a logic for regulating optimization done by other algorithms. First, it is examined in the one-dimensional case theoretically and through simple examples. Then, to deal with higher dimensions, multilevel search is combined with the Monte Carlo method; this hybrid algorithm is tested on standard problems and is found to perform extremely well for a derivative-free method.
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  • 22
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    Journal of global optimization 2 (1992), S. 281-311 
    ISSN: 1573-2916
    Keywords: Renormalization group ; global optimization ; conformation ; microcluster ; annealing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We outline a new global minimization method in which the Gibbs distribution of the objective function is deterministically annealed by tracing the evolution of a multiple-Gaussian-packet approximation. Solutions are reached by iterative approximations with decreasing coarse-graining of both objective-function and spatial scales. Results from application of a partial implementation to the atomic-microcluster conformation problem are presented.
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  • 23
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    Journal of global optimization 2 (1992), S. 379-410 
    ISSN: 1573-2916
    Keywords: Bilinear programming ; nonconvex programming ; global optimization ; branch-and-bound ; reformulation-linearization technique
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the development of an algorithm for general bilinear programming problems. Such problems find numerous applications in economics and game theory, location theory, nonlinear multi-commodity network flows, dynamic assignment and production, and various risk management problems. The proposed approach develops a new Reformulation-Linearization Technique (RLT) for this problem, and imbeds it within a provably convergent branch-and-bound algorithm. The method first reformulates the problem by constructing a set of nonnegative variable factors using the problem constraints, and suitably multiplies combinations of these factors with the original problem constraints to generate additional valid nonlinear constraints. The resulting nonlinear program is subsequently linearized by defining a new set of variables, one for each nonlinear term. This “RLT” process yields a linear programming problem whose optimal value provides a tight lower bound on the optimal value to the bilinear programming problem. Various implementation schemes and constraint generation procedures are investigated for the purpose of further tightening the resulting linearization. The lower bound thus produced theoretically dominates, and practically is far tighter, than that obtained by using convex envelopes over hyper-rectangles. In fact, for some special cases, this process is shown to yield an exact linear programming representation. For the associated branch-and-bound algorithm, various admissible branching schemes are discussed, including one in which branching is performed by partitioning the intervals for only one set of variables x or y, whichever are fewer in number. Computational experience is provided to demonstrate the viability of the algorithm. For a large number of test problems from the literature, the initial bounding linear program itself solves the underlying bilinear programming problem.
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  • 24
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    Journal of global optimization 2 (1992), S. 21-40 
    ISSN: 1573-2916
    Keywords: Complementary convex structure ; Generalized Rank k Property ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show the importance of exploiting the complementary convex structure for efficiently solving a wide class of specially structured nonconvex global optimization problems. Roughly speaking, a specific feature of these problems is that their nonconvex nucleus can be transformed into a complementary convex structure which can then be shifted to a subspace of much lower dimension than the original underlying space. This approach leads to quite efficient algorithms for many problems of practical interest, including linear and convex multiplicative programming problems, concave minimization problems with few nonlinear variables, bilevel linear optimization problems, etc...
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    Statistics and computing 2 (1992), S. 25-36 
    ISSN: 1573-1375
    Keywords: Reasoning under uncertainty ; causal probabilistic network ; influence diagram ; belief network ; knowledge-based systems ; evidence ; fast retraction ; maxinlization ; explanation ; simulation ; junction tree ; charge ; potential function ; flow ; propagation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A probabilistic expert system provides a graphical representation of a joint probability distribution which can be used to simplify and localize calculations. Jensenet al. (1990) introduced a ‘flow-propagation’ algorithm for calculating marginal and conditional distributions in such a system. This paper analyses that algorithm in detail, and shows how it can be modified to perform other tasks, including maximization of the joint density and simultaneous ‘fast retraction’ of evidence entered on several variables.
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    Statistics and computing 2 (1992), S. 7-17 
    ISSN: 1573-1375
    Keywords: Simulated annealing ; global optimization ; Monte Carlo algorithms ; graph decomposition ; probabilistic networks ; NP-complete problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper investigates the applicability of a Monte Carlo technique known as ‘simulated annealing’ to achieve optimum or sub-optimum decompositions of probabilistic networks under bounded resources. High-quality decompositions are essential for performing efficient inference in probabilistic networks. Optimum decomposition of probabilistic networks is known to be NP-hard (Wen, 1990). The paper proves that cost-function changes can be computed locally, which is essential to the efficiency of the annealing algorithm. Pragmatic control schedules which reduce the running time of the annealing algorithm are presented and evaluated. Apart from the conventional temperature parameter, these schedules involve the radius of the search space as a new control parameter. The evaluation suggests that the inclusion of this new parameter is important for the success of the annealing algorithm for the present problem.
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