We study the almost sure asymptotic behaviour of decreasing stepsized stochastic algorithms used for the search of zeros of a function. We prove a law of the iterated logarithm, which gives the almost sure convergence...
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We study the almost sure asymptotic behaviour of decreasing stepsized stochastic algorithms used for the search of zeros of a function. We prove a law of the iterated logarithm, which gives the almost sure convergence rate of the algorithm, and we establish a quadratic strong law of large numbers. (C) 1998 Published by Elsevier Science B.V. All rights reserved.
This paper introduces ordinal hill climbing algorithms for addressing discrete manufacturing process design optimization problems using computer simulation models. Ordinal hill climbing algorithms combine the search s...
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This paper introduces ordinal hill climbing algorithms for addressing discrete manufacturing process design optimization problems using computer simulation models. Ordinal hill climbing algorithms combine the search space reduction feature of ordinal optimization with the global search feature of generalized hill climbing algorithms. By iteratively applying the ordinal optimization strategy within the generalized hill climbing algorithm framework, the resulting hybrid algorithm can be applied to intractable discrete optimization problems. Computational results on an integrated blade rotor manufacturing process design problem are presented to illustrate the application of the ordinal hill climbing algorithm. The relationship between ordinal hill climbing algorithms and genetic algorithms is also discussed. This discussion provides a framework for how the ordinal hill climbing algorithm fits into currently applied algorithms, as well as to introduce a bridge between the two algorithms.
Discrete manufacturing process design optimization curt be difficult, due to the large number of manufacturing process design sequences and associated input parameter setting combinations that exist. Generalized hill ...
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Discrete manufacturing process design optimization curt be difficult, due to the large number of manufacturing process design sequences and associated input parameter setting combinations that exist. Generalized hill climbing algorithms have been introduced to address such manufacturing design problems. Initial results with generalized hill climbing algorithms required the manufacturing process design sequence to be fixed with the generalized hill climbing algorithm used to identify optimal input parameter settings. This paper introduces a new neighborhood function that allows generalized hill climbing algorithms to be used to also identify the optimal discrete manufacturing process design sequence among a set of valid design sequences. The neighborhood function uses a switch function for all the input parameters, hence allows the generalized hill climbing algorithm to simultaneously optimize over both the design sequences and the inputs parameters. Computational results are reported with art integrated blade rotor discrete manufacturing process design problem under study at the Materials Process Design. Branch of the Air Force Research Laboratory, Wright Patterson Air Force Base (Dayton, Ohio, USA). [S1050-0472(00)01002-3].
Simulated annealing is a robust and easy-to-implement algorithm for material simulation, However, it consumes a huge amount of computational time, especially on the studies of percolation networks. To reduce the runni...
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Simulated annealing is a robust and easy-to-implement algorithm for material simulation, However, it consumes a huge amount of computational time, especially on the studies of percolation networks. To reduce the running time, we parallelize the simulated annealing algorithm in our studies of the thermoelastic scaling behavior of percolation networks. The critical properties of the thermoelastic moduli of percolation networks near the threshold p(c) are investigated by constructing a square percolation network. The properties are tested by simulations of a series of two-dimensional (2-D) percolation networks near p(c). The simulations are performed using a novel parallelizing scheme on the simulated annealing algorithm. To further accelerate the computational speed, we also propose a new conjectural method to generate better initial configurations, which speeds up the simulation significantly. Preliminary simulation results show surprisingly that the percolating phenomenon of thermal expansion does exist under certain conditions. The behavior seems to be governed by the elastic properties of a percolation network.
An approach for establishing stability of annealing schemes and related processes is described. This extends the approach developed in Borkar and Meyn (SIAM J. Control Optim. 38 (2000) 447) for stochastic approximatio...
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An approach for establishing stability of annealing schemes and related processes is described. This extends the approach developed in Borkar and Meyn (SIAM J. Control Optim. 38 (2000) 447) for stochastic approximation algorithms. The proof uses a possibly degenerate stochastic differential equation obtained as a scaling limit of the interpolated algorithm. (C) 2000 Elsevier Science B.V. All rights reserved.
This paper presents a structure of classes based on Object-Oriented Programming, which allows the development of an Optimization Library, In this library, deterministic and stochastic optimization algorithms are consi...
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This paper presents a structure of classes based on Object-Oriented Programming, which allows the development of an Optimization Library, In this library, deterministic and stochastic optimization algorithms are considered, as well as algorithms that work with constrained or unconstrained objective functions. First of all,,we will present the characteristics of some main optimization methods used in the last years, mainly in the electromagnetic area. Later on, based on these characteristics, we will show the classes created for the implementation of this optimization library. Finally, we will present the communication architecture used for data exchange between this library and a Finite Element Method software.
This paper offers a counter-argument to Friedman's (In: Essays in Positive Economics, University of Chicago Press, Chicago, 1953) claim that irrational agents are bound to be eliminated by market forces. Consider ...
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This paper offers a counter-argument to Friedman's (In: Essays in Positive Economics, University of Chicago Press, Chicago, 1953) claim that irrational agents are bound to be eliminated by market forces. Consider a financial market where some traders irrationally over- or under-estimate the dividend flow. We show that this irrationality can enhance their bargaining power, so that these agents can obtain larger gains from trade than rational agents. We analyze the stochastic evolutionary dynamics of the fraction of agents who are irrational, and show that they may well survive in the long term. (C) 2000 Elsevier Science B.V. All rights reserved. JEL classification: D84;G12;G14.
It is known that various deterministic and stochastic processes such as asymptotically autonomous differential equations or stochastic approximation processes can be analyzed by relating them to an appropriately chose...
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An approach for analysis of the small signal response of the carriers in semiconductors is presented. The integro-differential equation, describing the phenomenon in the time domain is transformed into a Fredholm inte...
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An approach for analysis of the small signal response of the carriers in semiconductors is presented. The integro-differential equation, describing the phenomenon in the time domain is transformed into a Fredholm integral equation of the second kind. The response of the carrier system to a small signal of a general time dependence can be calculated by the knowledge of the response to an impulse signal, defined by a delta function in time. For an impulse signal, the obtained integral equation resembles the basic structure of the integral form of the time dependent (evolution) Boltzmann equation. Due to this similarity a physical model of the impulse response process is developed. The model explains the response to an impulse signal in terms of a relaxation process of two carrier ensembles, governed by a Boltzmann equation. A Monte-Carlo method is developed which consists of algorithms for modeling the initial distribution of the two ensembles. The numerical Monte-Carlo theory for evaluation of integrals is applied. The subsequent relaxation process can be simulated by the standard algorithms for solving the Boltzmann equation. The presented simulation results for Si and GaAs electrons serve as a test of the Monte-Carlo method and demonstrate that the physical model can be used for explanation of the small signal response process.
This article deals with the hybrid flow shop problem : scheduling of input jobs and resource assignment are both studied. We propose a predictive approach using metaheuristics : stochastic algorithms based on simulate...
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This article deals with the hybrid flow shop problem : scheduling of input jobs and resource assignment are both studied. We propose a predictive approach using metaheuristics : stochastic algorithms based on simulated annealing. These algorithms allow to study many types of hybrid flow shop problems (limited or unlimited storage, no storage, no wait, ...) and many types of criteria. We propose neighbouring systems and present results for literature problems, generated problems with identical, uniform or unrelated parallel machines (up to 500 jobs and 20 machines) and an industrial problem with 7000 jobs and 4 stages. We obtain good results, closed to lower bound or optimal solution in a short processing time.
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