Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains ch...
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Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains challenging for the existing modelling approaches based on continuum mathematics because they do not capture important local interactions between microstructure elements and spatial inhomogeneities in plastic strain. An effective discrete method for simulating CDRX is developed in this work. It employs algebraic topology, graph theory and statistical physics tools to represent an evolution of grain boundary networks as a sequence of conversions between low-angle grain boundaries (LAGBs) and high -angle grain boundaries (HAGBs) governed by the principle of minimal energy increase, similar to the well-known Ising model. The energy is minimised by a modified metropolis algorithm. The model is used to predict the equilibrium fractions of HAGBs in several SPD-processed copper alloys. The analysis captures non-equilibrium features of the transitions from sub-grain structures to new HAGB-dominated grain structures and provides estimations of critical values for HAGB fractions and accumulated strain at these transitions.
Order Picking in warehouses is often optimized using a method known as Order Batching, which means that one vehicle can be assigned to pick a batch of several orders at a time. There exists a rich body of research on ...
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The metropolis algorithm (MA) is a classic stochastic local search heuristic. It avoids getting stuck in local optima by occasionally accepting inferior solutions. To better and in a rigorous manner understand this ab...
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ISBN:
(纸本)9798400701191
The metropolis algorithm (MA) is a classic stochastic local search heuristic. It avoids getting stuck in local optima by occasionally accepting inferior solutions. To better and in a rigorous manner understand this ability, we conduct a mathematical runtime analysis of the MA on the CLIFF benchmark. Apart from one local optimum, cliff functions are monotonically increasing towards the global optimum. Consequently, to optimize a cliff function, the MA only once needs to accept an inferior solution. Despite seemingly being an ideal benchmark for the MA to profit from its main working principle, our mathematical runtime analysis shows that this hope does not come true. Even with the optimal temperature (the only parameter of the MA), the MA optimizes most cliff functions less efficiently than simple elitist evolutionary algorithms (EAs), which can only leave the local optimum by generating a superior solution possibly far away. This result suggests that our understanding of why the MA is often very successful in practice is not yet complete. Our work also suggests to equip the MA with global mutation operators, an idea supported by our preliminary experiments.
We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by...
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We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random transfers of charge between fluid cells, interspersed with ideal hydrodynamic time steps. The random charge transfers are accepted or rejected in a metropolis step using the entropy as a statistical weight. This procedure reproduces the expected stress of dissipative relativistic hydrodynamics in a specific (and noncovariant) hydrodynamic frame known as the density frame. Numerical results, both with and without noise, are presented and compared to relativistic kinetics and analytical expectations. An all order resummation of the density frame gradient expansion reproduces the covariant dynamics in a specific model. In contrast to all other numerical approaches to relativistic dissipative fluids, the dissipative fluid formalism presented here is strictly first order in gradients and has no nonhydrodynamic modes. The physical naturalness and simplicity of the metropolis algorithm, together with its convergence properties, make it a promising tool for simulating stochastic relativistic fluids in heavy ion collisions and for critical phenomena in the relativistic domain.
As demonstrated by empirical and theoretical work, the metropolis algorithm can cope with local optima by accepting inferior solutions with suitably small probability. This paper extends this research direction into m...
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ISBN:
(纸本)9798400704956
As demonstrated by empirical and theoretical work, the metropolis algorithm can cope with local optima by accepting inferior solutions with suitably small probability. This paper extends this research direction into multi-objective *** original metropolis algorithm has two components, one-bit mutation and the acceptance strategy, which allows accepting inferior solutions. When adjusting the acceptance strategy to multi-objective optimization in the way that an inferior solution that is accepted replaces its parent, then the metropolis algorithm is not very efficient on our multi-objective version of the multimodal DLB benchmark called DLTB. With one-bit mutation, this multi-objective metropolis algorithm cannot optimize the DLTB problem, with standard bit-wise mutation it needs at least Ω(n5) time to cover the full Pareto front. In contrast, we show that many other multi-objective optimizers, namely the GSEMO, SMS-EMOA, and NSGA-II, only need time O(n4). When keeping the parent when an inferior point is accepted, the multi-objective metropolis algorithm both with one-bit or standard bit-wise mutation solves the DLTB problem efficiently, with one-bit mutation experimentally leading to better results than several other ***, our work suggests that the general mechanism of the metropolis algorithm can be interesting in multi-objective optimization, but that the implementation details can have a huge impact on the *** paper for the Hot-off-the-Press track at GECCO 2024 summarizes the work Weijie Zheng, Mingfeng Li, Renzhong Deng, and Benjamin Doerr: How to Use the metropolis algorithm for Multi-Objective Optimization? In Conference on Artificial Intelligence, AAAI 2024, AAAI Press, 20883--20891. https://***/10.1609/aaai.v38i18.30078 [22].
This article studies the efficacy of the metropolis algorithm for the minimum-weight codeword problem. The input is a linear code C given by its generator matrix and our task is to compute a nonzero codeword in the co...
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This article studies the efficacy of the metropolis algorithm for the minimum-weight codeword problem. The input is a linear code C given by its generator matrix and our task is to compute a nonzero codeword in the code C of least weight. In particular, we study the metropolis algorithm on two possible search spaces for the problem: 1) the codeword space and 2) the generator space. The former is the space of all codewords of the input code and is the most natural one to use and hence has been used in previous work on this problem. The latter is the space of all generator matrices of the input code and is studied for the first time in this article. In this article, we show that for an appropriately chosen temperature parameter the metropolis algorithm mixes rapidly when either of the search spaces mentioned above are used. Experimentally, we demonstrate that the metropolis algorithm performs favorably when compared to previous attempts. When using the generator space, the metropolis algorithm is able to outperform the previous algorithms in most of the cases. We have also provided both theoretical and experimental justification to show why the generator space is a worthwhile search space to use for this problem.
metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered, and a generalization of the preconditioned Crank-Nicolson (pCN) proposal is introduced. The...
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metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered, and a generalization of the preconditioned Crank-Nicolson (pCN) proposal is introduced. The new proposal is able to incorporate information on the measure of interest. A numerical simulation of a Bayesian inverse problem indicates that a metropolis algorithm with such a proposal performs independently of the state-space dimension and the variance of the observational noise. Moreover, a qualitative convergence result is provided by a comparison argument for spectral gaps. In particular, it is shown that the generalization inherits geometric convergence from the metropolis algorithm with pCN proposal.
The Storage Location Assignment Problem (SLAP) is of central importance in warehouse operations. An important research challenge lies in generalizing the SLAP such that it is not tied to certain order-picking methodol...
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We perform Monte Carlo simulation to study the effects of random disorder on equilibrium phase transition of three-dimensional single-site anisotropic XY ferromagnet. The disorder is incorporated in two ways;having a ...
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We perform Monte Carlo simulation to study the effects of random disorder on equilibrium phase transition of three-dimensional single-site anisotropic XY ferromagnet. The disorder is incorporated in two ways;having a randomly distributed anisotropy and presence of a quenched random field. The ferro-para transition temperature has been found to increase with the increase of the strength of constant (over the space) anisotropy. In contrast, the system gets ordered at lower temperatures if the anisotropy has random distribution. The effects of quenched random fields are also studied in single-site anisotropic XY ferromagnet. The transition temperature reduces due to the presence of quenched random field. The compensating field (the required amount of field which preserves the critical temperature for isotropic XY ferromagnet) linearly depends on the strength of constant single-site anisotropy. We compute the magnetic and susceptibility exponent ratios for constant single-site anisotropic XY system only via detailed finite-size scaling analysis.
The metropolis algorithm involves producing a Markov chain to converge to a specified target density pi. To improve its efficiency, we can use the Rejection-Free version of the metropolis algorithm, which avoids the i...
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The metropolis algorithm involves producing a Markov chain to converge to a specified target density pi. To improve its efficiency, we can use the Rejection-Free version of the metropolis algorithm, which avoids the inefficiency of rejections by evaluating all neighbors. Rejection-Free can be made more efficient through parallelism hardware. However, for some specialized hardware, such as Digital Annealing Unit, the number of neighbors being considered at each step is limited. Hence, we propose an enhanced version of Rejection-Free known as Partial Neighbor Search, which only considers a portion of the neighbors. This method will be tested on several examples to demonstrate its effectiveness and advantages under different circumstances. Our method has already been used in the industry.
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