Showing papers on "Stochastic simulation published in 2021"

Robust Dynamic Programming for Temporal Logic Control of Stochastic Systems

Abstract: Discrete-time stochastic systems are an essential modeling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification and synthesis of control strategies are computationally hard and generally rely on the use of approximate abstractions. Building on approximate abstractions, we compute control strategies with lower- and upper-bounds for satisfying unbounded temporal logic specifications. First, robust dynamic programming mappings over the abstract system are introduced to solve the control synthesis and verification problem. These mappings yield a control strategy and a unique lower bound on the satisfaction probability for temporal logic specifications that is robust to the incurred approximation errors. Second, upper-bounds on the satisfaction probability are quantified, and properties of the mappings are analyzed and discussed. Finally, we show the implications of these results to continuous state space of linear stochastic dynamic systems. This abstraction-based synthesis framework is shown to be able to handle infinite-horizon properties. Approximation errors expressed as deviations in the outputs of the models and as deviations in the probabilistic transitions are allowed and are quantified using approximate stochastic simulation relations.

Bi-Objective Modeling and Optimization for Stochastic Two-Stage Open Shop Scheduling Problems in the Sharing Economy

Abstract: Nowadays, many manufacturing and service industries prefer to share resources such as facilities and workers to cooperatively perform tasks, which can efficiently improve resource utilization and customer satisfaction. Generally, the decision-makers need to pay more for resource usage, leading to an urgent demand to decrease operational costs. This article proposes a stochastic bi-objective two-stage open shop scheduling problem that models a vehicle maintenance process where tasks are appointed to be completed by multiple third-party companies with professional equipment. We formulate this optimization problem by minimizing the total tardiness and processing cost subject to various resource constraints. A hybrid multiobjective migrating birds optimization combined with a genetic operation and a discrete event system is designed by considering problem characteristics to solve the problem. In this method, the migrating birds optimization with some particular strategies aims at searching candidate solutions from the entire solution domain. Simultaneously, the discrete event system, by using stochastic simulation and discrete event-based simulation approaches, focuses on evaluating the performance of searched solutions. Simulation experiments are performed, and state-of-the-art algorithms are used as competitive approaches. The results confirm that this approach has an excellent performance in handling our considered problem.

Multiobjective Modeling and Optimization for Scheduling a Stochastic Hybrid Flow Shop With Maximizing Processing Quality and Minimizing Total Tardiness

Abstract: Currently, manufacturing enterprises attach great importance to improving processing quality and customer satisfaction. Hybrid flow shops have widespread applications in real-world manufacturing systems such as steel production and chemical industry. In a practical production process, uncertainty commonly arises due to the difficulty of knowing exact information of facilities and jobs beforehand. In order to improve processing quality and customer satisfaction of manufacturing systems in uncertain environments, this article proposes a stochastic multiobjective hybrid flow shop scheduling problem aiming at maximizing processing quality and minimizing total tardiness, where the processing time of jobs obeys a known random distribution. To describe jobs’ processing quality mathematically, a quality-based cost function is presented, and further a chance-constrained programming approach is used to formulate this problem. Then, a multiobjective artificial bee colony algorithm incorporating a stochastic simulation approach is designed by considering its characteristics. Simulation experiments are performed on a set of instances and several state-of-the-art multiobjective optimization algorithms are chosen as peer approaches. Experiment results confirm that the proposed algorithm has an excellent performance in handling this problem.

Towards Generic Simulation for Demanding Stochastic Processes

Abstract: We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation The simulation method is genuine as it uses the process of interest directly, without any transformation (eg, normalization) We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence) All examples studied show the satisfactory performance of the method

Towards Generic Simulation for Demanding Stochastic Processes

Abstract: We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly, without any transformation (e.g., normalization). We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

Towards network-wide safe and efficient traffic signal timing optimization based on costly stochastic simulation

Abstract: This study proposes a stochastic simulation-based network-wide signal timing optimization model with the balance consideration of traffic safety and efficiency, and solves it with a Bi-objective Stochastic Simulation-based Optimization (BOSSO) algorithm. During numerical experiments, an urban road network with 15 signalized and 5 non-signalized intersections in Changsha, China is modelled as an experimental scenario. The calibrated simulator VISSIM, Surrogate Safety Assessment Model (SSAM) and MATLAB are integrated to construct the VISSIM-SSAM-Matlab platform, based on which the network-wide signal timing optimization problems without and with coordination are solved by the BOSSO algorithm to trade-off traffic conflicts and total delay. Numerical results show that only hundreds of simulations are cost to obtain the ultimate non-dominated non-coordinated and coordinated signal timing plans, and validate a competing relationship between traffic conflicts and total delay. By the bi-objective comparison of three various signal plans from the overall and local aspects, the coordinated signal plan outperforms the non-coordinated one, which is followed by the field implemented one. It successfully demonstrates the effectiveness of the BOSSO method.

Constraining stochastic 3-D structural geological models with topology information using approximate Bayesian computation in GemPy 2.1

Abstract: . Structural geomodeling is a key technology for the visualization and quantification of subsurface systems. Given the limited data and the resulting necessity for geological interpretation to construct these geomodels, uncertainty is pervasive and traditionally unquantified. Probabilistic geomodeling allows for the simulation of uncertainties by automatically constructing geomodel ensembles from perturbed input data sampled from probability distributions. But random sampling of input parameters can lead to construction of geomodels that are unrealistic, either due to modeling artifacts or by not matching known information about the regional geology of the modeled system. We present a method to incorporate geological information in the form of known geomodel topology into stochastic simulations to constrain resulting probabilistic geomodel ensembles using the open-source geomodeling software GemPy. Simulated geomodel realizations are checked against topology information using an approximate Bayesian computation approach to avoid the specification of a likelihood function. We demonstrate how we can infer the posterior distributions of the model parameters using topology information in two experiments: (1) a synthetic geomodel using a rejection sampling scheme (ABC-REJ) to demonstrate the approach and (2) a geomodel of a subset of the Gullfaks field in the North Sea comparing both rejection sampling and a sequential Monte Carlo sampler (ABC-SMC). Possible improvements to processing speed of up to 10.1 times are discussed, focusing on the use of more advanced sampling techniques to avoid the simulation of unfeasible geomodels in the first place. Results demonstrate the feasibility of using topology graphs as a summary statistic to restrict the generation of geomodel ensembles with known geological information and to obtain improved ensembles of probable geomodels which respect the known topology information and exhibit reduced uncertainty using stochastic simulation methods.

Training Image Free High-Order Stochastic Simulation Based on Aggregated Kernel Statistics

Abstract: A training image free, high-order sequential simulation method is proposed herein, which is based on the efficient inference of high-order spatial statistics from the available sample data. A statistical learning framework in kernel space is adopted to develop the proposed simulation method. Specifically, a new concept of aggregated kernel statistics is proposed to enable sparse data learning. The conditioning data in the proposed high-order sequential simulation method appear as data events corresponding to the attribute values associated with the so-called spatial templates of various geometric configurations. The replicates of the data events act as the training data in the learning framework for inference of the conditional probability distribution and generation of simulated values. These replicates are mapped into spatial Legendre moment kernel spaces, and the kernel statistics are computed thereafter, encapsulating the high-order spatial statistics from the available data. To utilize the incomplete information from the replicates, which partially match the spatial template of a given data event, the aggregated kernel statistics combine the ensemble of the elements in different kernel subspaces for statistical inference, embedding the high-order spatial statistics of the replicates associated with various spatial templates into the same kernel subspace. The aggregated kernel statistics are incorporated into a learning algorithm to obtain the target probability distribution in the underlying random field, while preserving in the simulations the high-order spatial statistics from the available data. The proposed method is tested using a synthetic dataset, showing the reproduction of the high-order spatial statistics of the sample data. The comparison with the corresponding high-order simulation method using TIs emphasizes the generalization capacity of the proposed method for sparse data learning.

On the approximation and simulation of iterated stochastic integrals and the corresponding Lévy areas in terms of a multidimensional Brownian motion

Abstract: A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding Levy areas driven by a multidimensional Brownian motion is proposed. Th...

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Abstract: Random tessellations are well suited for probabilistic modeling of three-dimensional (3D) grain microstructures of polycrystalline materials. The present paper is focused on so-called Gibbs-Laguerre tessellations, in which the generators of the Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process such that the resulting tessellation matches some desired geometrical properties. Since the model is analytically intractable, our main tool of analysis is stochastic simulation based on Markov chain Monte Carlo. Such simulations enable us to investigate the properties of the models, and, in the next step, to apply the knowledge gained to the statistical reconstruction of the 3D microstructure of an aluminum alloy extracted from 3D tomographic image data.

A Multi-Peak Evolutionary Model for Stochastic Simulation of Ground Motions Based on Time-Domain Features

Abstract: This paper introduces an efficient stochastic method to produce fully nonstationary records having multiple peaks in power spectrum. The zero-crossing characteristics of the acceleration, velocity,...

A Compact and Power-Efficient Noise Generator for Stochastic Simulations

Abstract: This paper describes an adaptive noise generator circuit suitable for on-chip simulations of stochastic chemical kinetics. The circuit uses amplified BJT white noise and adaptive low-pass filtering to emulate the power spectrum and auto-correlation of random telegraph signals (RTS) with Poisson-distributed level transitions. A current-mode implementation in the IHP 0.25 µm BiCMOS process shows excellent agreement with theoretical results from the Gillespie stochastic simulation algorithm over a 60 dB range in mean current levels (modeling molecule count numbers). The circuit has an estimated layout area of 0.01 mm2 and typically consumes 100 µA, which are 10× and 8× better, respectively, than prior implementations.

Optimized algorithm for multipoint geostatistical facies modeling based on a deep feedforward neural network.

Abstract: Reservoir facies modeling is an important way to express the sedimentary characteristics of the target area. Conventional deterministic modeling, target-based stochastic simulation, and two-point geostatistical stochastic modeling methods are difficult to characterize the complex sedimentary microfacies structure. Multi-point geostatistics (MPG) method can learn a priori geological model and can realize multi-point correlation simulation in space, while deep neural network can express nonlinear relationship well. This article comprehensively utilizes the advantages of the two to try to optimize the multi-point geostatistical reservoir facies modeling algorithm based on the Deep Forward Neural Network (DFNN). Through the optimization design of the multi-grid training data organization form and repeated simulation of grid nodes, the simulation results of diverse modeling algorithm parameters, data conditions and deposition types of sedimentary microfacies models were compared. The results show that by optimizing the organization of multi-grid training data and repeated simulation of nodes, it is easier to obtain a random simulation close to the real target, and the simulation of sedimentary microfacies of different scales and different sedimentary types can be performed.

Application of Random Simulation Algorithm in Physical Education Teaching Evaluation

Abstract: In the classical comprehensive evaluation theory, the information form of evaluation conclusion is usually absolute. In view of the absoluteness of judging the advantages and disadvantages of traditional physical education (PE) teaching evaluation and the inconsistency of multiple evaluation conclusions, this paper constructs an independent advantage evaluation method which highlights its own advantages, and puts forward a comprehensive evaluation mode of random simulation. In other words, by setting parameters, the traditional evaluation mode can be transformed into a random mode, and the possibility ranking conclusion of the comparison between the advantages and disadvantages of the schemes can be obtained. Because of the independence of the stochastic simulation solution method, this paper applies it to the evaluation model of PE, and constructs a new independent evaluation method to evaluate the advantages of the evaluation object by calculating the winning degree of each evaluation object. Finally, the random simulation comprehensive evaluation model was taken as the experimental group, and the traditional sports evaluation model as the control group. The results showed that each index of the experimental group was higher than that of the control group, and the comprehensive score was 0.83 higher than that of the control group. Thus, the random simulation evaluation model is an extension of the traditional evaluation model, providing a structural framework for various information forms and evaluators’ preferences, so that the evaluation process is no longer limited by single or limited data form and information structure, and can further enhance the practical application scope of comprehensive evaluation method.

Genetic Algorithm-Based Fuzzy Programming Method for Multi-objective Stochastic Transportation Problem Involving Three-Parameter Weibull Distribution

Abstract: In real-life situations, it is difficult to handle multi-objective stochastic transportation problems. It can’t be solved directly using traditional mathematical programming approaches. In this paper, we proposed a solution procedure to handle the above problem. The proposed solution procedure is a hybridization of the evolutionary algorithm called a genetic algorithm and a classical mathematical programming technique called fuzzy programming method. This hybrid approach is called a genetic algorithm-based fuzzy programming method. The supply and demand parameters of the constraints follow a three-parameter Weibull distribution. To complete the proposed problem a total of three steps are required. Initially, the probabilistic constraints are handled using stochastic simulation. Then, we checked the feasibility of probability constraints by the stochastic programming with the genetic algorithm without deriving the deterministic equivalents. Then, the genetic algorithm-based fuzzy programming method is considered to generate non-dominated solutions for the given problem. Finally, a numerical case study is presented to illustrate the methodology.

Physics Information Aided Kriging using Stochastic Simulation Models

Abstract: In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually t...

Noise and delay can shape distribution functions in stochastic reaction dynamics

Abstract: Noise can drive the dynamics of stochastic systems to different important states. Delay is another significant parameter that may impart non-Markovian behavior in the system dynamics. The interplay of noise and delay can exhibit interesting, complex behaviors in stochastic systems. In this work, we considered the stochastic gene expression model and studied this interplay of noise and delay in describing the functioning of a gene via transcription and translation processes. The calculated probability distributions of mRNA and protein, both in non-delay and delay, are found to obey certain universal classes, namely Poisson distribution at $$u,N\rightarrow large$$ limit, and Normal distribution at $$u,\langle u\rangle ,N\rightarrow large$$ limit. Analytical result of noise, measured by the Fano factor, indicates that, both in delay and non-delay cases, the gene expression system follows sub-Poissonian processes when the values of parameters are far from asymptotic values and that it becomes Poissonian at asymptotic values of the system parameters. We provided a detailed study of the noise using the Fano Factor with respect to different parameters such as mean, initial population, and time delay for the gene expression process. Again, the stochastic simulation results of the model indicate the transition of mRNA states (low and high transcription and translation) driven by the translation rate.

Improved Penalty Function with Memory for Stochastically Constrained Optimization via Simulation

Abstract: Penalty function with memory (PFM) in Park and Kim [2015] is proposed for discrete optimization via simulation problems with multiple stochastic constraints where performance measures of both an objective and constraints can be estimated only by stochastic simulation. The original PFM is shown to perform well, finding a true best feasible solution with a higher probability than other competitors even when constraints are tight or near-tight. However, PFM applies simple budget allocation rules (e.g., assigning an equal number of additional observations) to solutions sampled at each search iteration and uses a rather complicated penalty sequence with several user-specified parameters. In this article, we propose an improved version of PFM, namely IPFM, which can combine the PFM with any simulation budget allocation procedure that satisfies some conditions within a general DOvS framework. We present a version of a simulation budget allocation procedure useful for IPFM and introduce a new penalty sequence, namely PS2+, which is simpler than the original penalty sequence yet holds convergence properties within IPFM with better finite-sample performances. Asymptotic convergence properties of IPFM with PS2+ are proved. Our numerical results show that the proposed method greatly improves both efficiency and accuracy compared to the original PFM.

Application of Random Dynamic Grouping Simulation Algorithm in PE Teaching Evaluation

Abstract: The probability ranking conclusion is an extension of the absolute form evaluation conclusion. Firstly, the random simulation evaluation model is introduced; then, the general idea of converting the traditional evaluation method to the random simulation evaluation model is analyzed; on this basis, based on the rule of “further ensuring the stability of the ranking chain on the basis of increasing the possibility of the ranking chain,” two methods of solving the probability ranking conclusion are given. Based on the rule of “further guaranteeing the stability of the ranking chain on the basis of improving the likelihood of the ranking chain,” two methods are given to solve the likelihood conclusion. This paper argues that this absolute form of conclusion hinders the approximation of the theory to the essence of the actual problem and is an important reason for the problem of “non-consistency of multi-evaluation conclusions.” To address this problem, a stochastic simulation-based comprehensive evaluation solution algorithm based on the idea of “Monte Carlo simulation” is proposed, and the corresponding ranking method is investigated, which is characterized by generating evaluation conclusions with probability (reliability) information, and thus has more advantages than the absolute conclusion form in terms of problem interpretability. The method is characterized by the generation of evaluation conclusions with probabilistic (reliability) information and thus has more advantages than the absolute conclusion form in terms of problem interpretation. Because of the independence of the stochastic simulation solution method, it is applied to the “bottom-up” evaluation model as an example, and a novel autonomous evaluation method is constructed. Finally, the application of the stochastic simulation evaluation model is illustrated by an example and compared with the absolute form evaluation. The evaluation model is an extension of the traditional evaluation model, which can further broaden the practical application of comprehensive evaluation theory.

Space-time histories approach to fast stochastic simulation of bimolecular reactions.

Abstract: Computational models of reaction–diffusion systems involving low copy numbers or strongly heterogeneous molecular spatial distributions, such as those frequently found in cellular signaling pathways, require approaches that account for the stochastic dynamics of individual particles, as opposed to approaches representing them through their average concentrations. Efforts to remedy the high computational cost associated with particle-based stochastic approaches by taking advantage of Green’s functions are hampered by the need to draw random numbers from complicated, and therefore costly, non-standard probability distributions to update particle positions. Here, we introduce an approach that permits the reconstruction of entire molecular trajectories, including bimolecular encounters, in retrospect, after a simulated time step, while avoiding inefficient draws from non-standard distributions. This means that highly accurate stochastic simulations can be performed for system sizes that would be prohibitively costly to simulate with conventional Green’s function based methods. The algorithm applies equally well to one, two, and three dimensional systems and can be readily extended to include deterministic forces specified by an interaction potential, such as the Coulomb potential.