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An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

Computers, Materials & Continua 2022年第1期70卷 817-829页

作者： Prachi Agrawal Khalid Alnowibet Talari Ganesh Adel F.Alrasheedi Hijaz Ahmad Ali Wagdy Mohamed Department of Mathematics and Scientific Computing National Institute of Technology HamirpurHimachal Pradesh177005India Statistics and Operations Research Department College of ScienceKing Saud UniversityRiyadh11451Kingdom of Saudi Arabia Section of Mathematics International Telematic University UninettunoRoma00186Italy Operations Research Department Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Wireless Intelligent Networks Center(WINC) School of Engineering and Applied SciencesNile UniversityGizaEgypt

Recent years witness a great deal of interest in artificial intelligence(AI)tools in the area of *** has developed a large number of tools to solve themost difficult search-and-optimization problems in computer science and operations ***,metaheuristic-based algorithms are a sub-field of *** study presents the use of themetaheuristic algorithm,that is,water cycle algorithm(WCA),in the transportation problem.A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull *** the parameters are stochastic,the corresponding constraints are *** are converted into deterministic constraints using the stochastic programming *** this study,we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization *** is influenced by the water cycle process of how streams and rivers flow toward the sea(optimal solution).WCA is applied to the stochastic transportation problem,and obtained results are compared with that of the new metaheuristic optimization algorithm,namely the neural network algorithm which is inspired by the biological nervous *** is concluded that WCA presents better results when compared with the neural network algorithm.

关键词： Artificial intelligence metaheuristic algorithm stochastic programming transportation problem water cycle algorithm weibull distribution

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Entropic Gromov-Wasserstein distances: stability and algorithms

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 17738-17789页

作者： Gabriel Rioux Ziv Goldfeld Kengo Kato Center for Applied Mathematics Cornell University Ithaca NY School of Electrical and Computer Engineering Cornell University Ithaca NY Department of Statistics and Data Science Cornell University Ithaca NY

The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP-complete, entropic regularization provides an avenue towards a computationally tractable proxy. Leveraging a recently derived variational representation for the quadratic entropic GW (EGW) distance, this work derives the first efficient algorithms for solving the EGW problem subject to formal, nonasymptotic convergence guarantees. To that end, we derive smoothness and convexity properties of the objective in this variational problem, which enables its resolution by the accelerated gradient method. Our algorithms employ Sinkhorn's fixed point iterations to compute an approximate gradient, which we model as an inexact oracle. We furnish convergence rates towards local and even global solutions (the latter holds under a precise quantitative condition on the regularization parameter), characterize the effects of gradient inexactness, and prove that stationary points of the EGW problem converge towards a stationary point of the unregularized GW problem, in the limit of vanishing regularization. We provide numerical experiments that validate our theory and empirically demonstrate the state-of-the-art empirical performance of our algorithm.

关键词： Algorithms convergence rate global guarantees Gromov-Wasserstein distances entropic regularization inexact gradient methods

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Some converse Lyapunov-like results for strong forward invariance

Some converse Lyapunov-like results for strong forward invar...

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IEEE Conference on Decision and Control

作者： Rafal Goebel Ricardo G. Sanfelice Andrew R. Teel Department of Mathematics & Statistics Loyola University Chicago Chicago Electrical and Computer Engineering Department University of California Santa Cruz Electrical and Computer Engineering Department University of California Santa Barbara

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

In the setting of a differential inclusion, strong forward invariance of a closed or a compact set is studied. Main results are novel necessary Lyapunov-like conditions for this property. They involve time-varying and autonomous Lyapunov/barrier functions that are smooth everywhere or at least outside the invariant set and are decreasing or at least not increasing faster than exponentially.

关键词： Sufficient conditions Perturbation methods Differential equations Safety Asymptotic stability US department of Defense Terminology Surveys mathematics Lyapunov methods

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ASYNCHRONOUS DECENTRALIZED Q-LEARNING: TWO TIMESCALE ANALYSIS BY PERSISTENCE

arXiv

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arXiv 2023年

作者： Yongacoglu, Bora Arslan, Gürdal Yüksel, Serdar Department of Mathematics and Statistics Queen's University Canada Department of Electrical Engineering University of Hawaii Manoa United States

Non-stationarity is a fundamental challenge in multi-agent reinforcement learning (MARL), where agents update their behaviour as they learn. Many theoretical advances in MARL avoid the challenge of non-stationarity by coordinating the policy updates of agents in various ways, including synchronizing times at which agents are allowed to revise their policies. Synchronization enables analysis of many MARL algorithms via multi-timescale methods, but such synchrony is infeasible in many decentralized applications. In this paper, we study an asynchronous variant of the decentralized Q-learning algorithm, a recent MARL algorithm for stochastic games. We provide sufficient conditions under which the asynchronous algorithm drives play to equilibrium with high probability. Our solution utilizes constant learning rates in the Q-factor update, which we show to be critical for relaxing the synchrony assumptions of earlier work. Our analysis also applies to asynchronous generalizations of a number of other algorithms from the regret testing tradition, whose performance is analyzed by multi-timescale methods that study Markov chains obtained via policy update dynamics. This work extends the applicability of the decentralized Q-learning algorithm and its relatives to settings in which parameters are selected in an independent manner, and tames non-stationarity without imposing the coordination assumptions of prior work. © 2023, CC BY.

关键词： Reinforcement learning

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Inference of Utilities and Time Preference in Sequential Decision-Making

arXiv

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arXiv 2024年

作者： Cao, Haoyang Wu, Zhengqi Xu, Renyuan Department of Applied Mathematics and Statistics Johns Hopkins University United States Epstein Department of Industrial and Systems Engineering University of Southern California United States

This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages a continuous-time model that incorporates utility functions and a generic discounting scheme of a time-varying rate, tailored to each client's risk tolerance, valuation of daily consumption, and significant life goals. We address the resulting time inconsistency issue through state augmentation and the establishment of the dynamic programming principle and the verification theorem. Additionally, we provide sufficient conditions for the identifiability of client investment preferences. To complement our theoretical developments, we propose a learning algorithm based on maximum likelihood estimation within a discrete-time Markov Decision Process framework, augmented with entropy regularization. We prove that the log-likelihood function is locally concave, facilitating the fast convergence of our proposed algorithm. Practical effectiveness and efficiency are showcased through two numerical examples, including Merton's problem and an investment problem with unhedgeable risks. Our proposed framework not only advances financial technology by improving personalized investment advice but also contributes broadly to other fields such as healthcare, economics, and artificial intelligence, where understanding individual preferences is crucial. © 2024, CC BY.

关键词： Investments

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Reinforcement Learning Under Uncertainty: Expected Versus Unexpected Uncertainty and State Versus Reward Uncertainty

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Computational Brain and Behavior 2023年第4期6卷 626-650页

作者： Ez-zizi, Adnane Farrell, Simon Leslie, David Malhotra, Gaurav Ludwig, Casimir J.H. School of Engineering Arts Science and Technology University of Suffolk Ipswich United Kingdom School of Psychological Science University of Western Australia Perth Australia Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom School of Psychological Science University of Bristol Bristol United Kingdom

Two prominent types of uncertainty that have been studied extensively are expected and unexpected uncertainty. Studies suggest that humans are capable of learning from reward under both expected and unexpected uncertainty when the source of variability is the reward. How do people learn when the source of uncertainty is the environment’s state and the rewards themselves are deterministic? How does their learning compare with the case of reward uncertainty? The present study addressed these questions using behavioural experimentation and computational modelling. Experiment 1 showed that human subjects were generally able to use reward feedback to successfully learn the task rules under state uncertainty, and were able to detect a non-signalled reversal of stimulus-response contingencies. Experiment 2, which combined all four types of uncertainties—expected versus unexpected uncertainty, and state versus reward uncertainty—highlighted key similarities and differences in learning between state and reward uncertainties. We found that subjects performed significantly better in the state uncertainty condition, primarily because they explored less and improved their state disambiguation. We also show that a simple reinforcement learning mechanism that ignores state uncertainty and updates the state-action value of only the identified state accounted for the behavioural data better than both a Bayesian reinforcement learning model that keeps track of belief states and a model that acts based on sampling from past experiences. Our findings suggest a common mechanism supports reward-based learning under state and reward uncertainty. © 2023, The Author(s).

关键词： Bayesian reinforcement learning Expected and unexpected uncertainty Reinforcement learning Sampling-based learning

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ANY GRAPH IS A MAPPER GRAPH

arXiv

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arXiv 2024年

作者： Alvarado, Enrique G. Belton, Robin Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie Tymochko, Sarah Department of Mathematics University of California at Davis DavisCA United States Department Mathematical Sciences Smith College NorthamptonMA United States Research Institute of Mathematics Seoul National University Seoul Korea Republic of Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI United States Department of Mathematics and Statistics University of New Mexico AlbuquerqueNM United States Mathematics Statistics and Data Science Pacific Northwest National Laboratory SeattleWA United States Department of Mathematics University of California Los Angeles Los AngelesCA United States

The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset X and a graph G, does there exist a set of Mapper parameters such that the output Mapper graph of X is isomorphic to G? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph. Copyright © 2024, The Authors. All rights reserved.

关键词： Data centers

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Fractional Modeling in Action: a Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

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Journal of Peridynamics and Nonlocal Modeling 2023年第3期5卷 392-459页

作者： Suzuki, Jorge L. Gulian, Mamikon Zayernouri, Mohsen D’Elia, Marta Department of Mechanical Engineering & Computational Mathematics Science and Engineering Michigan State University East Lansing MI United States Quantitative Modeling and Analysis Sandia National Laboratories Livermore CA United States Department of Mechanical Engineering & Statistics and Probability Michigan State University East Lansing MI United States Microvast Power Solutions Lake Mary FL United States

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas — subsurface transport, turbulence, and anomalous materials — in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models. © 2022, Springer Nature Switzerland AG.

关键词： Anomalous diffusion Anomalous materials Fractional models Nonlocal models Stochastic processes Subsurface transport Turbulence

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A multi-objective two-echelon vehicle routing problem with multiple delivery options

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Transportation Research Procedia 2024年 79卷 377-384页

作者： Amin Karimi Lele Zhang Mark Fackrell Russell Thompson School of Mathematics and Statistics The University of Melbourne ARC Training Centre in Optimisation Technologies Integrated Methodologies and Applications (OPTIMA) Australia The Department of Infrastructure Engineering The University of Melbourne Melbourne VIC Australia

The classical two-echelon vehicle routing problem (2E-VRP) has commodities transported from depots to intermediate facilities and then delivered to customers from these facilities. In this study, we consider another type of 2E-VRP, in which vehicles from both echelons can be used for home delivery. We also present a sustainable model, which considers customers' preferred delivery locations, economic and environmental costs. Also, we present a meta-heuristic algorithm to solve real-world size instances in a timely manner. The computational results demonstrate that the proposed solution method can effectively solve small instances with a minimal gap when compared to an exact solver, and it can also handle large instances in a timely manner.

关键词： Two-echelon vehicle routing problem Two-echelon logistics mixed integer programming multi-objective

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Study of Soret Effect in Magnetized Dissipative Chemically Reactive Sisko Nanofluid Flow: A Numerical Insight

SSRN

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SSRN 2024年

作者： Jain, Reema Dadhich, Yogesh Islam, Saiful Department of Mathematics and Statistics Manipal University Jaipur Rajasthan Jaipur303007 India Civil Engineering Department College of Engineering King Khalid University Abha61421 Saudi Arabia

This article examines the characteristics of mass and heat transfer in Sisko fluid flow. The consideration is given to continuous, two-dimensional movement of Sisko fluid exhibiting incompressible and viscous characteristics. The fluid flows over a sheet that is stretched exponentially and subjected to the Soret effect and magnetic field. The arising set of interconnected PDEs is converted to nonlinear ODEs using similarity transformations. This study presents simulation outcomes across different values of physical parameters within the flow regime as part of its findings. Following the calculations, the results for the heat, mass transfer rate and skinfriction coefficient, are compiled and presented in a tabulated form. An increase in the Soret number induces an upward shift in the concentration profile across the flow region The thorough discussion of similarity solutions in comparison with established findings not only validates the accuracy of the numerical results but also underlines the reliability and robustness of the methodology applied in this study. © 2024, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

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