Metropolis Sampling

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based sampling's world.Comment: Wiley StatsRef-Statistics Reference Online, 201

A short introduction to stochastic optimization

We present some typical algorithms used for finding global min­imum/maximum of a function defined on a compact finite dimensional set, discuss commonly observed procedures for assessing and comparing the algo­rithms’ performance and quote theoretical results on convergence of a broad class of stochastic algorithms

Locating Leaks in Water Distribution Networks with Simulated Annealing and Graph Theory

AbstractThis paper addresses the problem of locating leaks in water distribution networks. The approach presented here is based on steady-state modelling, supported by monitoring tank flow and pressure at strategic nodes. The selection of the pressure monitoring nodes is done applying graph theory concepts adapted to water distribution networks. Pressure monitoring data is then used to build an optimization problem: the objective function is the minimization of the differences between estimated and measured pressures at the monitoring points, the constraints are the common energy and mass conservation laws and the decision variables are the leak locations and flows. This optimization problem is solved by a simulated annealing algorithm presented in a previous work. The application of this approach in a set of case studies produced some encouraging results and this paper describes the complete procedure and draws some conclusions

A Short Introduction to Stochastic Optimization

We present some typical algorithms used for finding global minimum/ maximum of a function defined on a compact finite dimensional set, discuss commonly observed procedures for assessing and comparing the algorithms’ performance and quote theoretical results on convergence of a broad class of stochastic algorithms

On the convergence rate issues of general Markov search for global minimum

This paper focuses on the convergence rate problem of general Markov search for global minimum. Many of existing methods are designed for overcoming a very hard problem which is how to efficiently localize and approximate the global minimum of the multimodal function f while all information which can be used are the f-values evaluated for generated points. Because such methods use poor information on f, the following problem may occur: the closer to the optimum, the harder to generate a “better” (in sense of the cost function) state. This paper explores this issue on theoretical basis. To do so the concept of lazy convergence for a globally convergent method is introduced: a globally convergent method is called lazy if the probability of generating a better state from one step to another goes to zero with time. Such issue is the cause of very undesired convergence properties. This paper shows when an optimization method has to be lazy and the presented general results cover, in particular, the class of simulated annealing algorithms and monotone random search. Furthermore, some attention is put on accelerated random search and evolution strategies

Plum: Prompt Learning using Metaheuristic

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in \url{https://github.com/research4pan/Plum}

Orthogonal parallel MCMC methods for sampling and optimization

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called {\it orthogonal MCMC} (O-MCMC), where a set of "vertical" parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters

Flux analysis in central carbon metabolism in plants: 13C NMR experiments and analysis

Metabolic flux analysis is crucial in metabolic engineering. This research concentrated on improvements in 13C labeling-based flux analysis, a powerful flux quantification method, particularly oriented toward application to plants. Furthermore, systemic 13C flux analyses were performed on two model plant systems: Glycine max (soybean) embryos, and Catharanthus roseus hairy roots.;The concepts \u27bond integrity\u27, \u27bondomer\u27 and the algorithm \u27Boolean function mapping\u27 were introduced, to facilitate efficient flux evaluation from carbon bond labeling experiments, and easier flux identifiability analysis.;13C labeling experiments were performed on developing soybean (Glycine max) embryos and C. roseus hairy roots. A computer program, NMR2Flux, was developed to automatically calculate fluxes from the labeling data. This program accepts a user-defined metabolic network model, and incorporates recent mathematical advances toward accurate and efficient evaluation of fluxes and their standard deviations. Several physiological insights were obtained from the flux results. For instance, in soybean embryos, the reductive pentose phosphate pathway was active in the plastid and negligible in the cytosol. Also, unknown fluxes (such as plastidic fructose-1,6-bisphosphatase) could be identified and quantified. To the best of the author\u27s knowledge, this is the most comprehensive flux analysis of a plant system to date.;Investigations on flux identifiability were carried out for the soybean embryo system. Using these, optimal labeling experiments were designed, that utilize judicious combinations of labeled varieties of two substrates (sucrose and glutamine), to maximize the statistical quality of the evaluated fluxes.;The identity of four intense peaks observed in the 2-D [13C, 1H] spectra of protein isolated from soybean embryos, was investigated. These peaks were identified as levulinic acid and 5-hydroxymethyl furfural, and were degradation products of glycosylating sugars associated with soybean embryo protein. A 2-D NMR study was conducted on them, and it was shown that the metabolic information in the degradation products can be used toward metabolic flux or pathway analysis.;In addition, the elemental make-up and composition of the biomass of C. roseus hairy roots (crucial toward flux analysis) is reported. 89.2% (+/-9.7%) of the biomass was accounted for.*;*This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation). The CD requires the following system requirements: Adobe Acrobat

関数最適化問題に対する適応型差分進化法の研究

学位の種別: 課程博士審査委員会委員 : （主査）東京大学准教授 福永 アレックス, 東京大学教授 池上 高志, 東京大学教授 植田 一博, 東京大学教授 山口 泰, 東京大学教授 伊庭 斉志University of Tokyo(東京大学