Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

MCMC Analysis for Optimization of Stochastic Models

In any decision making under uncertainties, the goal is mostly to minimize the expected cost. The minimization of cost under uncertainties is usually done by optimization. For simple models, the optimization can easily be done using deterministic methods.However, many models practically contain some complex and varying parameters that can not easily be taken into account using usual deterministic methods of optimization. Thus, it is very important to look for other methods that can be used to get insight into such models. MCMC method is one of the practical methods that can be used for optimization of stochastic models under uncertainty. This method is based on simulation that provides a general methodology which can be applied in nonlinear and non-Gaussian state models. MCMC method is very important for practical applications because it is a uni ed estimation procedure which simultaneously estimates both parameters and state variables. MCMC computes the distribution of the state variables and parameters of the given data measurements. MCMC method is faster in terms of computing time when compared to other optimization methods. This thesis discusses the use of Markov chain Monte Carlo (MCMC) methods for optimization of Stochastic models under uncertainties .The thesis begins with a short discussion about Bayesian Inference, MCMC and Stochastic optimization methods. Then an example is given of how MCMC can be applied for maximizing production at a minimum cost in a chemical reaction process. It is observed that this method performs better in optimizing the given cost function with a very high certainty.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Jatkuvavaletun teräksen leikkaussuunnitelman optimointi

Teollisuuden tuotannon eri prosessien optimointi on hyvin ajankohtainen aihe. Monet ohjausjärjestelmät ovat ajalta, jolloin tietokoneiden laskentateho oli hyvin vaatimaton nykyisiin verrattuna. Työssä esitetään tuotantoprosessi, joka sisältää teräksen leikkaussuunnitelman muodostamisongelman. Valuprosessi on yksi teräksen valmistuksen välivaiheita. Siinä sopivaan laatuun saatettu sula teräs valetaan linjastoon, jossa se jähmettyy ja leikataan aihioiksi. Myöhemmissä vaiheissa teräsaihioista muokataan pienempiä kokonaisuuksia, tehtaan lopputuotteita. Jatkuvavaletut aihiot voidaan leikata tilauskannasta riippuen monella eri tavalla. Tätä varten tarvitaan leikkaussuunnitelma, jonka muodostamiseksi on ratkaistava sekalukuoptimointiongelma. Sekalukuoptimointiongelmat ovat optimoinnin haastavin muoto. Niitä on tutkittu yksinkertaisempiin optimointiongelmiin nähden vähän. Nykyisten tietokoneiden laskentateho on kuitenkin mahdollistanut raskaampien ja monimutkaisempien optimointialgoritmien käytön ja kehittämisen. Työssä on käytetty ja esitetty eräs stokastisen optimoinnin menetelmä, differentiaalievoluutioalgoritmi. Tässä työssä esitetään teräksen leikkausoptimointialgoritmi. Kehitetty optimointimenetelmä toimii dynaamisesti tehdasympäristössä käyttäjien määrittelemien parametrien mukaisesti. Työ on osa Syncron Tech Oy:n Ovako Bar Oy Ab:lle toimittamaa ohjausjärjestelmää.

Analyzing Carbon Trade Permits in Optimization Framework

The threats caused by global warming motivate different stake holders to deal with and control them. This Master's thesis focuses on analyzing carbon trade permits in optimization framework. The studied model determines optimal emission and uncertainty levels which minimize the total cost. Research questions are formulated and answered by using different optimization tools. The model is developed and calibrated by using available consistent data in the area of carbon emission technology and control. Data and some basic modeling assumptions were extracted from reports and existing literatures. The data collected from the countries in the Kyoto treaty are used to estimate the cost functions. Theory and methods of constrained optimization are briefly presented. A two-level optimization problem (individual and between the parties) is analyzed by using several optimization methods. The combined cost optimization between the parties leads into multivariate model and calls for advanced techniques. Lagrangian, Sequential Quadratic Programming and Differential Evolution (DE) algorithm are referred to. The role of inherent measurement uncertainty in the monitoring of emissions is discussed. We briefly investigate an approach where emission uncertainty would be described in stochastic framework. MATLAB software has been used to provide visualizations including the relationship between decision variables and objective function values. Interpretations in the context of carbon trading were briefly presented. Suggestions for future work are given in stochastic modeling, emission trading and coupled analysis of energy prices and carbon permits.

Parameter estimation for Chaotic or Stochastic Dynamics

Since its discovery, chaos has been a very interesting and challenging topic of research. Many great minds spent their entire lives trying to give some rules to it. Nowadays, thanks to the research of last century and the advent of computers, it is possible to predict chaotic phenomena of nature for a certain limited amount of time. The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood, and give some hints for a more optimized use of it, together with a possible application to the industry. The main part of our study concerned two chaotic attractors whose general behaviour is diff erent, in order to capture eventual di fferences in the results. In the various simulations that we performed, the initial conditions have been changed in a quite exhaustive way. The results obtained show that, under certain conditions, this method works very well in all the case. In particular, it came out that the most important aspect is to be very careful while creating the training set and the empirical likelihood, since a lack of information in this part of the procedure leads to low quality results.

Optimization of centrifugal separation of Ó-lactalbumin and ¿̐ư-lactoglobulin

Selostus: Ó-lactalbumiinin ja ¿̐ư-lactoglobuliinin sentrifugointierotuksen optimointi

New directions in Stochastic Multicriteria Acceptability Analysis

Decisions taken in modern organizations are often multi-dimensional, involving multiple decision makers and several criteria measured on different scales. Multiple Criteria Decision Making (MCDM) methods are designed to analyze and to give recommendations in this kind of situations. Among the numerous MCDM methods, two large families of methods are the multi-attribute utility theory based methods and the outranking methods. Traditionally both method families require exact values for technical parameters and criteria measurements, as well as for preferences expressed as weights. Often it is hard, if not impossible, to obtain exact values. Stochastic Multicriteria Acceptability Analysis (SMAA) is a family of methods designed to help in this type of situations where exact values are not available. Different variants of SMAA allow handling all types of MCDM problems. They support defining the model through uncertain, imprecise, or completely missing values. The methods are based on simulation that is applied to obtain descriptive indices characterizing the problem. In this thesis we present new advances in the SMAA methodology. We present and analyze algorithms for the SMAA-2 method and its extension to handle ordinal preferences. We then present an application of SMAA-2 to an area where MCDM models have not been applied before: planning elevator groups for high-rise buildings. Following this, we introduce two new methods to the family: SMAA-TRI that extends ELECTRE TRI for sorting problems with uncertain parameter values, and SMAA-III that extends ELECTRE III in a similar way. An efficient software implementing these two methods has been developed in conjunction with this work, and is briefly presented in this thesis. The thesis is closed with a comprehensive survey of SMAA methodology including a definition of a unified framework.

Optimization of the ink removal in deinking plant

Diplomityön tarkoituksena oli parantaa Stora Enso Sachsenin siistausprosessissa tuotetun uusiomassan vaaleuden kehitystä ja tutkia siihen vaikuttavia tekijöitä. Työn kirjallisessa osassa käsiteltiin uusiomassan kuidutusta ja vaahdotussiistausprosessia, sekä keräyspaperin ominaisuuksia ja käyttöä paperiteollisuuden raaka-aineena. Kokeellisessa osassa keskityttiin modifioidun natriumsilikaatin annostuksenoptimointiin ja vaikutuksiin laboratorio- ja prosessioloissa, sekä kesäefektin vaikutuksen tutkimiseen kuidutuksessa ja flotaation eri vaiheissa. Natriumsilikaatin laboratoriotutkimuksessa havaittiin, että korkein vaaleus suhteellisesti pienimmällä laboratorioflotaation häviöllä saavutettiin korkeimmalla tutkitulla natriumsilikaatin annostuksella, joka oli 1,1 %. Korkea natriumsilikaattiannostus yhdistettyinä korkeisiin vetyperoksidiannostukseen, 0,5 %, sekä korkeaan kokonaisalkaliteettiin, 0.33 %, johti korkeimpaan massan vaaleuteen ja pienimpiin häviöihin. Laboratoriotutkimuksen pohjalta modifioidulla natriumsilikaatilla suoritettiin koeajoja prosessissa. Noin 1 % natriumsilikaatin annostuksella havaittiin parempi pH:n bufferointikyky, pienempi kalsiumkarbonaatin määrä flotaation primäärivaiheissa, sekä lievästi parempi massan vaaleus verrattuna prosessissa aiemmin käytettyyn standardinatriumsilikaattiin. Kesäefektitutkimuksessa havaittiin, että kesäefektillä on suurin vaikutus esiflotaation primäärivaiheeseen, sillä primäärivaiheessa kuitujen osuus on huomattavasti suurempi kuin sekundäärivaiheissa. Esiflotaation primäärivaiheen uusiomassojen laboratorioflotaatioiden avulla saavutettujen maksimivaaleuksien ero kesän ja talven välillä oli noin 1,5 %ISO. Kesäefektin ei havaittu suuresti vaikuttavan flotaation sekundäärivaiheisiin.

Optimization of energy consumption in wastewater pumping

Pumppauksessa arvioidaan olevan niin teknisesti kuin taloudellisestikin huomattavia mahdollisuuksia säästää energiaa. Maailmanlaajuisesti pumppaus kuluttaa lähes 22 % sähkö-moottorien energiantarpeesta. Tietyillä teollisuudenaloilla jopa yli 50 % moottorien käyttämästä sähköenergiasta voi kulua pumppaukseen. Jäteveden pumppauksessa pumppujen toiminta perustuu tyypillisesti on-off käyntiin, jolloin pumpun ollessa päällä se käy täydellä teholla. Monissa tapauksissa pumput ovat myös ylimitoitettuja. Yhdessä nämä seikat johtavat kasvaneeseen energian kulutukseen. Työn teoriaosassa esitellään perusteet jätevesihuollosta ja jäteveden käsittelystä sekä pumppaussysteemin pääkomponentit: pumppu, putkisto, moottori ja taajuusmuuttaja. Työn empiirisessä osassa esitellään työn aikana kehitetty laskuri, jonka avulla voidaan arvioida energiansäästöpotentiaalia jäteveden pumppaussysteemeissä. Laskurilla on mandollista laskea energiansäästöpotentiaali käytettäessä pumpun tuoton ohjaustapana pyörimisnopeuden säätöä taajuusmuuttajalla on-off säädön sijasta. Laskuri ilmoittaa optimaalisimmanpumpun pyörimisnopeuden sekä ominaisenergiankulutuksen. Perustuen laskuriin, kolme kunnallista jätevedenpumppaamoa tutkittiin. Myös laboratorio-testitsuoritettiin laskurin simuloimiseksi sekä energiansäästöpotentiaalin arvioimiseksi. Tutkimukset osoittavat, että jätevedenpumppauksessa on huomattavia mandollisuuksia säästää energiaa pumpun pyörimisnopeutta pienentämällä. Geodeettisen nostokorkeuden ollessa pieni, voidaan energiaa säästää jopa 50 % ja pitkällä aikavälillä säästö voi olla merkittävä. Tulokset vahvistavat myös tarpeen jätevedenpumppaussysteemien toiminnan optimoimiseksi.

Optimization of the procedure for removing iron deposits on ceramic filter media

In this thesis, cleaning of ceramic filter media was studied. Mechanisms of fouling and dissolution of iron compounds, as well as methods for cleaning ceramic membranes fouled by iron deposits were studied in the literature part. Cleaning agents and different methods were closer examined in the experimental part of the thesis. Pyrite is found in the geologic strata. It is oxidized to form ferrous ions Fe(II) and ferric ions Fe(III). Fe(III) is further oxidized in the hydrolysis to form ferric hydroxide. Hematite and goethite, for instance, are naturally occurring iron oxidesand hydroxides. In contact with filter media, they can cause severe fouling, which common cleaning techniques competent enough to remove. Mechanisms for the dissolution of iron oxides include the ligand-promoted pathway and the proton-promoted pathway. The dissolution can also be reductive or non-reductive. The most efficient mechanism is the ligand-promoted reductive mechanism that comprises two stages: the induction period and the autocatalytic dissolution.Reducing agents(such as hydroquinone and hydroxylamine hydrochloride), chelating agents (such as EDTA) and organic acids are used for the removal of iron compounds. Oxalic acid is the most effective known cleaning agent for iron deposits. Since formulations are often more effective than organic acids, reducing agents or chelating agents alone, the citrate¿bicarbonate¿dithionite system among others is well studied in the literature. The cleaning is also enhanced with ultrasound and backpulsing.In the experimental part, oxalic acid and nitric acid were studied alone andin combinations. Also citric acid and ascorbic acid among other chemicals were tested. Soaking experiments, experiments with ultrasound and experiments for alternative methods to apply the cleaning solution on the filter samples were carried out. Permeability and ISO Brightness measurements were performed to examine the influence of the cleaning methods on the samples. Inductively coupled plasma optical emission spectroscopy (ICP-OES) analysis of the solutions was carried out to determine the dissolved metals.

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.