An Integrated Probability-Based Approach for Multiple Response Surface Optimization

Nearly all real life systems have multiple quality characteristics where individual modeling and optimization approaches can not provide a balanced compromising solution. Since performance, cost, schedule, and consistency remain the basics of any design process, design configurations are expected to meet several conflicting requirements at the same time. Correlation between responses and model parameter uncertainty demands extra scrutiny and prevents practitioners from studying responses in isolation. Like any other multi-objective problem, multi-response optimization problem requires trade-offs and compromises, which in turn makes the available algorithms difficult to generalize for all design problems. Although multiple modeling and optimization approaches have been highly utilized in different industries, and several software applications are available, there is no perfect solution to date and this is likely to remain so in the future. Therefore, problem specific structure, diversity, and the complexity of the available approaches require careful consideration by the quality engineers in their applications

The Two Kinds of Free Energy and the Bayesian Revolution

The concept of free energy has its origins in 19th century thermodynamics, but has recently found its way into the behavioral and neural sciences, where it has been promoted for its wide applicability and has even been suggested as a fundamental principle of understanding intelligent behavior and brain function. We argue that there are essentially two different notions of free energy in current models of intelligent agency, that can both be considered as applications of Bayesian inference to the problem of action selection: one that appears when trading off accuracy and uncertainty based on a general maximum entropy principle, and one that formulates action selection in terms of minimizing an error measure that quantifies deviations of beliefs and policies from given reference models. The first approach provides a normative rule for action selection in the face of model uncertainty or when information processing capabilities are limited. The second approach directly aims to formulate the action selection problem as an inference problem in the context of Bayesian brain theories, also known as Active Inference in the literature. We elucidate the main ideas and discuss critical technical and conceptual issues revolving around these two notions of free energy that both claim to apply at all levels of decision-making, from the high-level deliberation of reasoning down to the low-level information processing of perception

Evolutionary Computation and QSAR Research

[Abstract] The successful high throughput screening of molecule libraries for a specific biological property is one of the main improvements in drug discovery. The virtual molecular filtering and screening relies greatly on quantitative structure-activity relationship (QSAR) analysis, a mathematical model that correlates the activity of a molecule with molecular descriptors. QSAR models have the potential to reduce the costly failure of drug candidates in advanced (clinical) stages by filtering combinatorial libraries, eliminating candidates with a predicted toxic effect and poor pharmacokinetic profiles, and reducing the number of experiments. To obtain a predictive and reliable QSAR model, scientists use methods from various fields such as molecular modeling, pattern recognition, machine learning or artificial intelligence. QSAR modeling relies on three main steps: molecular structure codification into molecular descriptors, selection of relevant variables in the context of the analyzed activity, and search of the optimal mathematical model that correlates the molecular descriptors with a specific activity. Since a variety of techniques from statistics and artificial intelligence can aid variable selection and model building steps, this review focuses on the evolutionary computation methods supporting these tasks. Thus, this review explains the basic of the genetic algorithms and genetic programming as evolutionary computation approaches, the selection methods for high-dimensional data in QSAR, the methods to build QSAR models, the current evolutionary feature selection methods and applications in QSAR and the future trend on the joint or multi-task feature selection methods.Instituto de Salud Carlos III, PIO52048Instituto de Salud Carlos III, RD07/0067/0005Ministerio de Industria, Comercio y Turismo; TSI-020110-2009-53)Galicia. Consellería de Economía e Industria; 10SIN105004P

Industrial Applications of Intelligent Adaptive Sampling Methods for Multi-Objective Optimization

Multi-objective optimization is an essential component of nearly all engineering design. However, for industrial applications, the design process typically demands running expensive computer code and/or real-world experiments putting the design process at risk of finding suboptimal solutions and/or not meeting budget constraints. As a first step toward a remedy, meta-models are built to mimic the response surface at a much lower query cost. We cover a time-tested technology specifically tailored to limited-data scenarios called Bayesian hybrid modeling (GEBHM) developed and maintained at General Electric (GE) research. GEBHM offers Bayesian mean and principled uncertainty predictions allowing a second technology called intelligent design and analysis of experiments (GE-IDACE/IDACE) to perform the optimization task using an adaptive sampling strategy. This chapter first covers the theoretical framework of both GEBHM and GE-IDACE. Then, the impact of GEBHM/GE-IDACE is demonstrated on multiple real-world engineering applications including additive manufacturing, combustion testing, and computational fluid dynamic design modeling. GEBHM and GE-IDACE are used daily and extensively within GE with huge impact in the form of 30–90% cost reduction and superior engineering designs of competitive products

Multivariate Steepest Ascent Using Bayesian Reliability

The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found

Bayesian hierarchical models for housing prices in the Helsinki-Espoo-Vantaa region

Tässä tutkielmassa esitellään bayesläisten hierarkisten mallien käyttöä asuntojen hintojen mallintamiseen. Tutkielmassa käytetään aineistoa, jossa kuvataan tapahtuneita asuntokauppoja Helsingistä, Espoosta ja Vantaalta. Tutkielmassa estimoidaan yhteensä viisi robustia regressiomallia. Malleissa käytetään Studentin t-jakaumaa likelihood-jakaumana, sillä aineistotarkastelut antavat viitteitä tietojen kirjausvirheistä. Neljässä mallissa on hierarkinen rakenne, joka perustuu myytyjen asuntojen kaupunginosiin. Malleista tuotetaan myös yhdistelmämalli käyttäen n.k. model stacking-menetelmää. Mallien toimivuutta tarkastellaan posterior-jakaumasta johdettavien ennustejakaumien perusteella: Ennustejakaumista poimitaan otos, jonka perusteella muodostetaan jakaumat valituille tunnusluvuille. Tunnuslukujen jakaumia verrataan oikeasta aineistosta laskettuihin, toteutuneisiin tunnuslukuihin. Mallien ennustekykyä vertaillaan tutkimalla ennustejakaumien kalibraatiota sekä terävyyttä. Lisäksi malleille lasketaan logaritmiset pisteet käyttäen leave-one-out ristiinvalidointia. Ristiinvalidoinnin laskennassa käytetään n.k. Pareto smoothed importance sampling-menetelmää. Ennustejakaumista tuotetaan myös piste-estimaatit käyttäen otoskeskiarvoja. Piste-estimaateille lasketaan R^2-suure. Mallien tulokset ovat valtaosin uskottavia. Malleissa käytetyt selittävät muuttujat käyttäytyvät pääosin etukäteen odotetulla tavalla ja mallien ennusteet ovat järkeviä valtaosalle havainnoista. Tulokset viittaavat siihen, että hintamekanismi eroaa oleellisesti Helsingin keskustassa verrattuna muihin tutkittuihin alueisiin. Mallit kärsivät kuitenkin huonosta kalibroinnista sekä siitä, että kalliiden asuntojen hintaennusteet ovat valtaosin liian alhaisia.Objectives: The objective of this thesis is to illustrate the advantages of Bayesian hierarchical models in housing price modeling. Methods: Five Bayesian regression models are estimated for the housing prices. The models use a robust Student’s t-distribution likelihood and are estimated with Hamiltonian Monte Carlo. Four of the models are hierarchical such that the apartments’ neighborhoods are used as a grouping. Model stacking is also used to produce an ensemble model. Model checks are conducted using the posterior predictive distributions. The predictive distributions are also evaluated in terms of calibration and sharpness and using the logarithmic score with leave-one-out cross validation. The logarithmic scores are calculated using Pareto smoothed importance sampling. The R^2-statistics from the point predictions averaged from the predictive distributions are also presented. Results: The results from the models are broadly reasonable as, for the most part, the coefficients of the explanatory variables and the predictive distributions behave as expected. The results are also consistent with the existence of a submarket in central Helsinki where the price mechanism differs markedly from the rest of the Helsinki-Espoo-Vantaa region. However, model checks indicate that none of the models is well-calibrated. Additionally, the models tend to underpredict the prices of expensive apartments

Scientific research trends about metaheuristics in process optimization and case study using the desirability function

This study aimed to identify the research gaps in Metaheuristics, taking into account the publications entered in a database in 2015 and to present a case study of a company in the Sul Fluminense region using the Desirability function. To achieve this goal, applied research of exploratory nature and qualitative approach was carried out, as well as another of quantitative nature. As method and technical procedures were the bibliographical research, some literature review, and an adopted case study respectively. As a contribution of this research, the holistic view of opportunities to carry out new investigations on the theme in question is pointed out. It is noteworthy that the identified study gaps after the research were prioritized and discriminated, highlighting the importance of the viability of metaheuristic algorithms, as well as their benefits for process optimization