MODELOS Y MÉTODOS DE OPTIMIZACIÓN LINEAL CON INCERTIDUMBRE: UNA BREVE REVISIÓN DEL ESTADO DEL ARTE

In the modeling of many problems on linear optimization is not possible to consider the classic deterministic model because the set of parameters is not fully known due to the significant variation of the data along time or because there is no uniformity on the values. These kind of problems are known as problems with uncertainty and there are different approaches about modeling and methods of solution to resolve them. In this paper we make a review of such approaches focusing basically in stochastic optimization, fuzzy optimization, intervaling optimization and hybrid optimization. The difference between these approaches is perceived in the nature of the data, notions of feasibility and optimality and computational requirements, among others.En la modelación de muchos problemas de optimización lineal no es posible considerar el modelo clásico determinista, porque el conjunto de los parámetros no son completamente conocidos debido a que los datos varian en forma significativa a lo largo del tiempo o porque no hay homogeneidad en los valores.Estos problemas son conocidos como problemas con incertidumbre, para los cuales existen diversos enfoques en la modelación y en los métodos de solución. En este artículo se revisa tales enfoques, incidiendo fundamentalmente en la optimización estocástica, optimización difusa, optimización intervalar y optimización híbrida. La diferencia entre estos enfoques se perciben en la naturaleza de los datos, nociones de factibilidad y optimalidad, requerimientos computacionales, entre otros

Optimization and inference under fuzzy numerical constraints

Εκτεταμένη έρευνα έχει γίνει στους τομείς της Ικανοποίησης Περιορισμών με διακριτά (ακέραια) ή πραγματικά πεδία τιμών. Αυτή η έρευνα έχει οδηγήσει σε πολλαπλές σημασιολογικές περιγραφές, πλατφόρμες και συστήματα για την περιγραφή σχετικών προβλημάτων με επαρκείς βελτιστοποιήσεις. Παρά ταύτα, λόγω της ασαφούς φύσης πραγματικών προβλημάτων ή ελλιπούς μας γνώσης για αυτά, η σαφής μοντελοποίηση ενός προβλήματος ικανοποίησης περιορισμών δεν είναι πάντα ένα εύκολο ζήτημα ή ακόμα και η καλύτερη προσέγγιση. Επιπλέον, το πρόβλημα της μοντελοποίησης και επίλυσης ελλιπούς γνώσης είναι ακόμη δυσκολότερο. Επιπροσθέτως, πρακτικές απαιτήσεις μοντελοποίησης και μέθοδοι βελτιστοποίησης του χρόνου αναζήτησης απαιτούν συνήθως ειδικές πληροφορίες για το πεδίο εφαρμογής, καθιστώντας τη δημιουργία ενός γενικότερου πλαισίου βελτιστοποίησης ένα ιδιαίτερα δύσκολο πρόβλημα. Στα πλαίσια αυτής της εργασίας θα μελετήσουμε το πρόβλημα της μοντελοποίησης και αξιοποίησης σαφών, ελλιπών ή ασαφών περιορισμών, καθώς και πιθανές στρατηγικές βελτιστοποίησης. Καθώς τα παραδοσιακά προβλήματα ικανοποίησης περιορισμών λειτουργούν βάσει συγκεκριμένων και προκαθορισμένων κανόνων και σχέσεων, παρουσιάζει ενδιαφέρον η διερεύνηση στρατηγικών και βελτιστοποιήσεων που θα επιτρέπουν το συμπερασμό νέων ή/και αποδοτικότερων περιορισμών. Τέτοιοι επιπρόσθετοι κανόνες θα μπορούσαν να βελτιώσουν τη διαδικασία αναζήτησης μέσω της εφαρμογής αυστηρότερων περιορισμών και περιορισμού του χώρου αναζήτησης ή να προσφέρουν χρήσιμες πληροφορίες στον αναλυτή για τη φύση του προβλήματος που μοντελοποιεί.Extensive research has been done in the areas of Constraint Satisfaction with discrete/integer and real domain ranges. Multiple platforms and systems to deal with these kinds of domains have been developed and appropriately optimized. Nevertheless, due to the incomplete and possibly vague nature of real-life problems, modeling a crisp and adequately strict satisfaction problem may not always be easy or even appropriate. The problem of modeling incomplete knowledge or solving an incomplete/relaxed representation of a problem is a much harder issue to tackle. Additionally, practical modeling requirements and search optimizations require specific domain knowledge in order to be implemented, making the creation of a more generic optimization framework an even harder problem.In this thesis, we will study the problem of modeling and utilizing incomplete and fuzzy constraints, as well as possible optimization strategies. As constraint satisfaction problems usually contain hard-coded constraints based on specific problem and domain knowledge, we will investigate whether strategies and generic heuristics exist for inferring new constraint rules. Additional rules could optimize the search process by implementing stricter constraints and thus pruning the search space or even provide useful insight to the researcher concerning the nature of the investigated problem

Fuzzy Linear Programming with Interval Type-2 fuzzy constraints

Doctorad

A Hybrid intelligent system for diagnosing and solving financial problems

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnologico. Programa de Pós-Graduação em Engenharia de Produção2012-10-16T09:55:39

Proceedings of the Second Joint Technology Workshop on Neural Networks and Fuzzy Logic, volume 2

Documented here are papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by NASA and the University of Texas, Houston. Topics addressed included adaptive systems, learning algorithms, network architectures, vision, robotics, neurobiological connections, speech recognition and synthesis, fuzzy set theory and application, control and dynamics processing, space applications, fuzzy logic and neural network computers, approximate reasoning, and multiobject decision making

Systems Analysis For Urban Water Infrastructure Expansion With Global Change Impact Under Uncertainties

Over the past decades, cost-effectiveness principle or cost-benefit analysis has been employed oftentimes as a typical assessment tool for the expansion of drinking water utility. With changing public awareness of the inherent linkages between climate change, population growth and economic development, the addition of global change impact in the assessment regime has altered the landscape of traditional evaluation matrix. Nowadays, urban drinking water infrastructure requires careful long-term expansion planning to reduce the risk from global change impact with respect to greenhouse gas (GHG) emissions, economic boom and recession, as well as water demand variation associated with population growth and migration. Meanwhile, accurate prediction of municipal water demand is critically important to water utility in a fast growing urban region for the purpose of drinking water system planning, design and water utility asset management. A system analysis under global change impact due to the population dynamics, water resources conservation, and environmental management policies should be carried out to search for sustainable solutions temporally and spatially with different scales under uncertainties. This study is aimed to develop an innovative, interdisciplinary, and insightful modeling framework to deal with global change issues as a whole based on a real-world drinking water infrastructure system expansion program in Manatee County, Florida. Four intertwined components within the drinking water infrastructure system planning were investigated and integrated, which consists of water demand analysis, GHG emission potential, system optimization for infrastructure expansion, and nested minimax-regret (NMMR) decision analysis under uncertainties. In the water demand analysis, a new system dynamics model was developed to reflect the intrinsic relationship between water demand and changing socioeconomic iv environment. This system dynamics model is based on a coupled modeling structure that takes the interactions among economic and social dimensions into account offering a satisfactory platform. In the evaluation of GHG emission potential, a life cycle assessment (LCA) is conducted to estimate the carbon footprint for all expansion alternatives for water supply. The result of this LCA study provides an extra dimension for decision makers to extract more effective adaptation strategies. Both water demand forecasting and GHG emission potential were deemed as the input information for system optimization when all alternatives are taken into account simultaneously. In the system optimization for infrastructure expansion, a multiobjective optimization model was formulated for providing the multitemporal optimal facility expansion strategies. With the aid of a multi-stage planning methodology over the partitioned time horizon, such a systems analysis has resulted in a full-scale screening and sequencing with respect to multiple competing objectives across a suite of management strategies. In the decision analysis under uncertainty, such a system optimization model was further developed as a unique NMMR programming model due to the uncertainties imposed by the real-world problem. The proposed NMMR algorithm was successfully applied for solving the real-world problem with a limited scale for the purpose of demonstration

Reviewing Evolution of Learning Functions and Semantic Information Measures for Understanding Deep Learning

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author’s semantic information G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shannon’s MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon’s MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks’ latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development

Applications of Fuzzy Set Theory, Fuzzy Measure Theory and Fuzzy Differential Calculus

This research tackles the issue of uncertainty due to lack of information, alternatively known as Knightian Uncertainty, and its impact on option pricing. In the presence of such uncertainty, Probability Theory becomes restrictive and alternative tools are called for. In this research, we consider tools of Fuzzy Theory. We introduce three Option Pricing Models the first of which is a fuzzy binomial model based on the standard CRR binomial model. The model performs option pricing in a fuzzy world characterized by blurred prices. In such a world, it is no longer possible to price by replication. So we introduce a fuzzy pricing approach that employs Sugeno integration and fuzzy measures, and generates bounds on the possible option price. The second model is a fuzzy Black-Scholes model, which prices options in the presence of uncertain or fuzzy volatility. We model such volatility by establishing bounds on the corresponding fuzzy values thereby generating fuzzy bounds on the possible option price. Finally, the third model is an extension on an existing one period fuzzy binomial model that prices options when the underlying price is characterized by opacity. The option price returned by this model is dependent on a market parameter that summarizes its completeness. However, it is possible to defuzzify the last two models to obtain one crisp price that summarizes market information. The last two models outperform their standard counterparts

Socio-Economic Assessment of Fusion Energy Research, Development, Demonstration and Deployment Programme

Providing safe, clean and affordable energy supply is essential for meeting the basic needs of human society and for supporting economic growth. From the historical perspective, the constantly growing energy use was one of the main factors, which drove the industrialised countries to the current level of prosperity. Meanwhile, in recent decades, the issue of global energy security became a topic of increasing concern in the international policy agenda. On the one hand, the world is facing the problem of exhaustion of most convenient and cheep fuel reserves. The situation is becoming worse, because of the constantly growing demand in developing countries, and the oligopolistic behaviour of major energy exporting countries. On the other hand, the society is becoming more and more sensitive to the environmental pollution problems, caused by the excessive consumption of fossil fuels. In the face of energy security challenge, national governments ought to implement adequate strategies aimed at liberalisation of energy markets, diversification of energy supply mix, enhancement of energy efficiency, encouragement of investments in energy infrastructures, and promotion of innovation in energy sector. In a longer term perspective, the latter point becomes increasingly important, because the world is relying currently on the consumption of non-renewable fossil fuels, and the development of new safe, clean and resource unconstraint energy technologies is vitally needed. In line with this strategy, the major world economies pursue the joint R&D programme on thermonuclear Fusion technology, which represents numerous advantages due to its inherent safety, avoidance of CO2 emissions, relatively small environmental impact, abundance and world-wide uniform distribution of fuel resources. Considering the importance of the projected environmental and economic benefits of Fusion, the questions are raised whether the current level of financial support is sufficient, and what could be the optimal strategy to proceed with the demonstration of Fusion technology, given the time span and potential risks of Fusion RDDD programme. To put these questions into the context, one has to consider the current trends in energy R&D funding, which has seen a drastic decline ( ~50%) over the last three decades. The liberalisation of energy sector poses additional problem due to the fact that free markets partially failure to provide public goods, such as basic science and R&D, because of the so-called spillover effects meaning that the firms are not able to appropriate the integral results of their R&D investments. Regarding the thermonuclear Fusion technology, the decision makers responsible for national energy policies and allocation of public R&D funds may face the following specific questions: What is the expected net socio-economic payoff (social rate of return) of Fusion R&D programme, including both internal and external costs and benefits? What are the reasonable economic arguments that could justify the increase in public funding of the ongoing and future Fusion R&D activities and would stimulate greater involvement of the private sector? What additional value can be obtained through undertaking a more ambitious Fusion R&D programme (accelerated development path), which requires bigger number of experimental facilities, increased funding, and more intense overall efforts of international scientific and industrial community? In order to provide sound arguments for policymakers seeking to optimise public R&D funding, a robust socio-economic evaluation of the whole Fusion research, development, demonstration and deployment (RDDD) programme is needed. At the present stage, prospective analyses of Fusion technology have been emphasised mainly on the investigation of technological issues, estimation of the direct costs of Fusion power and analysis of its potential role in future energy systems. Meanwhile, methodological tools and practical studies aiming at a more comprehensive socio-economic assessment of global long-term energy R&D programmes, such as Fusion, are still incomplete. The primary difficulty concerns the evaluation of positive externalities that may reveal through different types of spillover effects, including but not limited to knowledge, network and market spillovers. While the presence of these effects has been identified in the economic theory and confirmed by empirical studies, their quantitative analysis in the specific case of large scale energy R&D programmes represents some methodological lacuna and deserves further investigation. Another problem relates to the methodology of cost-benefit analysis, which oftentimes ignores the hidden value of R&D projects arising due to the possible flexibility in managerial decisions. In fact, throughout the course of any R&D project, its prospective cash-flows can be significantly improved by pro-active management of different implementation stages, e.g. expanding the production, if market conditions are favourable, or abandoning, if R&D process appears to be unproductive. As a result, the strategic value of any R&D project normally exceeds its net present value (NPV) calculated with the traditional discounted cash flow (DCF) method. Although this strategic approach to capital budgeting, known as Real Options, has been propagated recently in several publications dealing with appraisal of lumpy irreversible investments, its practical application in the context of Fusion RDDD programme has not been mastered yet to the required extent. A particular challenge consists in the need for adequate treatment of different types of uncertainty in the model structure, parameters and input data. Accordingly, the main objective of this thesis consists in complementing the existing studies with an in-depth analysis of the positive externalities (spillover benefits) of Fusion RDDD programme and calculation of its strategic real options value subject to different managerial strategies throughout demonstration and deployment stages. Net social present value of Fusion RDDD programme and potential impact of Fusion R&D activities on the economic performance of the involved private companies are estimated using an integrated modelling framework, which includes the following components: (1) assessment of technological potential for deployment of Fusion power plants based on the simulation of multi-regional long term electricity supply scenarios with PLANELEC model; (2) economic evaluation of Fusion RDDD programme and analysis of different implementation strategies using Real Options model; (3) estimation of the economic value of spillover benefits from participation in Fusion R&D projects at the microeconomic level with the help of financial evaluation model; (4) strategic evaluation of Fusion RDDD programme, taking into account both spillover benefits and real options value, and policy recommendations