Maria Augusta Soares Machado

Adaptive Simulated Annealing

Adaptive Simulated Annealing (ASA) is a C-language code that finds the best global fit of a nonlinear cost-function over a D-dimensional space. ASA has over 100 OPTIONS to provide robust tuning over many classes of nonlinear stochastic systems. These many OPTIONS help ensure that ASA can be used robustly across many classes of systems.

Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing - Volume 35

Stochastic global optimization is a very important subject, that hasapplications in virtually all areas of science and technology. Therefore there is nothing more opportune than writing a book about a successful and mature algorithm that turned out to be a good tool in solving difficult problems. Here we present some techniques for solving several problems by means of Fuzzy Adaptive Simulated Annealing (Fuzzy ASA), a fuzzy-controlled version of ASA, and by ASA itself. ASA is a sophisticated global optimization algorithm that is based upon ideas of the simulated annealing paradigm, coded in the C programming language and developed to statistically find the best global fit of a nonlinear constrained, non-convex cost function over a multi-dimensional space. By presenting detailed examples of its application we want to stimulate the readers intuition and make the use of Fuzzy ASA (or regular ASA) easier for everyone wishing to use these tools to solve problems. We kept formal mathematical requirements to a minimum and focused on continuous problems, although ASA isable to handle discrete optimization tasks as well. This book can be used by researchers and practitioners in engineering and industry, in courses on optimization for advanced undergraduate and graduate levels, and also for self-study.

Behavioral multi-criteria decision analysis: the TODIM method with criteria interactions

In this paper a multi-criteria decision aiding model is developed through the use of the Choquet integral. The proposed model is an extension of the TODIM method, which is based on nonlinear Cumulative Prospect Theory. The paper starts by reviewing the first steps of behavioral decision theory. A presentation of the TODIM method follows. The basic concepts of the Choquet integral as related to multi-criteria decision aiding are reviewed. It is also shown how the measures of dominance of the TODIM method can be rewritten through the application of the Choquet integral. From the ordering of decision criteria the fuzzy measures of criteria interactions are computed, which leads to the ranking of alternatives. A case study on the forecasting of property values for rent in a Brazilian city illustrates the proposed model. Results obtained from the use of the Choquet integral are then compared against a previously made usage of the TODIM method. It is concluded that significant advantages exist derived from the use of the Choquet integral. The paper closes with recommendations for future research.

Criteria Interactions in Multiple Criteria Decision Aiding: A Choquet Formulation for the TODIM Method

Abstract The problem of modeling interactions between criteria in Multiple Criteria Decision Aiding (MCDA) has been approached by a number of authors. That problem arises when there are visible redundancies and synergies among criteria. Aggregation models exist that have been conceived to take care of criteria interdependences. From these aggregation models a special attention has been given to the Choquet integral, and its possibilities and limitations have been pointed out. In this paper it is shown how measures of criteria interaction can be computed for the TODIM method of MCDA by using the Choquet integral. The key conclusions from this case study are listed below: (i) the use of the Choquet integral minimizes the calculations by TODIM since it is unnecessary to normalize the raw data; (ii) not only precise values can be used but also interval data; this second situation would lead to using a fuzzy triangular number; (iii) by using the Choquet integral more complex additive models can be used that allow for taking dependencies between criteria into consideration. As important elements of future research the authors plan to encompass in their analysis new concepts such as generalizations of Choquet integral and the bipolar Cumulative Prospect Theory.

A Fuzzy Water Quality Index for Watershed Quality Analysis and Management

Climate change and hydric stress are limiting the availability of clean water. Overexploitation of natural resources has led to environmental unbalance. Present decisions relative to the management of hydric resources will deeply affect the economy and our future environment. The use of indicators is a good alternative for the evaluation of environmental behavior as well as a management instrument, as long as the conceptual and structural parameters of the indicators are respected. The use of fuzzy logic to study the influence and the consequences of environmental problems has increased significantly in recent years. According to Silvert (1997), most activities, either natural of anthropic, have multiple effects and any environmental index should offer a consistent meaning as well as a coherent quantitative and qualitative appraisal of all these effects. Among the several reasons for applying fuzzy logic to complex situations, the most important is probably the need to combine different indicators. Maybe the most significant advantage of the use of fuzzy logic for the development of environmental indicators is that it combines different aspects with much more flexibility than other methods, such as, for example, binary indices of the kind “acceptable vs. unacceptable.” Methods to integrate several variables related to water quality in a specific index are increasingly needed in national and international scenarios. Several authors have integrated water quality variables into indices, technically called Water Quality Indices (WQIs) (Bolton et al., 1978; Bhargava, 1983; House, 1989; Mitchell, 1996; Pesce and Wunderlin, 1999; Cude, 2001; Liou et al., 2004; Said et al., 2004; Silva and Jardim, 2006; Nasiri et al., 2007). Most are based in a concept developed by the U. S. National Sanitation Foundation (NSF, 2007). There is an obvious need for more advanced techniques to assess the importance of water quality variables and to integrate the distinct parameters involved. In this context, new, alternative integration methods are being developed. Artificial Intelligence has thus become a tool for modeling water quality (Chau, 2006). Traditional methodologies cannot classify and quantify environmental effects of a subjective nature or even provide formalism for

Multi-criteria Analysis of Natural Gas Destination in Brazil: A Comparison of TODIM Against the Use of the Choquet Integral☆

Abstract This paper presents an application of the classical TODIM method that is compared against the use of the same approach, but extended through the Choquet Integral to evaluate and recommend alternatives for the destination of the discovery of natural gas reserves in Santos Basin. The application focus on the Mexilhao field, analyzing the uncertainties and risks involved, concerning the regional market (South America) as well as the influence of others (such as Europe and the US).In order to produce a decision, various quantitative as well as qualitative factors such as politics, available technologies, return vs. risk, balance between supply and demand in Brazil, environmental and social impacts, regulatory issues, timing of implementation and alignment with the companys strategies must be taken into account. This leads to a multi-criteria analysis. It can be seen through a non-parametric statistical sign test that there are no significant differences between the results from the two methods.

Ranking of Suppliers for a Steel Industry: A Comparison of the Original TODIM and the Choquet-extended TODIM Methods☆

Abstract This paper presents an application of both the originalTODIM and the Choquet-extended TODIM methods. Both approaches are used here in order to rank suppliers of specified materials and goods quite relevant for a steel industry located in the Brazilian state of Rio de Janeiro. One conceptual advantage from using the Choquet-extended TODIM method is that it can deal with interactions between evaluation criteria. Results from the application of these two methods practically lead to the same ranks. The non-parametric statistic sign test allows concluding that that both methods are indeed equivalent in terms of the final results for this particular application. As a conclusion it can be saidthat the importance of a formal procedure for ranking suppliers basically consists of contributing to greater clarity and a higher learning throughout the ranking process.

Using a Bipolar Choquet Neural Network to Locate a Retail Store

Abstract In this paper, we propose and apply a novel analytical method for solving a class of location problems. The method is based on the use of the bipolar Choquet integral in a neural network for classifying alternative locations. The method is applied to the case study that consists of finding a location for a new store of a major Brazilian retail company. A comparison between the use of the proposed method and the TODIM-FSE method is presented in the paper. The method can also be applied to a situation when one has millions of patterns and new patterns have to be recognized. The paper closes with identifying the proposed method as being efficient and ready to be used with structured and non-structured data systems in order to discover relevant and still unknown information.

THE MULTIPLE CHOICE PROBLEM WITH INTERACTIONS BETWEEN CRITERIA

An important problem in Multi-Criteria Decision Analysis arises when one must select at least two alternatives at the same time. This can be denoted as a multiple choice problem. In other words, instead of evaluating each of the alternatives separately, they must be combined into groups of n alternatives, where n = 2. When the multiple choice problem must be solved under multiple criteria, the result is a multi-criteria, multiple choice problem. In this paper, it is shown through examples how this problemcan be tackled on a bipolar scale. The Choquet integral is used in this paper to take care of interactions between criteria. A numerical application example is conducted using data from SEBRAE-RJ, a non-profit private organization that has the mission of promoting competitiveness, sustainable developmentand entrepreneurship in the state of Rio de Janeiro, Brazil. The paper closes with suggestions for future research.

Global Optimization and Its Applications

In this chapter we will introduce ideas about global optimization methods, their types and limitations, exposing, in a succint way, several of their main characteristics. As our focus in this book will be on adaptive simulated annealing and its applications, we’ll start to pave the way that will take us to pragmatic utilization of that method and stochastic optimization methods, in general.