Fernando Jiménez

Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach

Abstract The Solid Transportation Problem (STP) arises when bounds are given on three item properties. The Fuzzy Solid Transportation Problem (FSTP) appears when the nature of the data problem is fuzzy. This paper deals with the FSTP in the case in which the fuzziness affects the constraint set, and a fuzzy solution to the problem is required. Moreover, an arbitrary linear or nonlinear objective function is considered. In order to find a fuzzy solution to the problem, a parametric approach is used to obtain an auxiliary Parametric Solid Transportation Problem (PSTP) associated to the original problem. As there are no well-known solution methods proposed in literature to solve effectively the PSTP, in this paper an Evolutionary Algorithm (EA) based solution method is proposed to solve it, which can finally be applied to find a “good” fuzzy solution to the FSTP. Comparisons with another conventional method are presented and the results show the EA based approach to be better as a whole.

Uncertain solid transportation problems

The solid transportation problem arises when bounds are given on three item properties. Usually, these properties are source, destination and type of product or mode of transport, and often are given in a uncertain way. This paper deals with two of the ways in which uncertainty can appear in the problem: Interval solid transportation problem and fuzzy solid transportation problem. The first arises when data problem are expressed as intervals instead of point values, and the second when the nature of the information is vague. Both models are treated in the case in which the uncertainty affects only the constraint set. For interval case, an auxiliary problem is obtained in order to find a solution. This auxiliary problem is a standard solid transportation problem which can be solved with the efficient methods existing. For fuzzy case, a parametric approach which makes it possible to find a fuzzy solution to the former problem is used.

An evolutionary algorithm for constrained multi-objective optimization

The paper follows the line of the design and evaluation of new evolutionary algorithms for constrained multi-objective optimization. The evolutionary algorithm proposed (ENORA) incorporates the Pareto concept of multi-objective optimization with a constraint handling technique and with a powerful diversity mechanism to obtain multiple nondominated solutions through the simple run of the algorithm. Constraint handling is carried out in an evolutionary way and using the min-max formulation, while the diversity technique is based on the partitioning of search space in a set of radial slots along which are positioned the successive populations generated by the algorithm. A set of test problems recently proposed for the evaluation of this kind of algorithm has been used in the evaluation of the algorithm presented. The results obtained with ENORA were very good and considerably better than those obtained with algorithms recently proposed by other authors.

Fuzzy modeling with hybrid systems

In this paper we present different approaches to the problem of fuzzy rules extraction by using a combination of fuzzy clustering and genetic algorithms as the main tools. This combination of techniques let us define a hybrid system by which we can have different approaches in a fuzzy modeling process. For example, we can obtain a first approximation to the fuzzy rules that describe the system behavior represented by a collection of raw data, without any assumption about the structure of the data using a fuzzy clustering technique, and subsequently, these rules can be tuned using a genetic algorithm. Alternatively, this genetic algorithm can be used in order to generate and tune the fuzzy rules directly from the data with or without some priori information. Finally, their performances are compared.

(Un)sustainable territories: causes of the speculative bubble in Spain (1996–2010) and its territorial, environmental, and sociopolitical consequences

In this paper we analyse the causes of the Spanish property model and its territorial, social, and political consequences. Particular attention is paid to sociopolitical contexts. These consequences include excessive dependence on economic activity and employment in the housing construction sector, the irreversible disappearance of landmarks in the countrys collective history and culture, and examples of ‘policy capture’, especially at local and regional levels. This lengthy process has led to corruption in town planning and an increase in poor policy decisions, greatly harming Spains reputation.

Multi-objective evolutionary computation and fuzzy optimization

Abstract In fuzzy optimization it is desirable that all fuzzy solutions under consideration be attainable, so that the decision maker will be able to make “a posteriori” decisions according to current decision environments. No additional optimization runs will be needed when the decision environment changes or when the decision maker needs to evaluate several decisions to establish the most appropriate ones. In this sense, multi-objective optimization is similar to fuzzy optimization, since it is also desirable to capture the Pareto front composing the solution. The Pareto front in a multi-objective problem can be interpreted as the fuzzy solution for a fuzzy problem. Multi-objective evolutionary algorithms have been shown in the last few years to be powerful techniques in solving multi-objective optimization problems because they can search for multiple Pareto solutions in a single run of the algorithm. In this contribution, we first introduce a multi-objective approach for nonlinear constrained optimization problems with fuzzy costs and constraints, and then an “ad hoc” multi-objective evolutionary algorithm to solve the former problem. A case study of a fuzzy optimization problem arising in some import–export companies in the south of Spain is analyzed and the proposed solutions from the evolutionary algorithm considered here are given.

Accurate, Transparent, and Compact Fuzzy Models for Function Approximation and Dynamic Modeling through Multi-objective Evolutionary Optimization

Evolutionary algorithms to design fuzzy rules from data for systems modeling have received much attention in recent literature. Many approaches are able to find highly accurate fuzzy models. However, these models often contain many rules and are not transparent. Therefore, we propose several objectives dealing with transparency and compactness besides the standard accuracy objective. These objectives are used to find multiple Pareto-optimal solutions with a multi-objective evolutionary algorithm in a single run. Attractive models with respect to compactness, transparency and accuracy are the result.

Approximative fuzzy rules approaches for classification with hybrid-GA techniques

Abstract In this paper the use of different methods from the fuzzy modeling field for classification tasks is evaluated and the potential of their integration in producing better classification results is investigated. The methods considered, approximative in their nature, consider different integrations of techniques with an initial rule generation step and a following rule tuning approach using different evolutionary algorithms. We analyse the adaptation of existing techniques in the fuzzy modeling context for the classification problem, and the integration of these techniques in order to improve the classifiers performance. Finally a genetic algorithm (GA) for translation from approximative rules to similar descriptive ones trying to preserve the accuracy of the approximative classifier is presented. The classical Iris and Cancer data set are used throughout the evaluation process to form a common ground for comparison and performance analysis.

A multi-objective evolutionary approach for fuzzy optimization in production planning

This paper outlines, first, a real-world industrial problem for product-mix selection involving 8 variables and 21 constraints with fuzzy coefficients and thereafter, a multi-objective optimization approach to solve the problem. This problem occurs in production planning in which a decisionmaker plays a pivotal role in making decision under fuzzy environment. Decision-maker should be aware of his/her level-of-satisfaction as well as degree of fuzziness while making the product-mix decision. Thus, the authors have analyzed using a modified S-curve membership function the fuzziness patterns and fuzzy sensitivity of the solution found from the multi-objective optimization methodology. An ad hoc Pareto-based multi-objective evolutionary algorithm is proposed to capture multiple non dominated solutions in a single run of the algorithm. Results obtained have been compared with the well-known multi-objective evolutionary algorithm NSGA-II.

Multi-objective evolutionary algorithms for fuzzy classification in survival prediction

OBJECTIVE This paper presents a novel rule-based fuzzy classification methodology for survival/mortality prediction in severe burnt patients. Due to the ethical aspects involved in this medical scenario, physicians tend not to accept a computer-based evaluation unless they understand why and how such a recommendation is given. Therefore, any fuzzy classifier model must be both accurate and interpretable. METHODS AND MATERIALS The proposed methodology is a three-step process: (1) multi-objective constrained optimization of a patients data set, using Pareto-based elitist multi-objective evolutionary algorithms to maximize accuracy and minimize the complexity (number of rules) of classifiers, subject to interpretability constraints; this step produces a set of alternative (Pareto) classifiers; (2) linguistic labeling, which assigns a linguistic label to each fuzzy set of the classifiers; this step is essential to the interpretability of the classifiers; (3) decision making, whereby a classifier is chosen, if it is satisfactory, according to the preferences of the decision maker. If no classifier is satisfactory for the decision maker, the process starts again in step (1) with a different input parameter set. RESULTS The performance of three multi-objective evolutionary algorithms, niched pre-selection multi-objective algorithm, elitist Pareto-based multi-objective evolutionary algorithm for diversity reinforcement (ENORA) and the non-dominated sorting genetic algorithm (NSGA-II), was tested using a patients data set from an intensive care burn unit and a standard machine learning data set from an standard machine learning repository. The results are compared using the hypervolume multi-objective metric. Besides, the results have been compared with other non-evolutionary techniques and validated with a multi-objective cross-validation technique. Our proposal improves the classification rate obtained by other non-evolutionary techniques (decision trees, artificial neural networks, Naive Bayes, and case-based reasoning) obtaining with ENORA a classification rate of 0.9298, specificity of 0.9385, and sensitivity of 0.9364, with 14.2 interpretable fuzzy rules on average. CONCLUSIONS Our proposal improves the accuracy and interpretability of the classifiers, compared with other non-evolutionary techniques. We also conclude that ENORA outperforms niched pre-selection and NSGA-II algorithms. Moreover, given that our multi-objective evolutionary methodology is non-combinational based on real parameter optimization, the time cost is significantly reduced compared with other evolutionary approaches existing in literature based on combinational optimization.