Thomas A. Runkler

Selection of appropriate defuzzification methods using application specific properties

Defuzzification is used to transform fuzzy inference results into crisp output. The standard defuzzification methods fail in some applications. It is, therefore, important to select appropriate defuzzification methods depending on the application. This paper presents some of the most important defuzzification methods and investigates their properties. With three application examples, it illustrates how to select appropriate defuzzification methods using application specific properties.

Alternating cluster estimation: a new tool for clustering and function approximation

Many clustering models define good clusters as extrema of objective functions. Optimization of these models is often done using an alternating optimization (AO) algorithm driven by necessary conditions for local extrema. We abandon the objective function model in favor of a generalized model called alternating cluster estimation (ACE). ACE uses an alternating iteration architecture, but membership and prototype functions are selected directly by the user. Virtually every clustering model can be realized as an instance of ACE. Out of a large variety of possible instances of non-AO models, we present two examples: 1) an algorithm with a dynamically changing prototype function that extracts representative data and 2) a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions. We illustrate these non-AO instances on three problems: a) simple clustering of plane data where we show that creating an unmatched ACE algorithm overcomes some problems of fuzzy c-means (FCM-AO) and possibilistic c-means (PCM-AO); b) functional approximation by clustering on a simple artificial data set; and c) functional approximation on a 12 input 1 output real world data set. ACE models work pretty well in all three cases.

Web mining with relational clustering

Clustering is an unsupervised learning method that determines partitions and (possibly) prototypes from pattern sets. Sets of numerical patterns can be clustered by alternating optimization (AO) of clustering objective functions or by alternating cluster estimation (ACE). Sets of non-numerical patterns can often be represented numerically by (pairwise) relations. These relational data sets can be clustered by relational AO and by relational ACE (RACE). We consider two kinds of non-numerical patterns provided by the World Wide Web: document contents such as the text parts of web pages, and sequences of web pages visited by particular users, so-called web logs. The analysis of document contents is often called web content mining, and the analysis of log files with web page sequences is called web log mining. For both non-numerical pattern types (text and web page sequences) relational data sets can be automatically generated using the Levenshtein (edit) distance or using graph distances. The prototypes found for text data can be interpreted as keywords that serve for document classification and automatic archiving. The prototypes found for web page sequences can be interpreted as prototypical click streams that indicate typical user interests, and therefore serve as a basis for web content and web structure management.

Fuzzy Clustering by Particle Swarm Optimization

This paper deals with fuzzy clustering by minimizing the fuzzy c-means (FCM) model. We introduce two new methods for minimizing the two reformulated versions of the FCM objective function by particle swarm optimization (PSO). In PSO-V each particle represents a component of a cluster center. In PSO-U each particle represents an unsealed and unnormalized membership value. PSO-V and PSO-U are compared with alternating optimization (AO) and with ant colony optimization (ACO) on two benchmark data sets: the single outlier and the lung cancer data sets. The stochastic methods ACO, PSO-V, and PSO-U are slower than AO, but in each experiment one of the two PSO variants significantly outperforms the other algorithms.

Rescheduling and optimization of logistic processes using GA and ACO

This paper presents a comparative study of genetic algorithms (GA) and ant colony optimization (ACO) applied the online re-optimization of a logistic scheduling problem. This study starts with a literature review of the GA and ACO performance for different benchmark problems. Then, the algorithms are compared on two simulation scenarios: a static and a dynamic environment, where orders are canceled during the scheduling process. In a static optimization environment, both methods perform equally well, but the GA are faster. However, in a dynamic optimization environment, the GA cannot cope with the disturbances unless they re-optimize the whole problem again. On the contrary, the ant colonies are able to find new optimization solutions without re-optimizing the problem, through the inspection of the pheromone matrix. Thus, it can be concluded that the extra time required by the ACO during the optimization process provides information that can be useful to deal with disturbances.

Ant colony optimization of clustering models

The original ant system algorithm is simplified leading to a generalized ant colony optimization algorithm that can be used to solve a wide variety of discrete optimization problems. It is shown how objective function based clustering models such as hard and fuzzy c‐means can be optimized using particular extensions of this simplified ant optimization algorithm. Experiments with artificial and real datasets show that ant clustering produces better results than alternating optimization because it is less sensitive to local extrema.

Two cooperative ant colonies for feature selection using fuzzy models

The available set of potential features in real-world databases is sometimes very large, and it can be necessary to find a small subset for classification purposes. One of the most important techniques in data pre-processing for classification is feature selection. Less relevant or highly correlated features decrease, in general, the classification accuracy and enlarge the complexity of the classifier. The goal is to find a reduced set of features that reveals the best classification accuracy for a classifier. Rule-based fuzzy models can be acquired from numerical data, and be used as classifiers. As rule based structures revealed to be a useful qualitative description for classification systems, this work uses fuzzy models as classifiers. This paper proposes an algorithm for feature selection based on two cooperative ant colonies, which minimizes two objectives: the number of features and the classification error. Two pheromone matrices and two different heuristics are used for these objectives. The performance of the method is compared with other features selection methods, achieving equal or better performance.

Distributed supply chain management using ant colony optimization

Successful supply chain management requires a cooperative integration between all the partners in the network. At the operational level, the partners individual behavior should be optimal and therefore their activities have to be planned using sophisticated optimization tools. However, these tools should take into account the planning of the remaining partners, through the exchange of information, in order to allow some kind of cooperation between the elements of the chain. This paper introduces a new supply chain management technique, based on modeling a generic supply chain with suppliers, logistics and distributers, as a distributed optimization problem. The different operational activities are solved by the optimization meta-heuristic called ant colony optimization, which allows the exchange of information between different optimization problems by means of a pheromone matrix. The simulation results show that the new methodology is more efficient than a simple decentralized methodology for different instances of a supply chain.

Current and future development in neural computation in steel processing

Abstract A rolling mill process control system calculates the setup for the mills actuators based on models of the technological process. Neural networks are applied as components of hybrid neuro/analytical process models. They are the keys to fit the general physical models to the needs of the automation of a specific mill. Besides present applications, the paper describes future trends in application of neural networks in process control.

Soft computing optimization methods applied to logistic processes

This paper discusses the methodologies that can be used to optimize a logistic process of a supply chain described as a scheduling problem. First, a model of the system based on a real-world example is presented. Then, a new objective function called Global Expected Lateness is proposed, in order to describe multiple optimization criteria. Finally, three different optimization methodologies are proposed: a classical dispatching rule, and two soft computing techniques, Genetic Algorithms (GA) and Ant Colony Optimization (ACO). These methodologies are compared to the dispatching policy in the real-world example. The results show that dispatching heuristics are outperformed by the GA and ACO meta-heuristics. Further, it is shown that GA and ACO provide statistically identical scheduling solutions and from the optimization performance point of view, it is equivalent to use any of the meta-heuristics.