Solving multi-objective multicast routing problems by evolutionary multi-objective simulated annealing algorithms with variable neighbourhoods

This paper presents the investigation of an evolutionary multi-objective simulated annealing (EMOSA) algorithm with variable neighbourhoods to solve the multi-objective multicast routing problems in telecommunications. The hybrid algorithm aims to carry out a more flexible and adaptive exploration in the complex search space by using features of the variable neighbourhood search to find more non-dominated solutions in the Pareto front. Different neighbourhood strictures have been designed with regard to the set of objectives, aiming to drive the search towards optimising all objectives simultaneously. A large number of simulations have been carried out on benchmark instances and random networks with real world features including cost, delay and link utilisations. Experimental results demonstrate that the proposed EMOSA algorithm with variable neighbourhoods is able to find high-quality non-dominated solutions for the problems tested. In particular, the neighbourhood structures that are specifically designed for each objective significantly improved the performance of the proposed algorithm compared with variants of the algorithm with a single neighbourhood.     

Combining boosting and evolutionary algorithms for learning of fuzzy classification rules

This paper presents a novel boosting algorithm for genetic learning of fuzzy classification rules. The method is based on the iterative rule learning approach to fuzzy rule base system design. The fuzzy rule base is generated in an incremental fashion, in that the evolutionary algorithm optimizes one fuzzy classifier rule at a time. The boosting mechanism reduces the weight of those training instances that are classified correctly by the new rule. Therefore, the next rule generation cycle focuses on fuzzy rules that account for the currently uncovered or misclassified instances. The weight of a fuzzy rule reflects the relative strength the boosting algorithm assigns to the rule class when it aggregates the casted votes. The approach is compared with other classification algorithms for a number problem sets from the UCI repository.     

A fuzzy multi-objective programming for optimization of fire station locations through genetic algorithms

Location of fire stations is an important factor in its fire protection capability. This paper aims to determine the optimal location of fire station facilities. The proposed method is the combination of a fuzzy multi-objective programming and a genetic algorithm. The original fuzzy multiple objectives are appropriately converted to a single unified ‘min–max’ goal, which makes it easy to apply a genetic algorithm for the problem solving. Compared with the existing methods of fire station location our approach has three distinguish features: (1) considering fuzzy nature of a decision maker (DM) in the location optimization model; (2) fully considering the demands for the facilities from the areas with various fire risk categories; (3) being more understandable and practical to DM. The case study was based on the data collected from the Derbyshire fire and rescue service and used to illustrate the application of the method for the optimization of fire station locations.     

Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-known metric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied.     

An interpretability improvement for fuzzy rule bases obtained by the iterative rule learning approach

Interpretability is one of the key concepts in many of the applications using the fuzzy rule-based approach. It is well known that there are many different criteria around this concept, the complexity being one of them. In this paper, we focus our efforts in reducing the complexity of the fuzzy rule sets. One of the most interesting approaches for learning fuzzy rules is the iterative rule learning approach. It is mainly characterized by obtaining rules covering few examples in final stages, being in most cases useless to represent the knowledge. This behavior is due to the specificity of the extracted rules, which eventually creates more complex set of rules. Thus, we propose a modified version of the iterative rule learning algorithm in order to extract simple rules relaxing this natural trend. The main idea is to change the rule extraction process to be able to obtain more general rules, using pruned searching spaces together with a knowledge simplification scheme able to replace learned rules. The experimental results prove that this purpose is achieved. The new proposal reduces the complexity at both, the rule and rule base levels, maintaining the accuracy regarding to previous versions of the algorithm.     

Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework

In this paper we propose a multi-objective evolutionary algorithm to generate Mamdani fuzzy rule-based systems with different good trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we introduce the concepts of virtual and concrete rule bases: the former is defined on linguistic variables, all partitioned with a fixed maximum number of fuzzy sets, while the latter takes into account, for each variable, a number of fuzzy sets as determined by the specific partition granularity of that variable. We exploit a chromosome composed of two parts, which codify the variables partition granularities, and the virtual rule base, respectively. Genetic operators manage virtual rule bases, whereas fitness evaluation relies on an appropriate mapping strategy between virtual and concrete rule bases. The algorithm has been tested on two real-world regression problems showing very promising results.     

On the convergence of multiobjective evolutionary algorithms

We consider the usage of evolutionary algorithms for multiobjective programming (MOP), i.e. for decision problems with alternatives taken from a real-valued vector space and evaluated according to a vector-valued objective function. Selection mechanisms, possibilities of temporary fitness deterioration, and problems of unreachable alternatives for such multiobjective evolutionary algorithms (MOEAs) are studied. Theoretical properties of MOEAs such as stochastic convergence with probability 1 are analyzed.     

On the efficiency of evolutionary fuzzy clustering

This paper tackles the problem of showing that evolutionary algorithms for fuzzy clustering can be more efficient than systematic (i.e. repetitive) approaches when the number of clusters in a data set is unknown. To do so, a fuzzy version of an Evolutionary Algorithm for Clustering (EAC) is introduced. A fuzzy cluster validity criterion and a fuzzy local search algorithm are used instead of their hard counterparts employed by EAC. Theoretical complexity analyses for both the systematic and evolutionary algorithms under interest are provided. Examples with computational experiments and statistical analyses are also presented.     

Optimal adaptation of acoustic black holes by evolutionary optimization algorithms

The interest of engineers is focusing increasingly on a reduced sound radiation of constructions. In particular, structures with a large surface, such as cabin linings of airplanes as well as a roof or a bottom plate of cars, tend to be good acoustic radiators and lead to an annoyance of passengers. As countermeasures, often complex and time consuming design changes or expensive active measures are used. In many cases, a more elegant and cheaper option is to improve the acoustic properties by using passive measures. Acoustic black holes are an innovative passive method which combine two advantages: A material reduction by improving acoustic properties is performed. The main idea is to guide and to focus acoustically critical bending waves by a specific wall thickness diminution. Through targeted local damping placement in the middle of an acoustic black hole, a structure can be globally damped in a very efficient way. The efficiency depends on the position and size of the acoustic black holes [1]. Finding the optimal size and position on the structure is therefore an important challenge. This paper introduces a new strategy to find an optimal position of acoustic black holes to reduce the sound radiation of plane structures by using evolutionary optimization algorithms. Numerical calculations are exemplarily shown on a rectangular plate. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interpretation of fuzzy data by means of fuzzy rules with applications to speech recognition

Recently, a speech recognition methodology has been proposed which has as one of its main principles the explicit assumption of intrinsic uncertainty of the data (speech signals) and inexactness of the knowledge (acoustic phonetic, etc…) available to interpret them. The main problem presented by this methodology is that of parsing ‘fuzzy data’ by means of ‘fuzzy rules’. To solve this problem, an appropriate fuzzy parsing and interpretation scheme has been proposed. It assumes the data to be represented as strings of ‘fuzzy symbols’, defined as fuzzy sets over the appropriate set of categories, and knowledge as finite-state networks with the arcs labelled by fuzzy symbols of the same type. A formal presentation of this scheme is the main topic of this paper. Included is a brief discussion of the application to Automatic Speech Recognition, and a summary of some results obtained from an implementation example.     

Approximation of function by Euler means

Let 蒖_n $$(q, f, x) = \frac{1}{{(1 + q)^n }}\sum\limits_{k = 0}^n {(_k^n )q^{n - k} s_k (f, x)} $$ denote the Euler means of the Fourier series of the 2π-perodic function f(x). For an integer q>0 and a function f(x)∈H^ω?C([0, 2π]), the main term of deviationf(x)-蒖_n(q, f, x) is calculated in this note. Asymptoteaally exact order 3 of decrease of the upper bound of such deviations over the class H^ω is also obtained.     

Improving the scalability of rule-based evolutionary learning

Evolutionary learning techniques are comparable in accuracy with other learning methods such as Bayesian Learning, SVM, etc. These techniques often produce more interpretable knowledge than, e.g. SVM; however, efficiency is a significant drawback. This paper presents a new representation motivated by our observations that Bioinformatics and Systems Biology often give rise to very large-scale datasets that are noisy, ambiguous and usually described by a large number of attributes. The crucial observation is that, in the most successful rules obtained for such datasets, only a few key attributes (from the large number of available ones) are expressed in a rule, hence automatically discovering these few key attributes and only keeping track of them contributes to a substantial speed up by avoiding useless match operations with irrelevant attributes. Thus, in effective terms this procedure is performing a fine-grained feature selection at a rule-wise level, as the key attributes may be different for each learned rule. The representation we propose has been tested within the BioHEL machine learning system, and the experiments performed show that not only the representation has competent learning performance, but that it also manages to reduce considerably the system run-time. That is, the proposed representation is up to 2–3 times faster than state-of-the-art evolutionary learning representations designed specifically for efficiency purposes.     

Characterization of fuzzy measures constructed by means of triangular norms

Following the ideas presented by the author (E. P. Klement, J. Math. Anal. Appl.85 (1982), 543–565) finite T-fuzzy measures are introduced, T being a measurable triangular norm. We show that a T-fuzzy measure is always a fuzzy measure, as considered earlier (E. P. Klement, J. Math. Anal. Appl.25 (1980), 330–339). Then we study the relation to the integral with respect to some classical measure. Finally, for some special triangular norms T, we give precise characterizations of the corresponding classes of T-fuzzy measures.     

An experimental evaluation of the efficacy of four multi-objective linear programming algorithms

Four multi-objective linear programming algorithms are implemented on microcomputer software packages and a large field experiment is conducted using the implemented algorithms. Two new algorithms which incorporate formal models of decision maker behavior are tested along with two established algorithms which include no formal models of decision maker behavior. The new algorithms are shown to outperform the established algorithms.     

CFD modeling and multi-objective optimization of cyclone geometry using desirability function,artificial neural networks and genetic algorithms

The low-mass loading gas cyclone separator has two performance parameters, the pressure drop and the collection efficiency (cut-off diameter). In this paper, a multi-objective optimization study of a gas cyclone separator has been performed using the response surface methodology (RSM) and CFD data. The effects of the inlet height, the inlet width, the vortex finder diameter and the cyclone total height on the cyclone performance have been investigated. The analysis of design of experiment shows a strong interaction between the inlet dimensions and the vortex finder diameter. No interaction between the cyclone height and the other three factors was observed. The desirability function approach has been used for the multi-objective optimization. A new set of geometrical ratios (design) has been obtained to achieve the best performance. A numerical comparison between the new design and the Stairmand design confirms the superior performance of the new design. As an alternative approach for applying RSM as a meta-model, two radial basis function neural networks (RBFNNs) have been used. Furthermore, the genetic algorithms technique has been used instead of the desirability function approach. A multi-objective optimization study using NSGA-II technique has been performed to obtain the Pareto front for the best performance cyclone separator.     

Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation

Numerical Algorithms - The main contribution of this article is to introduce new compact fourth-order, standard fourth-order, and standard second-order finite difference schemes for solving the...     

Improving the computational efficiency of metric-based spares algorithms

We propose a new heuristic algorithm to improve the computational efficiency of the general class of Multi-Echelon Technique for Recoverable Item Control (METRIC) problems. The objective of a METRIC-based decision problem is to systematically determine the location and quantity of spares that either maximizes the operational availability of a system subject to a budget constraint or minimizes its cost subject to an operational availability target. This type of sparing analysis has proven essential when analyzing the sustainment policies of large-scale, complex repairable systems such as those prevalent in the defense and aerospace industries. Additionally, the frequency of these sparing studies has recently increased as the adoption of performance-based logistics (PBL) has increased. PBL represents a class of business strategies that converts the recurring cost associated with maintenance, repair, and overhaul (MRO) into cost avoidance streams. Central to a PBL contract is a requirement to perform a business case analysis (BCA) and central to a BCA is the frequent need to use METRIC-based approaches to evaluate how a supplier and customer will engage in a performance based logistics arrangement where spares decisions are critical. Due to the size and frequency of the problem there exists a need to improve the efficiency of the computationally intensive METRIC-based solutions. We develop and validate a practical algorithm for improving the computational efficiency of a METRIC-based approach. The accuracy and effectiveness of the proposed algorithm are analyzed through a numerical study. The algorithm shows a 94% improvement in computational efficiency while maintaining 99.9% accuracy.     

On the mappings preserving the Lyapunov stability of Takagi–Sugeno fuzzy systems

We propose a general principle of comparison for stability-preserving mappings and establish sufficient conditions of stability for the Takagi – Sugeno continuous fuzzy systems.     

Improving and estimating the accuracy of Strassen's algorithm

Fast matrix multiplication algorithms of Strassen and Winograd are known to have weaker numerical accuracy than usual (inner product) multiplication. In this paper, we show that scaling usually improves accuracy when operands have elements of widely varying magnitude. We also propose estimators for numerical errors, based on samples of the result. All these estimators can be computed in operations. Experiments prove the effectiveness of the scaling idea and of the absolute error estimator. Received February 20, 1996/ Revised version received July 1, 1997