A survey on nature-inspired optimization algorithms with fuzzy logic for dynamic parameter adaptation

Metaheuristic optimization algorithms have become a popular choice for solving complex problems which are otherwise difficult to solve by traditional methods. However, these methods have the problem of the parameter adaptation and many researchers have proposed modifications using fuzzy logic to solve this problem and obtain better results than the original methods. In this study a comprehensive review is made of the optimization techniques in which fuzzy logic is used to dynamically adapt some important parameters in these methods. In this paper, the survey mainly covers the optimization methods of Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), and Ant Colony Optimization (ACO), which in the last years have been used with fuzzy logic to improve the performance of the optimization methods.     

Learning cooperative linguistic fuzzy rules using the best–worst ant system algorithm

Within the field of linguistic fuzzy modeling with fuzzy rule‐based systems, the automatic derivation of the linguistic fuzzy rules from numerical data is an important task. In the last few years, a large number of contributions based on techniques such as neural networks and genetic algorithms have been proposed to face this problem. In this article, we introduce a novel approach to the fuzzy rule learning problem with ant colony optimization (ACO) algorithms. To do so, this learning task is formulated as a combinatorial optimization problem. Our learning process is based on the COR methodology proposed in previous works, which provides a search space that allows us to obtain fuzzy models with a good interpretability–accuracy trade‐off. A specific ACO‐based algorithm, the Best–Worst Ant System, is used for this purpose due to the good performance shown when solving other optimization problems. We analyze the behavior of the proposed method and compare it to other learning methods and search techniques when solving two real‐world applications. The obtained results lead us to remark the good performance of our proposal in terms of interpretability, accuracy, and efficiency. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 433–452, 2005.     

Fuzzy systems design: direct and indirect approaches

A systematic classification of the data-driven approaches for design of fuzzy systems is given in the paper. The possible ways to solve this modelling and identification problem are classified on the basis of the optimisation techniques used for this purpose. One algorithm for each of the two basic categories of design methods is presented and its advantages and disadvantages are discussed. Both types of algorithms are self-learning and do not require interaction during the process of fuzzy model design. They perform adaptation of both the fuzzy model structure (rule-base) and the parameters. The indirect approach exploits the dual nature of Takagi-Sugeno (TS) models and is based on recently introduced recursive clustering combined with Kalman filtering-based procedure for recursive estimation of the parameter of the local sub-models. Both algorithms result in finding compact and transparent fuzzy models. The direct approach solves the optimisation problem directly, while the indirect one decomposes the original problem into on-line clustering and recursive estimation problems and finds a sub-optimal solution in real-time. The later one is computationally very efficient and has a range of potential applications in real-time process control, moving images recognition, autonomous systems design etc. It is extended in this paper for the case of multi-input–multi-output (MIMO systems). Both approaches have been tested with real data from an engineering process.     

A robust stabilization problem of fuzzy control systems and itsapplication to backing up control of a truck-trailer

A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions     

An approach to fuzzy control of nonlinear systems: stability anddesign issues

Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called “parallel distributed compensation” is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart     

Adaptive fuzzy model based inverse controller design using BB-BC optimization algorithm

The use of inverse system model as a controller might be an efficient way in controlling non-linear systems. It is also a known fact that fuzzy logic modeling is a powerful tool in representing nonlinear systems. Therefore, inverse fuzzy model can be used as a controller for controlling nonlinear plants. In this context, firstly, a new fuzzy model based inverse controller design methodology is presented in this study. The design methodology introduced here is based on a recursive optimization procedure that searches for an optimal inverse model control signal at every sampling time. Since the task of optimization should be accomplished in between two sampling periods the use of a fast optimization algorithm becomes essential. For this reason, Big Bang-Big Crunch (BB-BC) optimization algorithm is used due to its low computational time and high global convergence properties. Even though, inverse model controllers may produce perfect control while operating in an open loop fashion, this open loop control would not be sufficient in the case of modeling mismatches or disturbances that might occur over the system. In order to overcome this problem, secondly, an on-line adaptation mechanism via BB-BC optimization algorithm is introduced in addition to BB-BC optimization based fuzzy model inverse controller. The adaptation mechanism is used to update the related parameters of the model while minimizing the absolute value of the instantaneous error between the system and model outputs. In this manner, the system output is somehow fed back, the overall control form can be considered as a closed-loop system. The new fuzzy model based inverse control scheme with the new online adaptation mechanism has been implemented and tested on the two real time processes; namely, heat transfer and pH processes and very satisfactory results has been reported.     

Optimization of fuzzy partitions for inductive reasoning using genetic algorithms

Fuzzy Inductive Reasoning (FIR) is a data-driven methodology that uses fuzzy and pattern recognition techniques to infer system models and to predict their future behavior. It is well known that variations on fuzzy partitions have a direct effect on the performance of the fuzzy-rule-based systems. The FIR methodology is not an exception. The performance of the model identification and prediction processes of FIR is highly influenced by the discretization parameters of the system variables, i.e. the number of classes of each variable and the membership functions that define its semantics. In this work, we design two new genetic fuzzy systems (GFSs) that improve this modeling and simulation technique. The main goal of the GFSs is to learn the fuzzification parameters of the FIR methodology. The new approaches are applied to two real modeling problems, the human central nervous system and an electrical distribution problem.     

Formal approach for reengineering fuzzy XML in fuzzy object-oriented databases

Since semi-structured documents (e.g., XML) could benefit greatly from database support and more specifically from object-oriented (OO) database management systems, we study the methodology of reengineering XML to object-oriented databases when database migration occurs in this paper. In particular, considering the need of processing the imprecise and uncertain information existing in practical applications, we investigate the problem of migrating fuzzy XML to fuzzy object-oriented databases. To find the object-oriented schema that best describes the existing fuzzy XML schema (DTD), we devise a comprehensive approach centering on a set of mapping rules. Such reengineering practices could not only provide a significant consolidation of the interoperability between fuzzy OO and fuzzy XML modeling techniques, but also develop the practical design methodology for fuzzy OO databases.     

Classification model for product form design using fuzzy support vector machines

Consumer preferences regarding product design are often affected by a large variety of form features. Traditionally, the quality of product form design depended heavily on designers’ intuitions and did not always prove to be successful in the marketplace. In this study, to help product designers develop appealing products in a more effective manner, an approach based on fuzzy support vector machines (fuzzy SVM) is proposed. This constructs a classification model of product form design based on consumer preferences. The one-versus-one (OVO) method is adopted to handle a multiclass problem by breaking it into various two-class problems. Product samples were collected and their form features were systematically examined. To formulate a classification problem, each product sample was assigned a class label and a fuzzy membership that corresponded to this label. The OVO fuzzy SVM model was constructed using collected product samples. The optimal training parameter set for the model was determined by a two-step cross-validation. A case study of mobile phone design is given to demonstrate the effectiveness of the proposed methodology. The performance of fuzzy SVM is also compared with SVM. The results of the experiment show that fuzzy SVM performed better than SVM.     

Secure communications of chaotic systems with robust performancevia fuzzy observer-based design

This paper presents a systematic design methodology for fuzzy observer-based secure communications of chaotic systems with guaranteed robust performance. The Takagi-Sugeno fuzzy models are given to exactly represent chaotic systems. Then, the general fuzzy model of many well-known chaotic systems is constructed with only one premise variable in fuzzy rules and the same premise variable in the system output. Based on this general model, the fuzzy observer of chaotic system is given and leads the stability condition of a linear-matrix inequality problem. When taking the fuzzy observer-based design to applications on secure communications, the robust performance is presented by simultaneously considering the effects of parameter mismatch and external disturbances. Then, the error of the recovered message is stated in an H^∞ criterion. In addition, if the communication system is free of external disturbances, the asymptotic recovering of the message is obtained in the same framework. The main results also hold for applications on chaotic synchronization. Numerical simulations illustrate that this proposed scheme yields robust performance     

Ant Colony Optimization Incorporated With Fuzzy Q-Learning for Reinforcement Fuzzy Control

This paper proposes the design of fuzzy controllers by ant colony optimization (ACO) incorporated with fuzzy-Q learning, called ACO-FQ, with reinforcements. For a fuzzy inference system, we partition the antecedent part a priori and then list all candidate consequent actions of the rules. In ACO-FQ, the tour of an ant is regarded as a combination of consequent actions selected from every rule. Searching for the best one among all combinations is partially based on pheromone trail. We assign to each candidate in the consequent part of the rule a corresponding Q-value. Update of the Q-value is based on fuzzy-Q learning. The best combination of consequent values of a fuzzy inference system is searched according to pheromone levels and Q-values. ACO-FQ is applied to three reinforcement fuzzy control problems: (1) water bath temperature control; (2) magnetic levitation control; and (3) truck backup control. Comparisons with other reinforcement fuzzy system design methods verify the performance of ACO-FQ.     

Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control

In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results.     

Analysis and synthesis of discrete nonlinear passive systems via affine T–S fuzzy models

The article considers the analysis and synthesis problem for the discrete nonlinear systems, which are represented by the discrete affine Takagi–Sugeno (T–S) fuzzy models. The state feedback fuzzy controller design methodology is developed to guarantee that the affine T–S fuzzy models achieve Lyapunov stability and strict input passivity. In order to find a suitable fuzzy controller, an Iterative Linear Matrix Inequality (ILMI) algorithm is employed in this article to solve the stability conditions for the closed-loop affine T–S fuzzy models. Finally, the application of the proposed fuzzy controller design methodology is manifested via a numerical example with computer simulations.     

Incorporating domain-specific knowledge into a genetic algorithm to implement case-based reasoning adaptation

In case-based reasoning systems the adaptation phase is a notoriously difficult and complex step. The design and implementation of an effective case adaptation algorithm is generally determined by the type of application which decides the nature and the structure of the knowledge to be implemented within the adaptation module, and the level of user involvement during this phase. A new adaptation approach is presented in this paper which uses a modified genetic algorithm incorporating specific domain knowledge and information provided by the retrieved cases. The approach has been developed for a CBR system (CBEM) supporting the use and design of numerical models for estuaries. The adaptation module finds the values of hundreds of parameters for a selected numerical model retrieved from the case-base that is to be used in a new problem context. Without the need of implementing very specific adaptation rules, the proposed approach resolves the problem of acquiring adaptation knowledge by combining the search power of a genetic algorithm with the guidance provided by domain-specific knowledge. The genetic algorithm consists of a modifying version of the classical genetic operations of initialisation, selection, crossover and mutation designed to incorporate practical but general principles of model calibration without reference to any specific problems. The genetic algorithm focuses the search within the parameters' space on those zones that most likely contain the required solutions thus reducing computational time. In addition, the design of the genetic algorithm-based adaptation routine ensures that the parameter values found are suitable for the model approximation and hypotheses, and complies with the problem domain features providing correct and realistic model outputs. This adaptation method is suitable for case-based reasoning systems dealing with numerical modelling applications that require the substitution of a large number of parameter values.     

A two-stage evolutionary process for designing TSK fuzzy rule-basedsystems

Nowadays, fuzzy rule-based systems are successfully applied to many different real-world problems. Unfortunately, relatively few well-structured methodologies exist for designing and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. Takagi-Sugeno-Kang (TSK) fuzzy rule-based systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a two-stage evolutionary process for designing TSK fuzzy rule-based systems from examples combining a generation stage based on a (mu, lambda)-evolution strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary knowledge base, and a refinement stage in which both the antecedent and consequent parts of the fuzzy rules in this previous knowledge base are adapted by a hybrid evolutionary process composed of a genetic algorithm and an evolution strategy to obtain the final Knowledge base whose rules cooperate in the best possible way. Some aspects make this process different from others proposed until now: the design problem is addressed in two different stages, the use of an angular coding of the consequent parameters that allows us to search across the whole space of possible solutions, and the use of the available knowledge about the system under identification to generate the initial populations of the Evolutionary Algorithms that causes the search process to obtain good solutions more quickly. The performance of the method proposed is shown by solving two different problems: the fuzzy modeling of some three-dimensional surfaces and the computing of the maintenance costs of electrical medium line in Spanish towns. Results obtained are compared with other kind of techniques, evolutionary learning processes to design TSK and Mamdani-type fuzzy rule-based systems in the first case, and classical regression and neural modeling in the second.     

New CBR adaptation method combining with problem–solution relational analysis for mechanical design

Case based reasoning (CBR) methodology is proved to be a promising methodology on determining the parameter values of new mechanical product by adapting previously successful solutions to current problems. Compared with the sophisticated case retrieval technique, the case adaptation under K-nearest neighbour is still a bottleneck problem in CBR researches, which needs to be resolved urgently. According to the characteristics of parametric machinery design (PMD), i.e., less data and many parameters, this paper employs weighted mean (WM) as a basic model, and presents a new CBR adaptation method for PMD by integrating with problem–solution (PS) relational information. In our proposed adaptation method, prior to adapting the similar cases, the grey relational analysis (GRA) is utilized to investigate the PS relational information hidden in K retrieved cases, and the proposed method is called as GRA-WM. Different from classical WM method, the weighting factor of retrieved case for each solution element adaptation is calculated by multiplying similarity matrix (SM) and relational matrix (RM), and the adapted solution values of new mechanical product are subsequently obtained by calculating the weighted average of solution values of K similar cases. A case study on the power transformer design is given to prove the industrial applicability of GRA-WM. Moreover, the empirical comparisons between GRA-WM and other adaptation methods are carried out to validate its superiority. The empirical results indicate that GRA-WM can offer an acceptable adaptation proposal in application of CBR for mechanical design.     

GACO – A HYBRID ANT COLONY OPTIMIZATION METAHEURISTIC FOR THE DYNAMIC LOAD-BALANCED CLUSTERING PROBLEM IN AD HOC NETWORKS

We present the design of a novel hybrid genetic ant colony optimization (GACO) metaheuristic. Genetic ant colony optimization is designed to address the dynamic load-balanced clustering problem formulated from ad hoc networks. The main algorithm in GACO is ACO. Whenever an environment change occurs (i.e., nodes move), it makes use of a genetic algorithm to quickly achieve adaptation by refocusing the search process around promising areas of the search space induced by the new problem structure. Compared to other ACO approaches for dynamic problems, GACO does not depend on any problem-specific heuristics to repair or deconstruct solutions. Genetic ant colony optimization also does not require the knowledge of the specific changes that occurred. We compare GACO with three other adaptation methods, namely, P-ACO, PAdapt, and GreedyAnts. P-ACO is a population-based ACO approach that invokes a repair algorithm on its population of solutions when an environment change occurs. PAdapt works by adapting the values of major ACO parameters, while GreedyAnts employs a group of ants that construct solutions in a greedy manner. Empirical results show that GACO is able to react and recover faster from any performance degradation. Genetic ant colony optimization also produces better solutions within the allowable recovery window. These results are shown to be statistically significant.     

Designing Fuzzy-Rule-Based Systems Using Continuous Ant-Colony Optimization

This paper proposes the design of fuzzy-rule-based systems using continuous ant-colony optimization (RCACO). RCACO determines the number of fuzzy rules and optimizes all the free parameters in each fuzzy rule. It uses an online-rule-generation method to determine the number of rules and identify suitable initial parameters for the rules and then optimizes all the free parameters using continuous ant-colony optimization (ACO). In contrast to traditional ACO, which optimizes in the discrete domain, the RCACO optimizes parameters in the continuous domain and can achieve greater learning accuracy. In RCACO, the path of an ant is regarded as a combination of antecedent and consequent parameters from all the rules. A new path-selection method based on pheromone levels is proposed for initial-solution construction. The solution is modified by sampling from a Gaussian probability-density function and is then refined using the group best solution. Simulations on fuzzy control of three nonlinear plants are conducted to verify RCACO performance. Comparisons with other swarm intelligence and genetic algorithms demonstrate the advantages of RCACO.      

Structuring ship design project approval mechanism towards installation of operator-system interfaces via fuzzy axiomatic design principles

Managing the verification of primary design projects for ship machinery systems is one of the crucial stages in ship building processes. In particular, the design of operator-system interfaces such as remote controls, displays, alarms, workstations, and labels requires a high level of technical expertise and systematic control. This paper focuses on structuring a ship design project approval mechanism (SDPAM) based on fuzzy axiomatic design (FAD) methodology which is concerned with the system design of relevant interfaces on an engine room control console. Design characteristics such as accessibility and operational requirements are treated as “hard” constraints being encountered in this complex problem. Hence, the proposed methodology requires performance assessment using fuzzy values. This study provides original contributions to the existing approval procedures of classification societies, which are non-governmental construction and classification organizations in the shipping industry. Furthermore, the study proposes a new approach to handle uncertainty and vagueness by an axiomatic design extension to ship project execution problems.