Self-Organizing Multi-layer Fuzzy Polynomial Neural Networks Based on Genetic Optimization

Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons

In this paper, we propose a new design methodology of fuzzy-neural networks - fuzzy set-based polynomial neural networks (FSPNN) with symbolic genetic algorithms. Fuzzy set-based polynomial neural networks (FSPNN) are based on a fuzzy set-based polynomial neuron (FSPN) whose fuzzy rules include the information granules (about the real system) obtained through information granulation. The information granules are capable of show the specific characteristic of the system. We have developed a design methodology (genetic optimization using symbolic genetic algorithms) to find the optimal structure for fuzzy-neural networks that expanded from group method of data handling (GMDH). It is the number of input variables, the order of the polynomial, the number of membership functions, and a collection of the specific subset of input variables that are the parameters of FSPNN fixed by aid of symbolic genetic optimization that has search capability to find the optimal solution on the solution space. The augmented and genetically developed FPNN (gFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNNs. The GA-based design procedure being applied at each layer of FPNN leads to the selection of the most suitable nodes (or FSPNs) available within the FPNN. Symbolic genetic algorithms are capable of reducing the solution space more than conventional genetic algorithms with binary genetype chromosomes. The performance of genetically optimized FSPNN (gFSPNN) with aid of symbolic genetic algorithms is quantified through experimentation where we use a number of modeling benchmarks data which are already experimented with in fuzzy or neurofuzzy modeling

It is well-known that any nonlinear complex system can be modeled by using a collection of "if źthen" fuzzy rules. In spite of a number of successful models reported in the literature, there are still two open issues: (1) one is not able to reflect the heterogeneous partition of the input space; (2) it becomes very difficult to deal effectively with high dimensionality of the problem (data). In this study, we present a parallel fuzzy polynomial neural networks (PFPNNs) with the aid of heterogeneous partition of the input space. Like fuzzy rules encountered in fuzzy models, the PFPNNs comprises a collection of premise and consequent parts. In the design of the premise part of the rule a weighted fuzzy clustering method is used not only to realize a nonuniform partition of the input space but to overcome a possible curse dimensionality. While in the design of consequent part, fuzzy polynomial neural networks are exploited to construct optimal local models (high order polynomials) that describe the relationship between the input variables and output variable within some local region of the input space. Two types of information granulation-based fuzzy polynomial neurons are developed for FPNNs. Particle swarm optimization (PSO) is employed to adjust the design parameters of parallel fuzzy polynomial neural networks. To evaluate the performance of PFPNNs a series of experiments based on several benchmarks are included. A comparative analysis demonstrates that the proposed model comes with higher accuracy and generalization capabilities in comparison with some previous models reported in the literature.

We introduce an advanced architecture of genetically optimized Hybrid Fuzzy Neural Networks (gHFNN) and develop a comprehensive design methodology supporting their construction. The gHFNN architecture results from a synergistic usage of the hybrid system generated by combining Fuzzy Neural Networks (FNN) with Polynomial Neural Networks (PNN). We distinguish between two types of the linear fuzzy inference rule-based FNN structures showing how this taxonomy depends upon the type of a fuzzy partition of input variables. As to the consequence part of the gHFNN, the development of the PNN dwells on two general optimization mechanisms: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning.

Genetically optimized Hybrid Fuzzy Set-based Polynomial Neural Networks

In this paper, we introduce new fuzzy-neural networks – Fuzzy Set – based Polynomial Neural Networks (FSPNN) with a new fuzzy set-based polynomial neuron (FSPN) whose fuzzy rules include the information granules obtained through Information Granulation. We investigate the proposed networks from two different aspects to improve the performance of the fuzzy-neural networks. First, We have developed genetic optimization using Genetic Algorithms to find the optimal structure for fuzzy-neural networks. Second, we have been interested in the architecture of fuzzy rules that mimic the real world, namely sub-model composing the fuzzy-neural networks. We adopt fuzzy set-based fuzzy rules as substitute for fuzzy relation-based fuzzy rules and apply the concept of Information Granulation to the proposed fuzzy set-based rules. The performance of genetically optimized FSPNN (gFSPNN) with fuzzy set-based neural neuron (FSPN) involving information granules is quantified through experimentation.

Fashion products require a significant amount of customization due to differences in body measurements, diverse preferences on style and replacement cycle. It is necessary for today’s apparel industry to be responsive to the ever-changing fashion market. Just-in-time production is a must-go direction for apparel manufacturing. Apparel industry tends to generate more production orders, which are split into smaller jobs in order to provide customers with timely and customized fashion products. It makes the difficult task of production planning even more challenging if the due times of production orders are fuzzy and resource competing. In this paper, genetic algorithms and fuzzy set theory are used to generate just-in-time fabric-cutting schedules in a dynamic and fuzzy cutting environment. Two sets of real production data were collected to validate the proposed genetic optimization method. Experimental results demonstrate that the genetically optimized schedules improve the internal satisfaction of downstream production departments and reduce the production cost simultaneously.

In recent years, much attention is paid to the development of variable frequency drive (frequency-adjustable electric drive) for pumps of pipeline transport of oil. One of the most important problems that must be addressed during the optimization of the technological process of pumping using frequency-adjustable electric drive is the choice of the number of pumps, frequency converters and electric motors rotation speed. In the article the objectives and criteria of optimization of pumping oil by pipeline with frequency-regulated drive the pumps are discussed. For drives of main pump for pumping stations are used high-voltage electric motors. Each motor together with the pump can be switched on or off, and each motor can be powered directly from the network or from the frequency converter. While there are many possible structures as each of pump stations and technological area as a whole, with different number and combination included pumps, motors and frequency converters. In the modern system of pumping out «from the pump in the pump» mode all pumps technological area of interrelated. Changing the mode of one of the pumps changes the mode of pumping technological area, and, consequently, regimes of all other pumps. The modes of operation of all the pumps, motors and frequency converters of all pump stations technological area are interrelated. Therefore, when optimizing the process of pumping motors, frequency converters and pumps should be regarded as components of a single process. Thus, related how the composition of a component technological area and modes of their work. Therefore optimization of pumping oil is advisable to use structural-parametric optimization, which is a combination of structural and parametric optimization. Structural optimization using frequency-adjustable electric drive is the determination of the optimal number and combination included in regulated and non-regulated pumps. Parametric optimization when using a frequency regulation lies in selecting the optimal speed of rotation of each of the pumps. All criteria of optimization of modes pipeline using frequency-adjustable electric drive proposed to divide into three groups: energy criteria, the purpose of which - reduction of energy costs for pumping, technological criteria, the purpose of which is the optimization of technological parameters and to increase reliability, and operational criteria, which purpose is to reduce the cost of maintenance and repair of objects of the main pipeline. A block diagram of the structural and parametric optimization of the technological process of pumping with two contours optimization is offered. In the contours of the structural and parametric optimization the same or different criteria optimization can be used. The principles of selection criteria optimization are proposed.

Neural networks and fuzzy systems are two soft‐computing paradigms for system modelling. Adapting a neural or fuzzy system requires to solve two optimization problems: structural optimization and parametric optimization. Structural optimization is a discrete optimization problem which is very hard to solve using conventional optimization techniques. Parametric optimization can be solved using conventional optimization techniques, but the solution may be easily trapped at a bad local optimum. Evolutionary computation is a general‐purpose stochastic global optimization approach under the universally accepted neo‐Darwinian paradigm, which is a combination of the classical Darwinian evolutionary theory, the selectionism of Weismann, and the genetics of Mendel. Evolutionary algorithms are a major approach to adaptation and optimization. In this paper, we first introduce evolutionary algorithms with emphasis on genetic algorithms and evolutionary strategies. Other evolutionary algorithms such as genetic programming, evolutionary programming, particle swarm optimization, immune algorithm, and ant colony optimization are also described. Some topics pertaining to evolutionary algorithms are also discussed, and a comparison between evolutionary algorithms and simulated annealing is made. Finally, the application of EAs to the learning of neural networks as well as to the structural and parametric adaptations of fuzzy systems is also detailed.

In this paper, we introduce a new topology of fuzzy-neural networks-fuzzy-set-based polynomial neural networks (FSPNNs). The two underlying design mechanisms of such networks involve genetic optimization and information granulation (IG). The resulting constructs come in the form of fuzzy polynomial neural networks with fuzzy-set-based polynomial neurons, regarded as their generic processing elements. First, we introduce a comprehensive design methodology using which we determine the optimal structure of the FSPNNs. This methodology hinges on the extended group method of data handling and fuzzy-set-based rules. It concerns the optimization of the FSPNN-related parameters such as the number of input variables, the order of the polynomial, the number of membership functions, and a collection of a specific subset of input variables realized through the mechanism of genetic optimization. Second, the fuzzy rules used in the networks exploit a notion of information granules defined over a system's variables and formed through the process of IG. This granulation is realized with the aid of the hard C-means clustering algorithm. The performance of the network is quantified through experimentation in which we use a number of modeling benchmarks already experimented with in the realm of fuzzy or neurofuzzy modeling.

The Darwinian Theory serves as the authentic inspiration behind several mathematical techniques known as metaheuristic methods and evolutionary algorithms, which emulate aspects of biological species' development. Among these methods, Genetic Algorithms have emerged at the forefront and have become the most practical technique. Previous studies have highlighted their capabilities in solving complex problems and their wide utilization across numerous disciplines, particularly optimization. This paper focuses on implementing Genetic Algorithms for structural optimization within the context of reliability assessment and safety. The proposed methodology, termed Reliability Genetic Algorithms Optimization (RGAO), combines Genetic Algorithms with reliability constraints. These constraints are defined by the probability of violating safety criteria within the structural problem's limit state function. To convey the idea, the proposed approach is applied to two case studies: The first case involves the reliability optimization of a bridge pier subjected to seismic loading, utilizing response spectrum analysis. Formulating the reliability optimization problem involves considering minimal design requirements, buckling conditions, and allowable stress constraints to determine the optimal and reliable dimensions for the studied structural component. The second case involves the optimization of the height of a prestressed bridge deck slab, while ensuring reliability by considering prestress geometrical conditions according to the French standard BPEL 91 revised 99. This work contributes to enhancing the use of bio-inspired techniques in structural optimization and reliability analysis, offering valuable perspectives for researchers and engineers.

Genetic algorithms (GAs) have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures. In this paper, a versatile, robust and enhanced GA is proposed for structural topology optimization by using problem-specific knowledge. The original discrete black-and-white (0–1) problem is directly solved by using a bit-array representation method. To address the related pronounced connectivity issue effectively, the four-neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns. A simpler version of the perimeter control approach is developed to obtain a well-posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge-free design. To handle the problem of representation degeneracy effectively, a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner. An efficient FEM-based function evaluation method is developed to reduce the computational cost. A dynamic penalty method is presented for the GA to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy. With all these enhancements and appropriate choice of the GA operators, the present GA can achieve significant improvements in evolving into near-optimum solutions and viable topologies with checkerboard free, mesh independent and hinge-free characteristics. Numerical results show that the present GA can be more efficient and robust than the conventional GAs in solving the structural topology optimization problems of minimum compliance design, minimum weight design and optimal compliant mechanisms design. It is suggested that the present enhanced GA using problem-specific knowledge can be a powerful global search tool for structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

Grain drying control is a challenging task owing to the complex heat and mass exchange process. To precisely control the outlet grain moisture content (MC) of a continuous mixed‐flow grain dryer, in this paper, we proposed a genetically optimized inverse model proportional–integral–derivative (PID) controller based on support vector machines for regression algorithm which is named the GO‐SVR‐IMCPID controller. The structure of the GO‐SVR‐IMCPID controller consists of a genetic optimization algorithm, an indirect inverse model predictive controller, and a PID controller. In addition, to verify the control performances of the proposed controller in the simulation study, we have established a nonlinear mathematical model for the mixed‐flow grain dryer to represent the nonlinear grain drying process. Finally, the control performance and the robustness of the GO‐SVR‐IMCPID controller were simulated and compared with the other controllers. By the simulation results, it is shown that this proposed algorithm can track the target value precisely and has fewer steady errors and strong ability of anti‐interference. Furthermore, it has further confirmed the superiority of the proposed grain drying controller by comparing it with the other controllers.

In this study, we propose a space search algorithm (SSA) and then introduce a hybrid optimization of ANFIS-based fuzzy models based on SSA and information granulation (IG). In comparison with “conventional” evolutionary algorithms (such as PSO), SSA leads not only to better search performance to find global optimization but is also more computationally effective. In the hybrid optimization of ANFIS-based fuzzy inference system, SSA is exploited to carry out the parametric optimization of the fuzzy model as well as to realize its structural optimization. IG realized with the aid of C-Means clustering helps determine the initial values of the apex parameters of the membership function of fuzzy model. The overall hybrid identification of ANFIS-based fuzzy models comes in the form of two optimization mechanisms: structure identification (such as the number of input variables to be used, a specific subset of input variables, the number of membership functions, and polynomial type) and parameter identification (viz. the apexes of membership function). The structure identification is developed by SSA and C-Means while the parameter estimation is realized via SSA and a standard least square method. The evaluation of the performance of the proposed model was carried out by using three representative numerical examples such as Non-linear function, gas furnace, and Mackey-Glass time series. A comparative study of SSA and PSO demonstrates that SSA leads to improved performance both in terms of the quality of the model and the computing time required. The proposed model is also contrasted with the quality of some “conventional” fuzzy models already encountered in the literature.