طراحی سیستم فازی با استفاده از بهینه سازی کلونی مورچه پیوسته با هدایت نخبگان

This paper proposes recurrent fuzzy system design using elite-guided continuous ant colony optimization (ECACO). The designed recurrent fuzzy system is the Takagi–Sugeno–Kang (TSK)-type recurrent fuzzy network (TRFN), in which each fuzzy rule contains feedback loops to handle dynamic system processing problems. The ECACO optimizes all of the free parameters in each recurrent fuzzy rule in a TRFN. Unlike the general ant colony optimization that finds solutions in discrete space, the ECACO finds solutions in a continuous space. The ECACO is a population-based optimization algorithm. New solutions are generated by selection, Gaussian random sampling, and elite-guided movement. To verify the performance of ECACO, three examples of dynamic plant control are simulated using ECACO-optimized TRFNs. The ECACO performance is also compared with other continuous ant colony optimization, particle swarm optimization, and genetic algorithms in these simulations.

Recurrent fuzzy systems (RFSs) are fuzzy systems with feedback connections in their structure. For temporal characteristic problems, the performance of a RFS has been shown to outperform feed-forward fuzzy systems and recurrent neural networks in several studies [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] and [11]. Many feedback structures in RFSs have been proposed. One category of recurrent RFSs uses feedback loops from the network output(s) as a recurrence structure [1] and [2]. Another category of recurrent RFSs uses feedback loops from internal state variables as the recurrence structure [4], [5], [6], [7] and [8]. The local recurrence property of the RFSs in studies [3] and [4] is achieved by feeding the output of each membership function locally back to itself; thus, each membership value is only influenced by its past values. Recurrent self-organizing neural fuzzy inference networks (RSONFIN) [5] and Takagi–Sugeno–Kang (TSK)-type recurrent fuzzy networks (TRFN) [6] use a global feedback structure, where the firing strengths of each rule are summed and fed back as internal network inputs. The TRFN is constructed from a series of recurrent fuzzy if–then rules with TSK-type consequent parts, and its performance is shown to be better than RSONFIN, in which a fuzzy set is used as the consequence. Compared with other RFSs, which also use TSK-type consequences [1] and [9], one major advantage of TRFN is that no a priori knowledge of the plant order is required, which eases the design process. In [6] and [8], the superiority of TRFN to recurrent neural networks in spatial–temporal problems, including dynamic plant identification and control, was demonstrated. Therefore, this paper selects TRFN as the designed RFS. In addition to the difference in feedback structures, RFSs differ in their learning methods. Most RFSs are learned through gradient descent-based learning algorithms [1], [2], [3], [4], [5], [6], [7], [8] and [9]. One disadvantage of this type of learning algorithm is the local optima problem. When there are multiple peaks in a search space, search results usually get trapped in a local solution when the gradient descent learning algorithm is used. Another problem is that the input–output training data for gradient descent learning algorithms may not be directly available. For example, for the dynamic control problem considered in this paper, the desired control outputs for a RFS controller are unknown in advance for gradient descent learning. For the problems above, a design of RFSs using population-based optimization algorithms has been proposed [11], [12], [13], [14], [15], [16], [17] and [18]. One popular approach is the use of genetic algorithms (GAs) for RFS parameter optimization [6], [11] and [13]. In [6], an elite genetic algorithm (EGA) was proposed for TRFN parameter optimization. Another popular approach is the use of particle swarm optimization (PSO) [12], [15] and [16]. For example, TRFN design using PSO was proposed in [12]. Different approaches to combining GA and PSO for RFS designs were proposed in [12], [14] and [17]. For example, the hybrid of GA and PSO (HGAPSO) for TRFN design was proposed in [12]. The HGAPSO introduces the idea of crossover and mutation operations into individuals in PSO for performance improvement. In this paper, a new learning algorithm based on continuous ant colony optimization is proposed for TRFN design to further improve performance. The use of a new meta-heuristic, ant colony optimization (ACO), for solving optimization problems has been proposed recently [19]. The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems. In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. The ACO has been applied to feed-forward fuzzy system design problems in several studies [20], [21] and [22]. Because the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Recently, some continuous ACO algorithms for optimization in continuous space have been proposed [23], [24] and [25], where one promising approach is the ACO in real space (ACOℝ)(ACOℝ)[25]. The good performance of ACOℝACOℝ for continuous function optimization has been demonstrated. Based on the ACOℝACOℝ concept, this paper proposes elite-guided continuous ant colony optimization (ECACO) and applies it to TRFN design for dynamic plant control. The major contribution of this paper is twofold. First, a new continuous ACO, the ECACO, is proposed. Like GA and PSO, the ECACO works with a population of solutions. The ECACO proposes a new approach for new solution generation at each iteration. Second, the ECACO is applied to TRFN design. To the best of our knowledge, this is the first paper that applies continuous ACO to RFS design. The superiority of ECACO in comparison with ACOℝACOℝ, EGA, HGAPSO, and other advanced PSO algorithms is demonstrated in three simulation examples. This paper is organized as follows. Section 2 introduces the TSK-type recurrent fuzzy network (TRFN). Section 3 introduces the TRFN design by ECACO. Section 4 analyzes the ECACO algorithm. Section 5 presents simulation results of the ECACO-designed TRFN for dynamic plant control. This section also compares the ECACO performance with other optimization algorithms. Section 6 discusses the similarity and difference between the ECACO and discrete ACO. This section also discusses the major factors that the ECACO outperforms GAs and PSO in learning performance. Finally, Section 7 presents the conclusions.

This paper proposes a new recurrent fuzzy system design approach using a new continuous ACO algorithm, the ECACO. The ECACO can be regarded as a new population-based optimization algorithm. The framework of ECACO for parameter optimization is based on representing ant pheromone levels with a continuous Gaussian PDF in continuous variable space followed by elite-guided movement. In TRFN design for different dynamic control problems, the ECACO performance is shown to be better than the state-of-the-art continuous ACO, ACOℝACOℝ. In addition, performance comparisons with different swarm intelligence algorithms, genetic algorithms, and their hybrid algorithms verify the effectiveness and efficiency of ECACO. Application of ECACO to different optimization problems will be studied. Hybridization of other optimization algorithms and ECACO may further improve optimization performance and will also be studied in the future.