This research work describes the development of a novel generic methodology for eliciting optimal fuzzy rules of the Mamdani-type using Symbiotic Evolution. In this evolutionary computation-based approach a randomly selected group of rules sets up a fuzzy inference system, then based on the system’s performance a proportional score is allocated to each contributing rule. Subsequently, the overall fitness of all rules in the population is calculated and on the basis of these fitnesses the rules are selected to reproduce and survive to the next generation.
In contrast to the conventional Genetic Algorithm (GA) based fuzzy rule generation algorithms, in this proposed approach, the rules are evolved from one generation to another and not the rule-bases. This algorithm is implemented in two versions, namely the Self- Organising Symbiotic Evolution (SOSE) and the Self-Adaptive Symbiotic Evolution (SASE) methods. In the SOSE method the membership functions’ parameters are fixed and the method generates only the fuzzy rules, however, in the SASE method, the algorithm optimises both the inference system’s structure and the membership functions’ parameters.
In order to evaluate the capabilities of the proposed method, it was applied successfully to the design of active suspension systems. In this investigation, the Bond Graphs (BG) method is used to model the non-linear quarter and half-car models using parameters that relate to a Ford Fiesta MK2. Simulation results proved that Symbiotic Evolution, coupled with fuzzy logic to form a hybrid structure can be very successful in the design of an efficient active suspension system in terms of performance and size of the fuzzy rule-base.
The carried-out investigations demonstrated that the obtained optimal fuzzy controllers not only perform well for the training road surfaces but also in the face of unseen road surfaces. Moreover, these obtained controllers demonstrated a robust behaviour in the presence of uncertainties in the system’s parameters.
Almost all fuzzy rule-base generation algorithms produce rule-bases with redundant and overlapped membership functions that limit their interpretability and elegance. This problem is also addressed by applying an algorithm to merge any similar membership functions. It is shown that the applied algorithm leads generally to a more transparent and more interpretable rule-base with a minimum number of membership functions and a reduced number of elicited fuzzy rules. In addition, a new rule post-processing approach is proposed for recovering any lost performance following the above membership functions merging.
Furthermore, in order to improve the rule-generation process, the fuzzy rules’ average activating strength is used as a parameter which gives an indication of the rules activity in the rule-base and hence helps in the rules’ fitness assignment. Preliminary results following the application of this method are encouraging and further experiments are underway to validate this method.
It is worth noting that all procedures, simulations, and approximate reasoning computations are implemented in a versatile C++ environment that features a variety of Genetic Algorithms. The use of such environment reduces significantly all incurred computation times.
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