A balanced fuzzy Cultural Algorithm with a modified Levy flight search for real parameter optimization

Over the last few decades, a plethora of improved evolutionary algorithms was developed with exquisite performance on numerical and real-world problems. Among such algorithms, the Cultural Algorithm is a hyper-heuristic evolutionary algorithm, which explicitly utilizes the knowledge represented in the belief space as an essential component to guide the evolutionary search. In this paper, a new enhanced Cultural Algorithm incorporates a fuzzy system with a modified Levy flight search that is introduced as a new component. The new algorithm namely, b-fCA+mLF, utilizes a balanced search mode using a customized belief space with a quality function to harmonize how the knowledge sources work in parallel. The communication protocols between the population space and the belief space are established through the modified fuzzy acceptance and influence functions. Using these new functions, the best individuals are selected to create new knowledge in an effective manner. Similarly, the best knowledge is selected to evolve the individuals in the population space and guide the evolutionary search towards the promising regions. A modified Levy flight search is proposed and utilizes the information from the belief space as an input to support the evolution process to generate better solutions. The algorithm is tested on the benchmark suite taken from the IEEE-CEC’15 competition on learning-based real-parameter single objective optimization, and is compared with other algorithms including the best performer algorithms in this competition. The results suggest that the proposed algorithm is statistically better and is able to produce higher quality solutions than the other state-of-the-art algorithms. A case study on the well-known 120-bar dome truss design problem is also presented to test the validity of the proposed algorithm for the solution of complex design problems. The results of this problem show the ability of the proposed algorithm to generate good solutions with fewer function evaluations, compared to reported results in the literature and other well-known algorithms