A comprehensive study of chaos embedded bridging mechanisms and crossover operators for grasshopper optimisation algorithm

Abstract

In recent years, the trend of embedding chaos in the optimization algorithms has grown multifold. Usually, the chaotic algorithms employ chaotic sequences instead of random numbers, in the exploration phase or they employ chaotic numbers for decision making in the exploitation phase. In literature, the positive impact of chaos over the performance of algorithms have been studied and reported. However, very little work is reported on the implications of chaos on the bridging mechanism between the exploration and exploitation phases. This paper presents implications of different chaotic sequences on the performance of Grasshopper Optimisation Algorithm (GOA). A bridging mechanism based on sinusoidal truncated function is proposed first, then 10 different normalize chaotic sequences are employed with this function. Along with this bridging mechanism, a chaotic operator derived crossover scheme is also proposed. These experiments evolve 11 different variants of GOA. The proposed modifications maintain an effective balance between exploration and exploitation phases. Simultaneously, it reduces the attraction, repulsion and comfort zone chaotically. New variants are benchmarked on latest 29 Congress on Evolutionary Computation-2017 (CEC-2017) functions. Efficacy of these variants is validated with several statistical tests and plots. Further, some real life challenging problem of engineering domain are considered for evaluating the efficacy of the proposed variants. These problems are Model Order Reduction (MOR) of control engineering, Protein Structure Prediction (PSP) of bio informatics and Frequency Modulated Sound Wave Parameter Synthesis Problem of parameter estimation. Results reveal that proposed variants exhibit better exploration and exploitation properties as compared to the parent algorithm.