Modified group theory-based optimization algorithms for numerical optimization

摘要

Group Theory-based Optimization Algorithm (GTOA) is a novel population-based global optimization algorithm, which is used to solve combinatorial optimization problems. This paper studies the applicability of GTOA in numerical optimization and proposes two versions of GTOA based on binary coding (GTOA-b) and \(0\sim 9\) integer coding (GTOA-d). Firstly, the coding transformation methods for representing the feasible solutions are introduced, which make GTOA suitable for continuous optimization. On this basis, the original evolution operators are modified to reduce the deviation and speed up global convergence. The experiment using the CEC2017 test suit is carried out to validate the performance of the algorithms. The influence of parameter values and the differences between the calculated results are analyzed by nonparametric tests. Computation results showed that the convergence rate of GTOA-d is faster than that of GTOA-b, and it achieved better results on the benchmark functions with higher dimensions. The comparison against twelve state-of-the-art and recently introduced meta-heuristic algorithms showed that GTOA-d has the superiority on convergence stability, it obtained significantly better performance than seven of its competitors. Finally, all the algorithms are applied to an Amplitude Variation with Offset inversion case study. The simulation showed that the proposed GTOA-d achieved satisfactory inversion results, and it has better performance in terms of convergence rate and average accuracy. The results demonstrate that the proposed GTOA-d is an effective algorithm for numerical optimization.