Improved Lévy flight distribution algorithm with FDB-based guiding mechanism for AVR system optimal design

•A powerful and new metaheuristic search algorithm called FDB-LFD was developed.•FDB selection method was applied to prevent premature convergence and stagnation in local optima.•FDB-LFD was successfully tested and verified on CEC17 and CEC20 benchmark suites.•It is also applied to real-world AVR engineering design problems. This paper presents the improved version of the Lévy Flight Distribution (LFD) algorithm for solving real-valued numerical optimization problems. In the proposed algorithm, the Fitness-Distance Balance (FDB) selection method was used to determine the search agents that well know the migration routes and guide the herd. Thus, the FDB-LFD algorithm, which has a much stronger search performance, was developed. The performance of the proposed algorithm was tested and verified on CEC17 and CEC20 benchmark problems for low-, middle- and high-dimensional search spaces. Results of the FDB-LFD was compared to the performance of 11 other powerful and up-to-date metaheuristic search algorithms. According to Friedman statistical test results, the proposed FDB-LFD algorithm ranked first, whereas the LFD was ranked eleventh. This result demonstrated that the changes in the design of the LFD algorithm had been successful. Moreover, using the proposed algorithm, optimum solutions were found for one of the popular industrial engineering applications: the automatic voltage regulator (AVR) system design. The simulation results revealed that the FDB-LFD is an effective algorithm for solving both unconstrained benchmark and constrained industrial engineering design problems.