Advanced orthogonal moth flame optimization with Broyden–Fletcher–Goldfarb–Shanno algorithm: Framework and real-world problems

Abstract

As a typical emergent swarm intelligence algorithm, Moth-Flame Optimization (MFO) has been created to deal with global optimization problems. Since the introduction, it has been applied to various optimization problems. However, MFO may have the trouble of getting into the local best, and the convergence rate cannot be satisfying when handling the high-dimensional and some multimodal problems. In this work, an enhanced MFO integrated with orthogonal learning (OL) and Broyden-Fletcher-Goldfarb-Shanno (BFGS), which we called BFGSOLMFO, is proposed to alleviate the stagnation shortcomings and accelerate the performance of well-regarded MFO. In the BFGSOLMFO, OL is used to construct a better candidate solution for each moth and then guide the whole population to a reasonable potential area. Meanwhile, in each iteration, after the evolution of population finished and the global optima are obtainable, BFGS is employed to further excavate the potential of the global best moth in the current population. With the aim of evaluating the efficacy of the BFGSOLMFO, first of all, the IEEE CEC2014 benchmark set is utilized to measure the performance in solving function optimizations with high-dimensional and multimodal characteristics. Both sets of the IEEE CEC2011 real-world benchmark problems and the three constrained engineering optimization problems are adopted to estimate the performance of BFGSOLMFO in tackling practical scenarios. In all the experiments, the developed BFGSOLMFO is compared with state-of-the-art advanced algorithms. Experimental results and statistical tests demonstrate that the proposed method outperforms the basic MFO and a comprehensive set of advanced algorithms.