A new hybrid multi-level cross-entropy-based moth-flame optimization algorithm

Abstract

This study proposes an intelligent hybridization between the multi-level cross-entropy optimizer (MCEO) and moth-flame optimization (MFO) algorithms to keep a good compromise between exploration and exploitation. The proposed hybrid multi-level cross-entropy-based moth-flame (MCMF) algorithm uses MCEO as a global search engine during the first phase of the optimization process that allows for fast approximation of the global best position (BP). The boundaries of the search space are then adaptively confined within the effective region around the current BP by applying the proposed search space boundaries confining factor (SSBCF). The modified MFO with two different moth generation patterns is then employed as a local search engine to simultaneously probe for new and proper BPs within the confined and overall search space. This prevents MCMF from becoming trapped in local optima while maintaining a balance between exploration and exploitation. The hybridization between both algorithms allows MCMF to accelerate throughout the early steps of the search process using the high exploration ability of MCEO, whereas, in the later stages of optimization, promising solutions will possess a high probability to be exploited using the higher exploitation power of MFO in the confined space. The competence of the MCMF is compared with other well-known state-of-the-art algorithms on 15 unconstrained benchmark functions and 5 constrained engineering design problems having a wide range of dimensions and varied complexities. The statistical results on the benchmark functions and the solved engineering examples verify that the proposed algorithm can provide very competitive and promising results. The results demonstrate the comprehensive superiority of the hybrid MCMF compared to both MCEO and MFO in terms of fewer function calls, high escaping ability from local optima, and fast convergence speed.