Over the past few decades, there has been a surge of interest of using swarm intelligence (SI) in computer-aided optimization. SI algorithms have demonstrated their efficacy in solving various types of real-world optimization problems. However, it is impossible to find an optimization algorithm that can obtain the global optimum for every optimization problem. Therefore, researchers extensively try to improve methods of solving complex optimization problems. Many SI search algorithms are widely applied to solve such problems. ABC is one of the most popular algorithms in solving different kinds of optimization problems. However, it has a weak local search performance where the equation of solution search in ABC performs good exploration, but poor exploitation. Besides, it has a fast convergence and can therefore be trapped in the local optima for some complex multimodal problems. In order to address such issues, this paper proposes a novel hybrid ABC with outstanding local search algorithm called β -hill climbing ( β HC) and denoted by ABC– β HC. The aim is to improve the exploitation mechanism of the standard ABC. The proposed algorithm was experimentally tested with parameters tuning process and validated using selected benchmark functions with different characteristics, and it was also evaluated and compared with well-known state-of-the-art algorithms. The evaluation process was investigated using different common measurement metrics. The result showed that the proposed ABC– β HC had faster convergence in most benchmark functions and outperformed eight algorithms including the original ABC in terms of all the selected measurement metrics. For more validation, Wilcoxon’s rank sum statistical test was conducted, and the p values were found to be mostly less than 0.05, which demonstrates that the superiority of the proposed ABC– β HC is statistically significant.

中文翻译：

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一种用于数值函数优化的新型解释性混合人工蜂群算法

在过去的几十年里，在计算机辅助优化中使用群智能 (SI) 的兴趣激增。SI 算法已经证明了它们在解决各种类型的现实世界优化问题方面的有效性。然而，不可能找到一种优化算法，可以为每个优化问题获得全局最优。因此，研究人员广泛尝试改进解决复杂优化问题的方法。许多SI搜索算法被广泛应用于解决此类问题。ABC 是解决不同类型优化问题最流行的算法之一。然而，它具有较弱的局部搜索性能，其中 ABC 中的解搜索方程进行了良好的探索，但开发性较差。除了，它具有快速收敛性，因此对于一些复杂的多模态问题可能会陷入局部最优。为了解决这些问题，本文提出了一种具有出色局部搜索算法的新型混合ABC，称为β-爬坡（βHC），记为ABC-βHC。目的是完善标准ABC的开发机制。所提出的算法通过参数调整过程进行了实验测试，并使用具有不同特性的选定基准函数进行了验证，并与众所周知的最先进算法进行了评估和比较。使用不同的常见测量指标来研究评估过程。结果表明，所提出的 ABC-β HC 在大多数基准函数中具有更快的收敛性，并且在所有选定的测量指标方面都优于包括原始 ABC 在内的八种算法。为了进一步验证，进行了 Wilcoxon 秩和统计检验，发现 p 值大多小于 0.05，这表明所提出的 ABC-β HC 的优越性具有统计学意义。