Harmony Search algorithm: a variant with Self-regulated Fretwidth
Harmony Search algorithm: a variant with Self-regulated Fretwidth
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DOI：
10.1016/j.amc.2015.06.040
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
I. Amaya;Jorge Cruz;R. Correa
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文献类型：
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作者：
I. Amaya;Jorge Cruz;R. Correa
本文对和声搜索算法提出了一种新的改进算法，该算法能够随着搜索过程的进行而自调整。这种自适应行为与总迭代无关。此外，与HS的其他变体相比，它需要的迭代次数更少，并且提供了更高的精度。评估了它的有效性和性能，将我们的数据与HS的四个著名和最近的修改进行了比较：IHS(改进的和声搜索，2007)、ABHS(可调整带宽的和声搜索，2014)、PAHs(参数自适应和声搜索，2014)和IGS(智能全球和声搜索，2014)。与其他工作不同的是，我们没有分析给定迭代次数的数据。相反，我们运行每个算法，直到它达到给定的精度水平，并分析它所需的迭代次数。我们的测试基准包含30个标准测试函数，其分布如下：11个单峰函数、8个固定维度的多通道函数和11个可变维度的多通道函数。后者还包括一个函数，该函数的最优值位于每个维度的不同坐标。根据文献，每个功能的搜索域都是固定的，尽管我们也执行了关于改变它的效果的测试。我们进行了参数扫描，为我们提出的算法的每个参数找到了合适的值，分析了648种不同组合的100次独立运行。数据证实，实施的程序在2D和5D问题上的表现优于其他变种。将测试函数扩展到10D、30D和50D降低了实施过程的收敛速度，但它仍然优于IHS、ABHS和PAH。在某些情况下(例如30D中的Schwefel函数)，自调节频域调和搜索算法(SFHS)被发现是最快的方法。研究还发现，对于最优值在所有维度上都位于相同坐标的优化问题，IRS算法表现得很好，但在其他情况下就不那么好了。我们提出的算法(SFHS)不受此阻碍。SFHS能够实现测试函数的完全收敛，其中Optima位于不同的坐标，即使在50D和探索[-1250,1250]的搜索域时也是如此。SFHS能够实现比HS更精确的解决方案(数量级较小的几个数量级)，因此它是对HS以及测试变体(IHS、ABHS、PAHs、IHS)的很好改进。尽管如此，我们提出的方法仍然存在一些局限性，比如比其他变体需要更多的参数，对于所有高维函数不能100%收敛，有时需要多次迭代才能收敛。在第一种情况下，我们认为这允许在参数的演变中有更多的自由。在第二种情况下，我们认为可以通过将自调优行为复制到其余参数来解决此问题。在最后一个方面，我们估计，加快SFHS的演变可能被证明是一个非常有用的战略。至于其他优化策略，我们在多达30个维度上进行了测试，并将我们的数据与Firefly算法进行了比较。我们发现，我们提出的方法保持了100%的收敛速度，而萤火虫的收敛速度急剧下降(在某些情况下)，甚至在30维上的收敛速度为0%。
This article presents a novel modification of the Harmony Search (HS) algorithm that is able to self-tune as the search progress. This adaptive behavior is independent of total iterations. Moreover, it requires less iterations and provides more precision than other variants of HS. Its effectiveness and performance was assessed, comparing our data against four well known and recent modifications of HS: IHS (Improved Harmony Search, 2007), ABHS (Adjustable Bandwidth Harmony Search, 2014), PAHS (Parameter Adaptive Harmony Search, 2014), and IGHS (Intelligent Global Harmony Search, 2014). Unlike other works, we did not analyze the data for a given number of iterations. Instead, we ran each algorithm until it achieved a given level of precision, and analyzed the number of iterations it required. Our test benchmark contained 30 standard test functions distributed like this: 11 unimodal, 8 multimodal with fixed dimensions, and 11 multimodal with variable dimensions. The latter also included a function whose optima was located at a different coordinate in each dimension. The search domain for each function was fixed according to the literature, though we also executed tests regarding the effect of varying it. We carried out a parameter sweep to find adequate values for each parameter of our proposed algorithm, analyzing 100 independent runs for 648 different combinations. Data confirm the implemented procedure outperformed the other variants for problems in 2D and in 5D. Scaling the test functions to 10D, 30D, and 50D reduced the convergence rate of the implemented procedure, but it still outperformed IHS, ABHS, and PAHS. In some cases (e.g. Schwefel function in 30D), the Self-regulated Fretwidth Harmony Search algorithm (SFHS) was found to be the fastest approach. It was also found that IGHS performs well for optimization problems whose optima is located at the same coordinates in all dimensions, but not as well in other scenarios. Our proposed algorithm (SFHS) is not hindered by this. SFHS was able to achieve full convergence for a test function with optima located at different coordinates, even in 50D and while exploring a search domain of [–1250, 1250]. SFHS is able to achieve a more precise solution than HS (several orders of smaller magnitude), and so it stands as a good improvement over HS, as well as over the tested variants (IHS, ABHS, PAHS, IGHS). Still, our proposed method exhibited some limitations, such as requiring more parameters than other variants, being unable to converge 100% of the times for all high dimensional functions, and sometimes needing several iterations to converge. In the first case, we think this allows for more freedom in the evolution of parameters. In the second case, we consider it can be addressed by replicating the self-tuning behavior to the remaining parameters. In the final aspect, we estimate that accelerating the evolution of SFHS could prove a very useful strategy. Regarding other optimization strategies, we ran tests in up to 30 dimensions, and compared our data against the Firefly algorithm. We found that our proposed method retains 100% convergence rate, while the convergence rate of Firefly drops drastically (in some cases), even yielding 0% at 30 dimensions.