一种求解大规模优化问题的特征空间分治法
An Eigenspace Divide-and-Conquer Approach for Large-Scale Optimization
摘要：
基于分治的进化算法在处理大规模优化问题方面取得了显著的成功。然而，这种类型的算法的吸引人的性能通常需要一个高精度的分解的优化问题，这仍然是一个具有挑战性的任务，现有的分解方法。本研究试图从不同的角度来解决上述问题，并提出了一个特征空间分治（EDC）的方法。与现有的基于DC的算法在原始决策空间中进行分解和优化不同，EDC首先通过对从最近几代中选择的一组高质量解进行奇异值分解来建立特征空间。然后将优化问题转化到特征空间，从而大大削弱了相应特征变量之间的依赖关系。因此，这些特征变量可以有效地分组由一个简单的随机策略和每个由此产生的子问题可以更容易地解决传统的EA。为了验证EDC的效率，在两组基准函数上进行了全面的实验研究。实验结果表明，EDC对参数具有鲁棒性，对问题维度具有良好的可扩展性。与几种最先进算法的比较进一步证实了EDC具有相当的竞争力，并且在复杂的LSOP上表现得更好。
英文摘要：
Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a high-precision decomposition of the optimization problem, which is still a challenging task for existing decomposition methods. This study attempts to address the above issue from a different perspective and proposes an eigenspace divide-and-conquer (EDC) approach. Different from existing DC-based algorithms that perform decomposition and optimization in the original decision space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations. Then it transforms the optimization problem into the eigenspace, and thus significantly weakens the dependencies among the corresponding eigenvariables. Accordingly, these eigenvariables can be efficiently grouped by a simple random strategy and each of the resulting subproblems can be addressed more easily by a traditional EA. To verify the efficiency of EDC, comprehensive experimental studies were conducted on two sets of benchmark functions. Experimental results indicate that EDC is robust to its parameters and has good scalability to the problem dimension. The comparison with several state-of-the-art algorithms further confirms that EDC is pretty competitive and performs better on complicated LSOPs.
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