(2 作 2017 Michael Kirley)A Recursive Decomposition Method for Large Scale Continuous Optimization

Abstract

问题：

However, the main challenge when using this framework lies in problem decomposition. That is, deciding how to allocate decision variables to a particular subproblem, especially interacting decision variables. Existing decomposition methods are typically computationally expensive.

如何分配决策变量到子问题中，尤其针对相互作用的决策变量。现有的分解方法在计算上代价很大。

解决方法：

In this paper, we propose a new decomposition method, which we call recursive differential grouping (RDG), by considering the interaction between decision variables based on nonlinearity detection.

基于非线性检测的决策变量之间的相互作用，提出了一种新的分解方法，我们称之为递归差分分组（RDG）

RDG recursively examines the interaction between a selected decision variable and the remaining variables, placing all interacting decision variables into the same subproblem.

RDG递归地检查所选决策变量与其余变量之间的相互作用，将所有相互作用的决策变量置于同一子问题中。

结果：

RDG greatly improved the efficiency of problem decomposition in terms of time complexity. Significantly, when RDG was embedded in a CC framework, the optimization results were better than results from seven other decomposition methods.

RDG在时间复杂度方面极大地提高了问题分解的效率。 值得注意的是，当RDG嵌入CC框架时，优化结果优于其他七种分解方法的结果。

关键词：

Continuous optimization problem, cooperative co-evolution (CC), decomposition method, large scale global optimization (LSGO).

连续优化问题，协同协同进化（CC），分解方法，大规模全局优化（LSGO）。

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Conclution

方法：

A robust decomposition method—RDG—was proposed, which can decompose an n-dimensional problem using O(n log(n)) FEs based on a measure of nonlinearity between decision variables.

提出了一种鲁棒分解方法——RDG，它可以基于决策变量之间的非线性度量,使用O(n log(n))FEs来分解n维问题。

实验结果：

Significantly, RDG outperformed seven other decomposition methods when embedded into the DECC/CMAESCC framework and tested across a suite of benchmark LSGO problems. When compared against two other state-of-the-art hybrid algorithms, the CMAESCC-RDG algorithm achieved statistically significantly better results.

值得注意的是，当嵌入到DECC / CMAESCC框架中并在一系列基准LSGO问题中进行测试时，RDG的表现优于其他七种分解方法。 与其他两种最先进的混合算法进行比较时，CMAESCC-RDG算法在统计上获得了更好的结果。

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留给自己的问题

1 分解策略有哪些

2 分解原理是什么