Multi-parent crossover algorithms (MCAs) are widely used in solving optimization problems in many fields relying on encoding, crossover, variation and choice operators to produce iterative offspring chromosome. In this paper, a real-coded schema to support this genetic optimization process is considered. At each crossover stage, a linear combination of coefficients at the same scale hybridizes a fixed number of parent chromosomes. If parent chromosomes are iteratively selected, then coefficients will indicate these parent chromosomes: how to propagate. Essentially, all MCAs differentiate one algorithm from others through coefficient restriction. However, little work exists on analyzing techniques that efficiently create within-bound coefficients. The existing MCAs build coefficients following a uniform distribution, but at the same time, these coefficients violate constraints, thus propagating error. The error will cascade exponentially as the hybrid scale rises even slightly, leading to increased time consumption. To address this problem, an empirical distribution-based framework (EDBF) is proposed which takes multiple MCAs as its constituent members. Numerical results showed that proposed EDBF outperforms its members in terms of time consumption. As a general framework rather than a specific algorithm, EDBF is easy to implement and can easily accommodate any existing MCA.

多亲交叉算法（MCA）广泛用于解决依赖编码，交叉，变异和选择运算符来产生迭代后代染色体的许多领域中的优化问题。在本文中，考虑了支持该遗传优化过程的实编码方案。在每个交叉阶段，相同比例系数的线性组合会杂交固定数目的父染色体。如果父染色体被迭代选择，则系数将指示这些父染色体：如何繁殖。本质上，所有MCA通过系数限制将一种算法与其他算法区分开。但是，在分析有效创建界内系数的技术方面几乎没有工作。现有的MCA建立系数遵循均匀分布，但与此同时，这些系数违反约束，从而传播误差。随着混合比例的增加甚至很小，误差将成指数级地级联，从而增加了时间消耗。为了解决这个问题，提出了一个基于经验分布的框架（EDBF），该框架以多个MCA作为其组成成员。数值结果表明，提出的EDBF在时间消耗方面优于其成员。作为通用框架而不是特定算法，EDBF易于实现并且可以轻松容纳任何现有的MCA。数值结果表明，提出的EDBF在时间消耗方面优于其成员。作为通用框架而不是特定算法，EDBF易于实现并且可以轻松容纳任何现有的MCA。数值结果表明，提出的EDBF在时间消耗方面优于其成员。作为通用框架而不是特定算法，EDBF易于实现并且可以轻松容纳任何现有的MCA。