Empirical distribution-based framework for improving multi-parent crossover algorithms

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.