A Unified Framework for Multi-Parent Polynomial Crossover with Parent-Centric and Mean-Centric Sampling

Abstract

Real-coded genetic algorithms (RCGAs) rely heavily on the design of crossover operators to balance global exploration and local exploitation in continuous optimization. Existing operators such as SBX, BLX-α, UNDX, and PCX typically employ two- or three-parent recombination and sample offspring either around elite parents (parent-centric) or around the centroid of multiple parents (mean-centric). However, most of these operators lack adaptive control over offspring spread and do not fully exploit the geometric and statistical information contained in larger parent sets. This paper proposes two new multi-parent crossover operators; Multi-Parent Polynomial Parent-Centric Crossover (MPPX) and Multi-Parent Polynomial Mean-Centric Crossover (MPCX) that extend polynomial-distribution-based sampling to multi--parent settings. MPPX generates offspring in the neighborhood of the best parent, while MPCX samples around the centroid. Both operators adapt offspring dispersion using parent-set deviation, yielding self-regulated search dynamics. Extensive experiments on unimodal and multimodal benchmark functions demonstrate that the proposed operators achieve faster convergence, improved robustness, and more stable performance compared to classical and recent crossover operators. The study concludes that the elite-anchored diversity provided by MPPX establishes an effective balance between exploration and exploitation for solving continuous optimization problems.

Keywords: Real-Coded Genetic Algorithm (RCGA), Multi-Parent Crossover, Polynomial Distribution, Parent-Centric Crossover, Mean-Centric Crossover, Evolutionary computation