用二项式权重设计多父代遗传算法，提升收敛稳定性与性能
Pascal-Weighted Genetic Algorithms: A Binomially-Structured Recombination Framework
- 基于归一化二项式系数构造多父代重组算子，强调中心遗传
- 在4个基准测试中性能提升9-22%，收敛更平滑，方差更低
- 适用于各类编码类型，可无缝集成到多种遗传算法框架
本文提出一类新型多父代重组算子——帕斯卡加权重组（PWR），基于归一化的帕斯卡（二项式）系数。与传统双父代交叉不同，PWR将子代构造成多个父代的结构化凸组合，利用呈二项式分布的权重，强化中心遗传，抑制破坏性方差。我们建立了PWR的数学框架，推导其方差传递特性，并分析其对模式存活的影响。该算子扩展至实值、二进制/逻辑及排列编码。在四个代表性基准上评估：(i) 基于ITAE指标的PID控制器调参，(ii) 满足幅频响应约束的FIR低通滤波器设计，(iii) 考虑SINR耦合的无线功率调制优化，(iv) 旅行商问题（TSP）。结果表明，跨多个任务中，PWR均实现更平滑的收敛、更低方差，并相较标准重组算子获得9%-22%的性能提升。该方法简单、算法无关，可轻松嵌入多种遗传算法架构。
原文摘要 · Abstract (English)
This paper introduces a new family of multi-parent recombination operators for Genetic Algorithms (GAs), based on normalized Pascal (binomial) coefficients. Unlike classical two-parent crossover operators, Pascal-Weighted Recombination (PWR) forms offsprings as structured convex combination of multiple parents, using binomially shaped weights that emphasize central inheritance while suppressing disruptive variance. We develop a mathematical framework for PWR, derive variance-transfer properties, and analyze its effect on schema survival. The operator is extended to real-valued, binary/logit, and permutation representations. We evaluate the proposed method on four representative benchmarks: (i) PID controller tuning evaluated using the ITAE metric, (ii) FIR low-pass filter design under magnitude-response constraints, (iii) wireless power-modulation optimization under SINR coupling, and (iv) the Traveling Salesman Problem (TSP). We demonstrate how, across these benchmarks, PWR consistently yields smoother convergence, reduced variance, and achieves 9-22% performance gains over standard recombination operators. The approach is simple, algorithm-agnostic, and readily integrable into diverse GA architectures.
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