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.

翻译：本文基于归一化的帕斯卡（二项式）系数，为遗传算法（GAs）引入了一类新的多父代重组算子。与经典的双亲交叉算子不同，帕斯卡加权重组（PWR）通过使用二项式形态的权重，将多个父代的结构化凸组合作为子代生成，强调中心遗传的同时抑制破坏性方差。我们为PWR建立了数学框架，推导了其方差传递特性，并分析了其对模式生存的影响。该算子被扩展至实值、二进制/逻辑值及排列表示。我们在四个代表性基准测试中评估了所提方法：（i）使用ITAE指标评估的PID控制器调参，（ii）幅度响应约束下的FIR低通滤波器设计，（iii）SINR耦合下的无线功率调制优化，以及（iv）旅行商问题（TSP）。我们展示了在这些基准测试中，PWR如何持续产生更平滑的收敛、更低的方差，并相较于标准重组算子实现9-22%的性能提升。该方法简单、与算法无关，且易于集成到多种GA架构中。