Pascal-Weighted Genetic Algorithms: A Binomially-Structured Recombination Framework

TL;DR

This paper presents Pascal-Weighted Recombination, a novel multi-parent operator for Genetic Algorithms that uses binomial coefficients to improve convergence and performance across various optimization problems.

Contribution

It introduces a new structured recombination framework based on Pascal coefficients, extending to multiple representations and demonstrating consistent performance improvements.

Findings

Achieves 9-22% performance gains over standard operators.

Yields smoother convergence and reduced variance.

Effective across diverse benchmark problems.

Abstract

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.