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

2025-11-30

AI Summary

In conventional genetic algorithms, two-parent recombination often introduces high-destructive variance, impairing convergence and stability. To address this, we propose a family of multi-parent recombination operators grounded in Pascal (binomial) coefficients: normalized binomial weights construct structured convex combinations, enabling centralized genetic search and substantially suppressing offspring variance fluctuations. This work introduces the binomial weighting mechanism to multi-parent recombination for the first time, enhancing schema preservation while natively supporting real-valued, binary, and permutation encodings—ensuring universality and plug-and-play compatibility. Theoretical analysis establishes its variance decay property and schema survival advantage. Empirical evaluation across four benchmark problem classes demonstrates 9–22% performance improvement over standard genetic algorithms, with markedly enhanced convergence stability and optimization efficiency.

Technology Category

Search and Optimization: Mixed Discrete/Continuous SearchReasoning under Uncertainty: Stochastic OptimizationConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingSearch and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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.

Problem

• Develop binomial-coefficient-based multi-parent recombination for Genetic Algorithms
• Analyze variance-transfer and schema survival in the new recombination framework
• Evaluate performance on benchmarks like PID tuning, filter design, and TSP

Innovation

• Multi-parent recombination using Pascal coefficients
• Binomial weights emphasize central inheritance
• Reduces variance and improves convergence across benchmarks