Pascal-Weighted Genetic Algorithms: A Binomially-Structured Recombination Framework
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917253652414464 |
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| author | Basir, Otman A. |
| author_facet | Basir, Otman A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pascal-Weighted Genetic Algorithms: A Binomially-Structured Recombination Framework Basir, Otman A. Neural and Evolutionary Computing Artificial Intelligence Systems and Control Computing methodologies, Evolutionary algorithms, Theory of computation, Evolutionary algorithms and metaheuristics 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. |
| title | Pascal-Weighted Genetic Algorithms: A Binomially-Structured Recombination Framework |
| topic | Neural and Evolutionary Computing Artificial Intelligence Systems and Control Computing methodologies, Evolutionary algorithms, Theory of computation, Evolutionary algorithms and metaheuristics |
| url | https://arxiv.org/abs/2512.01249 |