Pascal-Weighted Genetic Algorithms: A Binomially-Structured Recombination Framework
This addresses the need for more efficient and stable genetic algorithms in optimization tasks, though it is incremental as it builds on existing recombination methods.
The paper tackles the problem of improving genetic algorithms by introducing Pascal-Weighted Recombination (PWR), a multi-parent recombination operator based on binomial coefficients, which results in smoother convergence, reduced variance, and 9-22% performance gains over standard operators across benchmarks like PID tuning and TSP.
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.