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arXiv · 2603.14801

Genetic Algorithms in Regression

Mo Li·QiQi Lu·Robert Lund·Xueheng Shi
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Abstract

Many statistical problems involve optimization over a discrete parameter space having an unknown dimension. In such settings, gradient-based methods often fail due to the non-differentiability of the objective function or a non-convex or massive search space with an objective function having many local maxima/minima. This paper presents GAReg, a unified genetic algorithm package that handles discrete optimization regression problems, which works well when standard algorithms are unjustified. GAReg provides a compact chromosome representation supporting optimal knot placement for regression splines, best-subset regression variable selection, and related problems. The package allows for uniform initialization, constraint-preserving crossover and mutation, steady-state replacement, and an optional island-model parallelization. GAReg efficiently searches high-dimensional model spaces, providing near-optimal solutions in settings where exhaustive enumeration or integer or dynamic programming approaches are infeasible.

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Mo Li, QiQi Lu, Robert Lund, Xueheng Shi. 2026-03-16. Genetic Algorithms in Regression. https://arxiv.org/abs/2603.14801

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