The XCSF classifier system solves regression problems iteratively online with a population of overlapping, local approximators. We show that problem solution stability and accuracy may be lost in particular settings -mainly due to XCSF's global deletion. We introduce local deletion, which prevents these detrimental effects to large extents. We show experimentally that local deletion can prevent forgetting in various problems -particularly where the problem space is non-uniformly or

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... ntly sampled. While we use XCSF with hyperellipsoidal receptive fields and linear approximations herein, local deletion can be applied to any XCS version where locality can be similarly defined. For future work, we propose to apply XCSF with local deletion to unbalanced, non-uniformly distributed, locally sampled problems with complex manifold structures, within which varying target error values may be reached selectively.