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Recent years have witnessed a growing interest in automatic learning mechanisms and applications. The concept of hyper-heuristics, algorithms that either select among existing algorithms or generate new ones, holds high relevance in this matter. Current research suggests that, under certain circumstances, hyper-heuristics outperform single heuristics when evaluated in isolation. When hyper-heuristics are selected among existing algorithms, they map problem states into suitable solvers. Unfortunately, identifying the features that accurately describe the problem state—and thus allow for a proper mapping—requires plenty of domain-specific knowledge, which is not always available. This work proposes a simple yet effective hyper-heuristic model that does not rely on problem features to produce such a mapping. The model defines a fixed sequence of heuristics that improves the solving process of knapsack problems. This research comprises an analysis of feature-independent hyper-heuristic performance under different learning conditions and different problem sets.