The No Free Lunch (NFL) theorem guarantees equal average performance only under uniform sampling of a function space closed under permutation (c.u.p.). We ask when this averaging ceases to reflect what benchmarking actually reports. We study an iterative-search setting with sampling without replacement, where algorithms differ only in evaluation order. Binary objectives allow exhaustive evaluation in the fully enumerable case, and efficiency is defined by the first time the global minimum is reached. We then construct two additional benchmarks by algebraically recombining the same baseline functions through sums and differences. Function-algorithm relations are examined via correlation structure, hierarchical clustering, delta heatmaps, and PCA. A one-way ANOVA with Tukey contrasts confirms that algebraic reformulations induce statistically meaningful shifts in performance patterns. The uniformly sampled baseline remains consistent with the global NFL symmetry. In contrast, the algebraically modified benchmarks yield stable re-rankings and coherent clusters of functions and sampling policies. Composite objectives can also exhibit non-additive search effort despite being built from simpler components. Monte Carlo experiments indicate that order effects persist in larger spaces and depend on function class. Taken together, the results show how objective reformulation and benchmark design can generate structured local departures from NFL intuition. They motivate algorithm choice that is aware of both the problem class and the objective representation. This message applies to evolutionary computation as well as to statistical procedures based on relabeling, resampling, and permutation tests.

翻译：无免费午餐定理仅保证在满足排列封闭性条件下均匀采样函数空间时，算法具有相等的平均性能。本文探究这种平均性何时不再反映基准测试的实际报告结果。我们在无放回采样的迭代搜索框架中展开研究，其中算法仅通过评估顺序进行区分。在完全可枚举场景下，二元目标函数允许进行穷举评估，而算法效率由首次达到全局最小值的时间定义。随后，我们通过代数求和与差分运算对相同基准函数进行重组，构建了两个附加基准测试集。通过相关性结构分析、层次聚类、增量热力图和主成分分析等方法，我们深入研究了函数与算法间的关联关系。单因素方差分析配合Tukey事后检验证实：代数重构会引发具有统计显著性的性能模式偏移。均匀采样的基准集仍符合全局无免费午餐对称性，而代数修改后的基准测试集则产生了稳定的算法重排序结果，并形成了函数与采样策略的连贯聚类簇。尽管复合目标函数由简单组件构建而成，其搜索过程仍可能表现出非加性特征。蒙特卡洛实验表明，顺序效应在更大规模的搜索空间中持续存在，且其表现依赖于函数类别。综合来看，本研究揭示了目标函数重构与基准测试设计如何引发结构化局部偏差，从而突破无免费午餐定理的直觉认知。这启示我们应结合问题类别与目标表示形式进行算法选择。该结论不仅适用于进化计算领域，同样适用于基于重标记、重采样及置换检验的统计流程。