Surrogates provide a cheap solution evaluation and offer significant leverage for optimizing computationally expensive problems. Usually, surrogates only approximate the original function. Recently, the perfect linear surrogates were proposed that ideally represent the original function. These surrogates do not mimic the original function. In fact, they are another (correct) representation of it and enable a wide range of possibilities, e.g., discovering the optimized function for problems where the direct transformation of the encoded solution into its evaluation is not available. However, many real-world problems can not be represented by linear models, making the aforementioned surrogates inapplicable. Therefore, we propose the Limited Monotonical Perfect Surrogate (LyMPuS), which overcomes this difficulty and enables the comparison of two solutions that differ by a single variable. Our proposition is suitable for limiting the cost of expensive local search procedures. The proposed surrogate is parameterless and can be trained on the fly without any separate surrogate-building step. It uses only the necessary fitness evaluations, and the already-paid costs are not wasted when the model is updated. Finally, it offers low-cost missing-linkage detection and low-cost linkage discovery, guaranteed to find a missing dependency in no more than $2\lceil\log_2(n)\rceil$ steps.

翻译：替代模型提供廉价的解评估，并为优化计算昂贵问题提供重要支撑。通常，替代模型仅近似原始函数。近期提出的完美线性替代模型能够理想地表示原始函数。这类替代模型并非模仿原始函数，而是作为其另一种（正确的）表示形式，开辟了广泛的应用可能性，例如在编码解到其评估值无法直接转换的问题中，发现优化函数。然而，许多实际问题无法用线性模型表示，导致前述替代模型难以适用。为此，我们提出有限单调完美替代模型（LyMPuS），该模型克服了这一困难，能够比较仅相差一个变量的两个解。该方案适用于降低昂贵局部搜索过程的开销。所提替代模型无参数，无需单独的模型构建步骤即可在线训练。它仅使用必要的适应度评估次数，且在模型更新时不会浪费已付出的计算成本。最后，该模型能够实现低成本的缺失关联检测与关联发现，保证在不超过 $2\lceil\log_2(n)\rceil$ 步内找到缺失的依赖关系。