Limited Perfect Monotonical Surrogates constructed using low-cost recursive linkage discovery with guaranteed output

TL;DR

This paper introduces LyMPuS, a low-cost, parameterless surrogate model that guarantees efficient linkage discovery and enables effective comparison of solutions in expensive optimization problems.

Contribution

The paper proposes LyMPuS, a novel limited perfect surrogate that overcomes linear model limitations, enabling on-the-fly training and guaranteed linkage discovery with minimal evaluations.

Findings

LyMPuS can be trained without a separate step.

It guarantees missing dependency detection in logarithmic steps.

It is suitable for limiting costs in local search procedures.

Abstract

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.