[Paper Review] Enhancing SAEAs with Unevaluated Solutions: A Case Study of Relation Model for Expensive Optimization

Hao Hao, Xiaoqun Zhang+1 more|arXiv (Cornell University)|Sep 21, 2023

Advanced Multi-Objective Optimization Algorithms4 citations

TL;DR

This paper proposes a novel surrogate-assisted evolutionary algorithm (DRSO) that enhances search efficiency in expensive optimization by generating high-potential offspring directly from unevaluated solutions predicted by a custom relation model. By using XGBoost-based relation models to rank solutions without evaluation, DRSO improves population diversity and convergence speed, outperforming regression and classification models in selection accuracy and algorithmic performance on benchmark problems.

ABSTRACT

Surrogate-assisted evolutionary algorithms (SAEAs) hold significant importance in resolving expensive optimization problems~(EOPs). Extensive efforts have been devoted to improving the efficacy of SAEAs through the development of proficient model-assisted selection methods. However, generating high-quality solutions is a prerequisite for selection. The fundamental paradigm of evaluating a limited number of solutions in each generation within SAEAs reduces the variance of adjacent populations, thus impacting the quality of offspring solutions. This is a frequently encountered issue, yet it has not gained widespread attention. This paper presents a framework using unevaluated solutions to enhance the efficiency of SAEAs. The surrogate model is employed to identify high-quality solutions for direct generation of new solutions without evaluation. To ensure dependable selection, we have introduced two tailored relation models for the selection of the optimal solution and the unevaluated population. A comprehensive experimental analysis is performed on two test suites, which showcases the superiority of the relation model over regression and classification models in the selection phase. Furthermore, the surrogate-selected unevaluated solutions with high potential have been shown to significantly enhance the efficiency of the algorithm.

Motivation & Objective

• To address the low population variance in SAEAs caused by limited real evaluations per generation.
• To improve search efficiency in expensive optimization by leveraging high-quality unevaluated solutions for offspring generation.
• To design a surrogate model that better captures solution quality ranking than traditional regression or classification models.
• To validate the effectiveness of unevaluated solutions in accelerating convergence and enhancing algorithm competitiveness.

Proposed method

• Introduces a dual-relation model framework (R-C1 and R-C2) that constructs relation pairs based on relative fitness or category ranking for surrogate modeling.
• Employs XGBoost to learn from relation pairs and predict solution quality with a voting-scoring strategy to improve robustness.
• Uses the best predicted solution for real evaluation while directly using other high-potential unevaluated solutions to generate new offspring.
• Applies reproduction operators (e.g., from EDA/LS) to unevaluated solutions to maintain population diversity and exploration.
• Maintains an external archive and updates the surrogate model iteratively using real evaluations and predicted rankings.
• Employs a parameter $ t $ to control the proportion of unevaluated solutions used for offspring generation, with $ t=50\% $ found optimal.

(a)

Experimental results

Research questions

• RQ1 Can unevaluated solutions predicted by a surrogate model effectively enhance population diversity and convergence in SAEAs?
• RQ2 How does a relation model compare to regression and classification models in selecting high-quality solutions for expensive optimization?
• RQ3 What is the optimal proportion $ t $ of unevaluated solutions to include in offspring generation for maximum algorithmic performance?
• RQ4 Does the use of unevaluated solutions significantly improve the runtime convergence speed of SAEAs?
• RQ5 Can the relation model accurately predict solution quality and maintain ranking order without overfitting?

Key findings

• The relation model (R-C1 and R-C2) outperformed XGBR and XGBC in selection accuracy, with R-C1 showing more concentrated interquartile range and R-C2 achieving better maximum performance.
• DRSO with $ t=50\% $ unevaluated solutions achieved the best convergence speed, outperforming variants with $ t=10\% $ and $ t=30\% $, especially on Ellipsoid and Griewank functions.
• The ablation study confirmed that removing unevaluated solutions (DRSO’) led to slower convergence, proving their critical role in accelerating search.
• The relation model effectively preserved ranking order between solutions while avoiding overfitting, unlike regression models, and provided more detailed partitioning than classification models.
• On the LZG and YLL test suites, DRSO demonstrated strong competitiveness against EAs, SAEAs, and Bayesian optimization methods in both 20D and 50D search spaces.
• The algorithm’s performance was stable across different functions, with $ t=50\% $ identified as the optimal balance between exploration and exploitation.

(a)