NeurGO: Learning to Generate Elite Candidates for Meta-Black-Box Expensive Optimization

Expensive black-box optimization is ubiquitous in science and engineering, where function evaluations are costly and the evaluation budget is limited. Traditional evolutionary algorithms and Meta-BlackBox Optimization (MetaBBO) approaches typically consume most evaluations on candidate selection, often wasting precious budget on inferior solutions. Although surrogate-assisted evolution and Bayesian optimization aim to reduce evaluations through surrogate models, constructing an accurate global model from limited data remains challenging, and model bias can easily trap the search in local optima. To overcome these limitations, we propose NeurGO, a generative MetaBBO framework that directly synthesizes elite candidates from historical population states. Specifically, we employ an attention-based encoder to capture the population-level search trend and condition a decoder on this representation to generate high-quality candidates, avoiding the expensive evaluation of large offspring pools. We then design a quality-diversity loss to maintain solution quality and population diversity throughout the search. Through extensive benchmarking on CEC 2008 and the COCO BBOB test suites, our method achieves better optimization performance under the same evaluation budget and exhibits faster convergence.

SPEA2$^+$: Improved Density Estimation in SPEA2 with Provable Runtime Guarantees

The Strength Pareto Evolutionary Algorithm 2 (SPEA2) is a popular and prominent evolutionary algorithm for solving multi-objective optimisation problems. Despite its popularity, theoretical analyses of SPEA2 have only appeared recently. Moreover, these analyses focus exclusively on how SPEA2 handles non-dominated solutions and disregard the algorithmic components responsible for handling dominated solutions. We conduct a first runtime analysis of SPEA2 for which these components are analysed. We prove that, unlike other prominent algorithms, including NSGA-II, NSGA-III and SMS-EMOA under the same setting of constant population size and duplicate elimination, SPEA2 is unable to cover the Pareto front of the OneTrapZeroTrap benchmark efficiently. Our results indicate that using k-th nearest-neighbour distance in the fitness assignment provides an insufficient signal to maintain diversity among dominated individuals. To address this issue, we propose an improved variant, SPEA2$^+$, that considers all pairwise distances. The new algorithm achieves the same performance guarantees as the other prominent algorithms on OneTrapZeroTrap, while matching the performance of the original SPEA2 on simpler problems. Experimental results complement our theoretical findings.