Bayesian Optimization with multi-objective acquisition functions such as q-Expected Hypervolume Improvement (qEHVI) requires efficient candidate optimization to maximize acquisition function values. Traditional approaches rely on continuous optimization methods like Sequential Least Squares Programming (SLSQP) for candidate selection. However, these gradient-based methods can become trapped in local optima, particularly in complex or high-dimensional objective landscapes. This paper presents a simulated annealing-based approach for candidate optimization in batch acquisition functions as an alternative to conventional continuous optimization methods. We evaluate our simulated annealing approach against SLSQP across four benchmark multi-objective optimization problems: ZDT1 (30D, 2 objectives), DTLZ2 (7D, 3 objectives), Kursawe (3D, 2 objectives), and Latent-Aware (4D, 2 objectives). Our results demonstrate that simulated annealing consistently achieves superior hypervolume performance compared to SLSQP in most test functions. The improvement is particularly pronounced for DTLZ2 and Latent-Aware problems, where simulated annealing reaches significantly higher hypervolume values and maintains better convergence characteristics. The histogram analysis of objective space coverage further reveals that simulated annealing explores more diverse and optimal regions of the Pareto front. These findings suggest that metaheuristic optimization approaches like simulated annealing can provide more robust and effective candidate optimization for multi-objective Bayesian optimization, offering a promising alternative to traditional gradient-based methods for batch acquisition function optimization.

翻译：使用多目标采集函数（如q-期望超体积改进qEHVI）的贝叶斯优化需要高效的候选优化以最大化采集函数值。传统方法依赖连续优化方法（如序列最小二乘规划SLSQP）进行候选选择。然而，这些基于梯度的方法容易陷入局部最优，特别是在复杂或高维目标空间中。本文提出一种基于模拟退火的批量采集函数候选优化方法，作为传统连续优化方法的替代方案。我们在四个基准多目标优化问题上将模拟退火方法与SLSQP进行对比评估：ZDT1（30维，2目标）、DTLZ2（7维，3目标）、Kursawe（3维，2目标）和Latent-Aware（4维，2目标）。实验结果表明，在大多数测试函数中，模拟退火相比SLSQP能持续获得更优的超体积性能。在DTLZ2和Latent-Aware问题上改进尤为显著，模拟退火达到了明显更高的超体积值并保持了更好的收敛特性。目标空间覆盖的直方图分析进一步表明，模拟退火能探索帕累托前沿更多样化且更优的区域。这些发现表明，模拟退火等元启发式优化方法能为多目标贝叶斯优化提供更鲁棒有效的候选优化，为批量采集函数优化提供了有前景的替代传统梯度方法的方案。