Simulated Annealing-based Candidate Optimization for Batch Acquisition Functions

TL;DR

This paper introduces a simulated annealing approach for optimizing batch acquisition functions in Bayesian optimization, outperforming traditional gradient-based methods like SLSQP in complex multi-objective problems.

Contribution

It proposes a novel simulated annealing-based candidate optimization method for multi-objective Bayesian optimization, demonstrating improved performance over SLSQP in benchmark tests.

Findings

Simulated annealing achieves higher hypervolume than SLSQP in most benchmarks.

The approach explores more diverse Pareto front regions.

Significant improvements observed in DTLZ2 and Latent-Aware problems.

Abstract

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.