Design and Tuning of Multi-Agent Systems Using Bayesian Evolutionary Optimization

Designing effective multi-agent systems (MAS) remains a challenging and resource-intensive task. We propose a Bayesian Evolutionary Optimization framework for automatically discovering task-specific MAS topologies. The approach combines evolutionary operators to generate diverse workflow graphs with Bayesian optimization to select promising candidates for expensive evaluation. In contrast to LLM-based candidate selection, our approach uses a graph-aware Gaussian Process and Expected Improvement to provide an explicit selection criterion during evolutionary search. We evaluate the method on BigCodeBench for code generation and on a tabular preprocessing benchmark using TabPFN. On BigCodeBench, evolved architectures achieve the highest overall performance among the evaluated agent systems. On temporal tabular datasets, optimized MAS preprocessing improves over the default TabPFN model on several tasks, while remaining competitive on IID datasets. Overall, the results demonstrate the potential of Bayesian selection for guiding evolutionary MAS search under expensive evaluation budgets.