The optimal assignment of Large Language Models (LLMs) to specialized roles in multi-agent systems is a significant challenge, defined by a vast combinatorial search space, expensive black-box evaluations, and an inherent trade-off between performance and cost. Current optimization methods focus on single-agent settings and lack a principled framework for this multi-agent, multi-objective problem. This thesis introduces MALBO (Multi-Agent LLM Bayesian Optimization), a systematic framework designed to automate the efficient composition of LLM-based agent teams. We formalize the assignment challenge as a multi-objective optimization problem, aiming to identify the Pareto front of configurations between task accuracy and inference cost. The methodology employs multi-objective Bayesian Optimization (MOBO) with independent Gaussian Process surrogate models. By searching over a continuous feature-space representation of the LLMs, this approach performs a sample-efficient exploration guided by the expected hypervolume improvement. The primary contribution is a principled and automated methodology that yields a Pareto front of optimal team configurations. Our results demonstrate that the Bayesian optimization phase, compared to an initial random search, maintained a comparable average performance while reducing the average configuration cost by over 45%. Furthermore, MALBO identified specialized, heterogeneous teams that achieve cost reductions of up to 65.8% compared to homogeneous baselines, all while maintaining maximum performance. The framework thus provides a data-driven tool for deploying cost-effective and highly specialized multi-agent AI systems.