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In multi-agent Bayesian optimization for Design Space Exploration (DSE), identifying a communication network among agents to share useful design information for enhanced cooperation and performance, considering the trade-off between connectivity and cost, poses significant challenges. To address this challenge, we develop a distributed multi-agent Bayesian optimization (DMABO) framework and study how communication network structures/connectivity and the resulting cost would impact the performance of a team of agents when finding the global optimum. Specifically, we utilize Lloyd’s algorithm to partition the design space to assign distinct regions to individual agents for exploration in the distributed multi-agent system (MAS). Based on this partitioning, we generate communication networks among agents using two models: 1) a range-limited model of communication constrained by neighborhood information; and 2) a range-free model without neighborhood constraints. We introduce network density as a metric to quantify communication costs. Then, we generate communication networks by gradually increasing the network density to assess the impact of communication costs on the performance of MAS in DSE. The experimental results show that the communication network based on the range-limited model can significantly improve performance without incurring high communication costs. This indicates that increasing the density of a communication network does not necessarily improve MAS performance in DSE. Furthermore, the results indicate that communication is only beneficial for team performance if it occurs between specific agents whose search regions are critically relevant to the location of the global optimum. The proposed DMABO framework and the insights obtained can help identify the best trade-off between communication structure and cost for MAS in unknown design space exploration. 

Effective coordination of design teams must account for the influence of costs incurred while searching for the best design solutions. This article introduces a cost-aware multi-agent system (MAS), a theoretical model to (1) explain how individuals in a team should search, assuming that they are all rational utility-maximizing decision-makers and (2) study the impact of cost on the search performance of both individual agents and the system. First, we develop a new multi-agent Bayesian optimization framework accounting for information exchange among agents to support their decisions on where to sample in search. Second, we employ a reinforcement learning approach based on the multi-agent deep deterministic policy gradient for training MAS to identify where agents cannot sample due to design constraints. Third, we propose a new cost-aware stopping criterion for each agent to determine when costs outweigh potential gains in search as a criterion to stop. Our results indicate that cost has a more significant impact on MAS communication in complex design problems than in simple ones. For example, when searching in complex design spaces, some agents could initially have low-performance gains, thus stopping prematurely due to negative payoffs, even if those agents could perform better in the later stage of the search. Therefore, global-local communication becomes more critical in such situations for the entire system to converge. The proposed model can serve as a benchmark for empirical studies to quantitatively gauge how humans would rationally make design decisions in a team.