Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability.

Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus.

We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization.

Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.