  We propose an ensembling framework that uses diverse open-sourced Large
Language Models (LLMs) to achieve high response quality while maintaining cost
efficiency. We formulate a bi-objective optimization problem to represent the
quality-cost tradeoff and then introduce an additional budget constraint that
reduces the problem to a straightforward 0/1 knapsack problem. We empirically
demonstrate that our framework outperforms the existing ensembling approaches
in response quality while significantly reducing costs.
