Large Language Models (LLMs) have garnered considerable attention owing to their remarkable capabilities, leading to an increasing number of companies offering LLMs as services. Different LLMs achieve different performance at different costs. A challenge for users lies in choosing the LLMs that best fit their needs, balancing cost and performance. In this paper, we propose a framework for addressing the cost-effective query allocation problem for LLMs. Given a set of input queries and candidate LLMs, our framework, named OptLLM, provides users with a range of optimal solutions to choose from, aligning with their budget constraints and performance preferences, including options for maximizing accuracy and minimizing cost. OptLLM predicts the performance of candidate LLMs on each query using a multi-label classification model with uncertainty estimation and then iteratively generates a set of non-dominated solutions by destructing and reconstructing the current solution. To evaluate the effectiveness of OptLLM, we conduct extensive experiments on various types of tasks, including text classification, question answering, sentiment analysis, reasoning, and log parsing. Our experimental results demonstrate that OptLLM substantially reduces costs by 2.40% to 49.18% while achieving the same accuracy as the best LLM. Compared to other multi-objective optimization algorithms, OptLLM improves accuracy by 2.94% to 69.05% at the same cost or saves costs by 8.79% and 95.87% while maintaining the highest attainable accuracy.

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