Since the advent of large language models (LLMs), prompt engineering has been a crucial step for eliciting desired responses for various Natural Language Processing (NLP) tasks. However, prompt engineering remains an impediment for end users due to rapid advances in models, tasks, and associated best practices. To mitigate this, Automatic Prompt Optimization (APO) techniques have recently emerged that use various automated techniques to help improve the performance of LLMs on various tasks. In this paper, we present a comprehensive survey summarizing the current progress and remaining challenges in this field. We provide a formal definition of APO, a 5-part unifying framework, and then proceed to rigorously categorize all relevant works based on their salient features therein. We hope to spur further research guided by our framework.

Routing incoming queries to the most cost-effective LLM while maintaining response quality poses a fundamental challenge in optimizing performance-cost trade-offs for large-scale commercial systems.We present IPR—a quality-constrained Intelligent Prompt Routing framework that dynamically selects optimal models based on predicted response quality and user-specified tolerance levels.IPR introduces three key innovations: (1) a modular architecture with lightweight quality estimators trained on 1.5M prompts annotated with calibrated quality scores, enabling fine-grained quality prediction across model families; (2) a user-controlled routing mechanism with tolerance parameter 𝜏 ∈ [0,1] that provides explicit control over quality-cost trade-offs; and (3) an extensible design using frozen encoders with model-specific adapters, reducing new model integration from days to hours. To rigorously train and evaluate IPR, we curate an industrial-level IPR dataset, a comprehensive benchmark containing 1.5 million examples with response quality annotations across 11 LLM candidates.Deployed on a major cloud platform, IPR achieves 43.9% cost reduction while maintaining quality parity with the strongest model in the Claude family and processes requests with sub-150ms latency.