Title: AutoMOAE: Multi-Objective Auto-Algorithm Evolution
Primary area: optimization
Keywords: Heuristic Search, Evaluation and Analysis, Algorithm Design Automation

Abstract: Algorithm design has traditionally relied on expert intuition, making it time-consuming and often unable to balance solution quality with computational efficiency. Although LLM-driven methods have shown remarkable progress in automating code synthesis, they seldom address multiple requirements simultaneously. Ignoring such multi-objective trade-offs greatly undermines practical applicability, as real-world algorithm design inevitably involves reconciling competing goals. However, balancing multiple requirements is inherently challenging, often leading to infeasible strategies or unintended side effects during the evolutionary process.

We propose AutoMOAE (Auto-Algorithm Evolution for Multi-Objective requirements), a framework that explicitly incorporates multiple demands into the design process. AutoMOAE leverages LLM prompting to dynamically synthesize crossover and mutation operators augmented with analytical modules, effectively reducing nonproductive optimization steps. Verification operations further ensure strict adherence to both syntactic and functional correctness. Evaluations on graph coloring and Traveling Salesman benchmarks show that AutoMOAE-generated algorithms consistently match or surpass expert-crafted solutions in both solution quality and computational efficiency. These results demonstrate the necessity and promise of integrating multi-objective considerations into automated algorithm design, paving the way for scalable, high-performance synthesis frameworks.

TL;DR: AAE introduces a framework that uses LLMs and evolutionary algorithms to automatically design and optimize algorithms for multi-objective problems like graph coloring and TSP, rivaling expert methods in performance and efficiency.