Combinatorial optimization problems are traditionally tackled with handcrafted heuristic algorithms, which demand extensive domain expertise and significant implementation effort. Recent progress has highlighted the potential of automatic heuristics design powered by large language models (LLMs), enabling the automatic generation and refinement of heuristics. These approaches typically maintain a population of heuristics and employ LLMs as mutation operators to evolve them across generations. While effective, such methods often risk stagnating in local optima. To address this issue, we propose the Experience-Guided Reflective Co-Evolution of Prompt and Heuristics (EvoPH) for automatic algorithm design, a novel framework that integrates the island migration model with the elites selection algorithm to simulate diverse heuristics populations. In EvoPH, prompts are co-evolved with heuristic algorithms, guided by performance feedback. We evaluate our framework on two problems, i.e., Traveling Salesman Problem and Bin Packing Problem. Experimental results demonstrate that EvoPH achieves the lowest relative error against optimal solutions across both datasets, advancing the field of automatic algorithm design with LLMs.

This paper introduces MeLA, a Metacognitive LLM-Driven Architecture that presents a new paradigm for Automatic Heuristic Design (AHD). Traditional evolutionary methods operate directly on heuristic code; in contrast, MeLA evolves the instructional prompts used to guide a Large Language Model (LLM) in generating these heuristics. This process of "prompt evolution" is driven by a novel metacognitive framework where the system analyzes performance feedback to systematically refine its generative strategy. MeLA's architecture integrates a problem analyzer to construct an initial strategic prompt, an error diagnosis system to repair faulty code, and a metacognitive search engine that iteratively optimizes the prompt based on heuristic effectiveness. In comprehensive experiments across both benchmark and real-world problems, MeLA consistently generates more effective and robust heuristics, significantly outperforming state-of-the-art methods. Ultimately, this research demonstrates the profound potential of using cognitive science as a blueprint for AI architecture, revealing that by enabling an LLM to metacogni-tively regulate its problem-solving process, we unlock a more robust and interpretable path to AHD.

Popular prompt strategies like Chain-of-Thought Prompting can dramatically improve the reasoning abilities of Large Language Models (LLMs) in various domains. However, such hand-crafted prompt-strategies are often sub-optimal. In this paper, we present Promptbreeder, a general-purpose self-referential self-improvement mechanism that evolves and adapts prompts for a given domain. Driven by an LLM, Promptbreeder mutates a population of task-prompts, and subsequently evaluates them for fitness on a training set. Crucially, the mutation of these task-prompts is governed by mutation-prompts that the LLM generates and improves throughout evolution in a self-referential way. That is, Promptbreeder is not just improving task-prompts, but it is also improving the mutationprompts that improve these task-prompts. Promptbreeder outperforms state-of-the-art prompt strategies such as Chain-of-Thought and Plan-and-Solve Prompting on commonly used arithmetic and commonsense reasoning benchmarks. Furthermore, Promptbreeder is able to evolve intricate task-prompts for the challenging problem of hate speech classification.

Synthesis of digital artifacts conditioned on user prompts has become an important paradigm facilitating an explosion of use cases with generative AI. However, such models often fail to connect the generated outputs and desired target concepts/preferences implied by the prompts. Current research addressing this limitation has largely focused on enhancing the prompts before output generation or improving the model's performance up front. In contrast, this paper conceptualizes prompt evolution, imparting evolutionary selection pressure and variation during the generative process to produce multiple outputs that satisfy the target concepts/preferences better. We propose a multi-objective instantiation of this broader idea that uses a multi-label image classifier-guided approach. The predicted labels from the classifiers serve as multiple objectives to optimize, with the aim of producing diversified images that meet user preferences. A novelty of our evolutionary algorithm is that the pre-trained generative model gives us implicit mutation operations, leveraging the model's stochastic generative capability to automate the creation of Pareto-optimized images more faithful to user preferences.