Combinatorial optimization has long been dominated by manually engineered heuristics, a paradigm requiring substantial expert intuition and implementation overhead. The advent of Large Language Models has disrupted this landscape, enabling the autonomous synthesis and optimization of algorithms. Recent approaches typically iterate on heuristic populations using LLMs as mutators; however, these strategies often suffer from limited exploration, leading to stagnation in local optima. To overcome this, we present the Experience-Driven Reflective Co-Evolution of Prompt and Heuristics (EvoPH) for autonomous algorithm design, a novel framework that couples an island migration model with elite selection to maintain population diversity. Uniquely, EvoPH co-evolves both the guiding prompts and the heuristics themselves, using a feedback loop driven by past experience to refine the search process. We demonstrate EvoPH’s efficacy on the Traveling Salesman and Bin Packing Problems. Our results show that EvoPH achieves superior accuracy compared to baselines, marking a significant step forward in LLM-aided algorithm design.