Symbolic AI Planning is a core technology of artificial intelligence. Recent works, largely by our research group at LiU, has shown that LLMs provide one avenue of designing domain-dependent heuristics capable of solving tasks within individual domains or problem classes. This project is aiming to evaluate their ability to generate domain-independent heuristics, solutions to any problem. Preliminary results are published at the LM4Plan workshop at ICAPS (A* conference) and have been highly appreciated. Several methods and approaches will be considered, such as AlphaEvolve-style genetic algorithms and AutoResearch-based agentic loops. Other related projects in the intersection between LLMs and Symbolic AI might also be enabled using these compute resources.