Evolving with Feasibility: Turning Failures into Feedback for LLM-Driven Algorithm Evolution

Large language models (LLMs) are increasingly used to automate algorithm design by evolving executable solver programs. However, generated offspring solvers may fail to execute, exceed runtime limits, or violate problem constraints, preventing their algorithmic changes from being meaningfully evaluated. Such failures are particularly costly under limited candidate budgets: they waste generation opportunities, can terminate useful search trajectories, and may recur across generations. We propose RevivEvo, a feasibility-guided framework that treats feasibility not only as an evaluation outcome, but as feedback for evolution. RevivEvo uses parent-specific search and failure experience to prevent known risks during generation, type-aware bounded repair to recover infeasible offspring, and failure and repair memory to reuse experience across generations. Across 14 tasks from CO-Bench and HeuriGym with a budget of 20 candidates, RevivEvo increases the final candidate feasibility rate from 35.60% to 92.38% over the strongest feasibility baseline and improves the macro-averaged Test Avg. Score from 0.665 to 0.832 over the strongest performance baseline. Moreover, 52.4% of final selected solvers either result from repair or descend from a repaired candidate, showing that recovery can benefit subsequent evolution beyond immediate candidate repair. These results demonstrate that incorporating feasibility feedback throughout evolution improves both the reliability and effectiveness of LLM-driven algorithm design.