Neighborhood Adaptive Differential Evolution

We introduce Neighborhood Adaptive DE, an automatically designed variant of Differential Evolution (DE) tuned specifically for Many Affine Black-Box Optimization benchmark functions. The algorithm was generated by the Large Language Model Evolutionary Algorithm LLaMEA approach, which employed a (4,12) Evolution Strategy in combination with the large language model Gemini-2.0-Flash to generate new optimization algorithms. Key features of Neighborhood Adaptive DE include sampling a small, randomly chosen subset of 'neighbors' for each individual and using the best among those as the base vector in mutation (instead of the global best). This neighborhood-based strategy, along with adaptive tuning of scale factor F and crossover rate CR, leads to greater diversity and mitigates premature convergence. Additionally, an automatic restart mechanism re-initializes the population upon detecting stagnation. Experimental benchmarking indicates that Neighborhood Adaptive DE outperforms other algorithms on the benchmark, including the winner of last-years Many Affine competition, suggesting that automated design with LLaMEA can yield novel, high-performance algorithms for challenging black-box optimization tasks.