In this paper, we propose a generic optimization approach for challenging objective functions that finds applications in various statistical problems. We focus on objective functions with two parameter blocks of one amenable to analytic optimization, and another that is irregular or computationally expensive. To address this setting, we propose the Voronoi-Elitism Genetic Algorithm (VEGA), a derivative-free optimization method that embeds geometric information into genetic search. The proposed algorithm retains elite candidates and constructs Voronoi-based neighborhoods around them, whose crossover and self-adaptive mutation balance exploitation of promising solutions with exploration of under-covered regions. We study the high dimensional behavior of genetic search by analyzing distance concentration, and the effects of population size and shrinking mutation, which shows that the algorithm improves spatial coverage and yields sharper distance bounds under limited computational budgets. Simulation studies are conducted to compare VEGA with two genetic-type algorithms competitors in finite samples. A real data application on Stack Exchange activity data further illustrates its ability to identify stable structural changes, implying the algorithm is computationally flexible for high-dimensional, derivative-free optimization and applicable for various statistical problems.

翻译：本文提出一种针对复杂目标函数的通用优化方法，可应用于多种统计问题。我们重点关注包含两个参数块的目标函数：其中一个参数块易于解析优化，另一个则具有非规则性或计算代价高昂的特性。为解决此类问题，我们提出Voronoi-精英遗传算法（VEGA），这是一种将几何信息嵌入遗传搜索的无导数优化方法。该算法保留精英候选解，并围绕其构建Voronoi邻域，通过交叉与自适应变异在开发优质解与探索未覆盖区域之间取得平衡。通过分析距离集中现象、种群规模及收缩变异的影响，我们研究了遗传搜索的高维行为，结果表明该算法在有限计算预算下能提升空间覆盖性能并得到更紧致的距离界。通过有限样本下的仿真研究，我们将VEGA与两种同类遗传算法进行对比。基于Stack Exchange活动数据的实际应用进一步验证了算法识别稳定结构变化的能力，表明该算法在高维无导数优化中具有计算灵活性，可适用于多种统计问题。