Parent selection methods are widely used in evolutionary computation to accelerate the optimization process, yet their theoretical benefits are still poorly understood. In this paper, we address this gap by proposing a parent selection strategy for the $(μ+1)$ genetic algorithm (GA) that prioritizes the selection of maximally distant parents for crossover. We show that, with an appropriately chosen population size, the resulting algorithm solves the Jump$_k$ problem in $O(k4^kn\log(n))$ expected time. This bound is significantly smaller than the best known bound of $O(nμ\log(μ)+n\log(n)+n^{k-1})$ for any $(μ+1)$~GA using no explicit diversity-preserving mechanism and a constant crossover probability.
To establish this result, we introduce a novel diversity metric that captures both the maximum distance between pairs of individuals in the population and the number of pairs achieving this distance. The main novelty of our analysis is that it relies on crossover as a mechanism for creating and maintaining diversity throughout the run, rather than using crossover only in the final step to combine already diversified individuals. The insights provided by our analysis contribute to a deeper theoretical understanding of the role of crossover in the population dynamics of genetic algorithms.
Improved discrete particle swarm optimization using Bee Algorithm and multi-parent crossover method (Case study: Allocation problem and benchmark functions)
K. N. Toosi University of Technology（K. N. Toosi理工大学）
A Seft-adaptive Multicellular GEP Algorithm Based On Fuzzy Control For Function Optimization
为了提高传统GEP算法的全局寻优能力，提出了一种基于模糊控制的多细胞基因表达式编程算法（Multicellular GEP Algorithm Based On Fuzzy Control，MGEP-FC）。MGEP-FC算法通过构造模糊隶属度函数来描述交叉率、变异率和实数变异率的大小。根据个体适应度值在种群中的集中度和分散度，动态调整遗传操作的交叉率、变异率和实数集变异率。为了使种群的多样性在迭代过程中得以延续，设计了一种新的遗传操作方案，将新个体与父代种群相结合构建临时种群，并对临时种群和子种群的多样性进行了优化。12个Benchmark优化实验结果表明，MGEP-FC算法在稳定性、全局收敛性和寻优速度等方面都有了很大的提高。
Already Moderate Population Sizes Provably Yield Strong Robustness to Noise
The University of Adelaide（阿德莱德大学）；CNRS（法国国家科学研究中心）；École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；HSE University（高等经济大学）；Skoltech（斯科尔科沃科学技术研究院）
