An optimal recombination operator for two-parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this article, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

双亲解决方案的最佳重组算子提供了从父母之一（基因传递属性）获取每个变量值的最佳解决方案。如果解是位串，则最优重组算子的后代在包含两个父解的最小超平面中是最优的。探索这个超平面的计算成本很高，一般来说，在最坏的情况下需要指数级的时间。但是，当目标函数的变量交互图稀疏时，可以在多项式时间内完成探索。在本文中，我们提出了一种称为动态势交叉 (DPX) 的重组算子，它在多项式时间内运行，并且表现得类似于低上位性组合问题的最优重组算子。我们比较这个运算符，在理论上和实验上，使用传统的交叉算子，如均匀交叉和网络交叉，以及最近定义的两个高效重组算子：分区交叉和关节点分区交叉。经验比较使用 NKQ Landscapes 和 MAX-SAT 实例。DPX 在后代质量方面优于其他交叉算子，并提供包含在轨迹和基于种群的元启发式中的更好结果，但它需要更多时间和内存来计算后代。