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 paper, 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.

翻译：针对双亲解的最优重组算子，能够在从每个亲本获取变量值（基因传递特性）的所有解中提供最优解。当解为比特串时，最优重组算子的后代位于包含两个亲本解的最小超平面内，且在该超平面中为最优。探索该超平面前提下计算成本高昂，最坏情况下需指数时间。然而，当目标函数的变量交互图稀疏时，可在多项式时间内完成探索。本文提出一种名为"王朝潜力交叉"（DPX）的重组算子，该算子以多项式时间运行，对低上位性组合问题具有类最优重组算子的性能。我们从理论与实验两个层面，将该算子与传统交叉算子（如均匀交叉和网络交叉）以及两种新近定义的高效重组算子（划分交叉与连接点划分交叉）进行比较。实验采用NKQ景观和MAX-SAT实例。DPX在后代质量方面优于其他交叉算子，并在轨迹搜索与种群元启发式框架中均取得更优结果，但其计算后代需耗费更多时间与内存。