In this work we investigate different heuristics for solving NP-hard problems. These heuristics explore the solution space in a parallel fashion, attempting to converge to an optimal solution by mimicking the way natural selection and genetics favor the fittest candidates. These randomized, but not directionless, search procedures were developed and labeled genetic algorithms by John Holland.
rnWe apply the heuristics to various classical optimization problems, including the knapsack problem and the maximum cut problem. The latter consists of partitioning the set V of vertices of a graph G = (V, E) into two disjoint sets V
Starting with a randomly chosen initial population, the genetic algorithm will move from one generation to a better one by using the operations of reproduction, crossover and mutation. We investigate and compare different crossover techniques. The survival of well fit individuals is based on the computation of a fitness function which is closely related to the objective function in the optimization problem. This study considers and compares various fitness functions. We thus make use of a fitness function that penalizes overfilled knapsacks for instance. We conclude this work by giving a few suggestions on the use of genetic algorithms in combinatorial optimization problems.
在这项工作中,我们研究了用于解决NP难题的不同启发式方法。这些启发式方法以并行方式探索解决方案空间,试图通过模仿自然选择和遗传学最适合的候选人的方式收敛到最佳解决方案。这些随机的但并非无方向的搜索程序是由约翰·霍兰德(John Holland)开发并标记遗传算法的。 P> rn
我们将启发式方法应用于各种经典的优化问题,包括背包问题和最大割问题。后者包括将图G =(V,E)的顶点集合V划分为两个不相交的集合V 从随机选择的初始位置开始人口,遗传算法将通过使用繁殖,交叉和变异的操作从一代到更好的一代。我们调查并比较了不同的交叉技术。适合个体的生存是基于适应度函数的计算,该适应度函数与优化问题中的目标函数密切相关。本研究考虑并比较了各种适应功能。因此,我们利用了适合度函数,例如对过度填充的背包进行惩罚。最后,通过在组合优化问题中使用遗传算法的一些建议,来结束这项工作。 P>
Dept. of Biomedical Eng, Johns Hopkins Medical School, Traylor Research Building, Baltimore, MD;
Dept. of Computer Science, Wellesley College, 106 Central St., Wellesley, MA;
机译:2015年11月20日在伦敦大学学院儿童健康研究所举行的第26届遗传学学会哺乳动物遗传与发展研讨会上发表的论文摘要
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