Abstract. This paper presents an empirical study of population diversity measure and adaptive control of diversity in the context of a permutation-based algorithm for Traveling Salesman Problems and Vehicle Routing Problems. Maintenance of diversity adaptive control is one of the most fundamental issues of Genetic Algorithm (GA). We are concerned in this paper with GA in which individual chromosomes are integer encoded, and the crossover operations are permutation-based [3]. Here, all individuals have the same set of distinct alleles (integers) in all generations. The different permutations of the individuals decode into different fitness values. Permutation-based GA is used to solve Traveling Salesman Problem (TSP) [2], Vehicle Routing Problem (VRP) [1], and many other problems. Permutation-based crossover operator Partially Matched Crossover(PMX) [3] is used in this research, with an application rate of pc. We use a sequence insertion mutation, which is defined as relocating a subseq...