## 1 Introduction  
The \(p\)-median problem is one of the most well-studied facility location problems in the field of management and operation research. In the classical \(p\)-median problem, a certain number of \(p\) facilities are located among \(n\) candidate locations and \(m\) demand points are allocated to the \(p\) opened facilities, while the objective is to minimize the sum of the transportation cost/distance to serve all of the demand points. The \(p\)-median problem and its extensions have been widely used in many practical situations including the location of plants, warehouses, distribution centers, hubs, and public service facilities [1]. Previous study has proven that the \(p\)-median problem is Non-deterministic Polynomial (NP) hard [2], and that its optimal solution is unlikely to be obtained through an exact approach with polynomial complexity. Thus, various approximate heuristics have been developed to find optimal or near optimal solutions. The genetic algorithm (GA) is a kind of metaheuristic inspired by the biological evolution process, which is one of the most efficient metaheuristics for solving the \(p\)-median problem. [PERSON] and [PERSON] [3] first reported the application of the GA for the \(p\)-median problem, and showed the advantage of the GA in the generality for approaching difficult optimization problems. [PERSON] et al. [4] improved the efficiency of the GA for solving the \(p\)-median problem by integrating the greedy heuristic in the evolution process, which showed better performance than the simulated annealing algorithm proposed by [PERSON] and [PERSON] [5]. [PERSON] et al. [6] employed a heuristic \"hypermutation\" operator in the GA to solve the capacitated \(p\)-median problem, which obtained better results from a comparison with the Tabu search algorithm. [PERSON] and [PERSON] [7] compared a class of GA based heuristicswith several other metaheuristics and reported their relative performances. Their experimental results indicated that the GA based algorithm had advantages of wide applicability, low implementation effort, and high accuracy. [PERSON] et al. [8] proposed two GAs with new coding schemes and genetic operators for solving the single allocation \(p\)-hub median problem. [PERSON] et al. [9] investigated the impacts of initial population generating strategies on the performance of the GA, and proposed an approach to enhance the quality of the initial population. Experimental results showed that the computational time could be reduced by improving the initial population. [PERSON] [10] introduced the parallel strategy in the GA to improve the efficiency in solving the capacitated \(p\)-median problem, and designed two parallel GAs that could run on computing clusters with high performance. [PERSON] et al. [11] proposed a modified firefly algorithm, which was used to solve a supply chain network problem. GA has also been used to efficiently solve many other problems in the industrial field such as material handling control [12], the transportation-production problem [13], and the works transport organization and control problem [14]. More metaheuristics in the facility location field can be found in [PERSON] et al. [1]. The \(p\)-median facility location problem is usually a long-term strategic decision problem, and most of the above studies assume that the facilities' operational environments is deterministic. However, in practical situations, the fierce competition, changes in customer taste, community growth, and economic vitality in the market area all make the demand quite uncertain in the planning period and difficult to estimate. In this situation, the demand is assumed to be an uncertain parameter, which can be modeled as a set of alternative future scenarios. Then, robust optimization approaches can be utilized to minimize the maximum regret of the overall transportation cost [15]. [PERSON] and [PERSON] [16] studied the \(p\)-median problem in a stochastic network, where the demand in each node was modeled as a set of discrete scenarios. [PERSON] et al.