The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy ran...The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy randomized adaptive search procedure with path-relinking （GRASP/PR） algorithm for the p-center problem, which combines both GRASP and path-relinking. Each iteration of GRASP/PR consists of the construction of a randomized greedy solution, followed by a tabu search procedure. The resulting solution is combined with one of the elite solutions by path-relinking, which consists in exploring trajectories that connect high-quality solutions. Experiments show that GRASP/PR is competitive with the state-of-the-art algorithms in the literature in terms of both solution quality and computational efficiency. Specifically, it virtually improves the previous best known results for 10 out of 40 large instances while matching the best known results for others.展开更多
We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is a rar...We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is a rarefaction wave with finite strength, there exists unique solution to the viscous problem with the same initial data which converges to the given inviscid solution as c goes to zero. The proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure.展开更多
基金The research was supported by the National Natural Science Foundation of China under Grant Nos. 61370183 and 61262011.
文摘The p-center problem consists of choosing a subset of vertices in an undirected graph as facilities in order to minimize the maximum distance between a client and its closest facility. This paper presents a greedy randomized adaptive search procedure with path-relinking （GRASP/PR） algorithm for the p-center problem, which combines both GRASP and path-relinking. Each iteration of GRASP/PR consists of the construction of a randomized greedy solution, followed by a tabu search procedure. The resulting solution is combined with one of the elite solutions by path-relinking, which consists in exploring trajectories that connect high-quality solutions. Experiments show that GRASP/PR is competitive with the state-of-the-art algorithms in the literature in terms of both solution quality and computational efficiency. Specifically, it virtually improves the previous best known results for 10 out of 40 large instances while matching the best known results for others.
文摘We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is a rarefaction wave with finite strength, there exists unique solution to the viscous problem with the same initial data which converges to the given inviscid solution as c goes to zero. The proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure.
