This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building...This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of minimum parametric cost flow problems with different objective functions. On each of the iterations, the flow is augmented along a cheapest path from the source node to the sink node in the time-space network avoiding the explicit time expansion of the network.展开更多
The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all ...The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all origins’ supply and all destinations’ demands as well as the expanding cost is minimum. Actually, MCCETLTPD is a balance transportation problem and a variant problem of minimum cost maximum flow problem. In this paper, by creating a mathematical model and constructing a network with lower and upper arc capacities, MCCETLTPD is transformed into searching feasible flow in the constructed network, and consequently, an algorithm MCCETLTPD-A is developed as MCCETLTPD’s solution method basing minimum cost maximum flow algorithm. Computational study validates that the MCCETLTPD-A algorithm is an efficient approach to solving the MCCETLTPD.展开更多
Let C be a set of colors, and let ?be an integer cost assigned to a color c in C. An edge-coloring of a graph ?is assigning a color in C to each edge ?so that any two edges having end-vertex in common have different c...Let C be a set of colors, and let ?be an integer cost assigned to a color c in C. An edge-coloring of a graph ?is assigning a color in C to each edge ?so that any two edges having end-vertex in common have different colors. The cost ?of an edge-coloring f of G is the sum of costs ?of colors ?assigned to all edges e in G. An edge-coloring f of G is optimal if ?is minimum among all edge-colorings of G. A cactus is a connected graph in which every block is either an edge or a cycle. In this paper, we give an algorithm to find an optimal edge- ??coloring of a cactus in polynomial time. In our best knowledge, this is the first polynomial-time algorithm to find an optimal edge-coloring of a cactus.展开更多
The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal.The modification cost is measured by different norms,such asl1,l2,l∞no...The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal.The modification cost is measured by different norms,such asl1,l2,l∞norms and the Hamming distance,and the goal is to adjust the parameters as little as possible.In this paper,we consider the inverse maximum flow problem under the combination of the weighted l2 norm and the weighted Hamming distance,i.e.,the modification cost is fixed in a given interval and depends on the modification out of the given interval.We present a combinatorial algorithm which can be finished in O(nm)to solve it due to the minimum cut of the residual network.展开更多
Given a generalized minimum cost flow problem,the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem.In this paper,we c...Given a generalized minimum cost flow problem,the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem.In this paper,we consider both types of the weighted Hamming distances for measuring the adjustment.In the sum-type case,it is shown that the inverse problem is APX-hard.In the bottleneck-type case,we present a polynomial time algorithm.展开更多
In the optimization of train diagrams, selecting the arrival and departure paths of the through gains has a great impact on the dwell time at district stations. In this paper, on the basis of train paths and the throu...In the optimization of train diagrams, selecting the arrival and departure paths of the through gains has a great impact on the dwell time at district stations. In this paper, on the basis of train paths and the through train connection time standard at district stations, we built a mathematical model aiming at minimizing dwell time of through trains at two adjacent district stations, and then converted this into a network flow model to which is added a source and a sink node. Then, we propose a new algorithm for solving the network flow model based on the minimum-cost flow algorithm. A case study for through trains from the Guiyang South Railway Station to the Chongqing West Railway Station shows that the algorithm is reliable and efficient for solving the problem of through train connections, and there is a reduction in the total dwell time that the through trains spend at two adjacent district stations.展开更多
文摘This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of minimum parametric cost flow problems with different objective functions. On each of the iterations, the flow is augmented along a cheapest path from the source node to the sink node in the time-space network avoiding the explicit time expansion of the network.
文摘The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all origins’ supply and all destinations’ demands as well as the expanding cost is minimum. Actually, MCCETLTPD is a balance transportation problem and a variant problem of minimum cost maximum flow problem. In this paper, by creating a mathematical model and constructing a network with lower and upper arc capacities, MCCETLTPD is transformed into searching feasible flow in the constructed network, and consequently, an algorithm MCCETLTPD-A is developed as MCCETLTPD’s solution method basing minimum cost maximum flow algorithm. Computational study validates that the MCCETLTPD-A algorithm is an efficient approach to solving the MCCETLTPD.
文摘Let C be a set of colors, and let ?be an integer cost assigned to a color c in C. An edge-coloring of a graph ?is assigning a color in C to each edge ?so that any two edges having end-vertex in common have different colors. The cost ?of an edge-coloring f of G is the sum of costs ?of colors ?assigned to all edges e in G. An edge-coloring f of G is optimal if ?is minimum among all edge-colorings of G. A cactus is a connected graph in which every block is either an edge or a cycle. In this paper, we give an algorithm to find an optimal edge- ??coloring of a cactus in polynomial time. In our best knowledge, this is the first polynomial-time algorithm to find an optimal edge-coloring of a cactus.
基金This research is supported by the Fundamental Research Funds for the Central Universities(No.20720190068)the China Scholarship Council(No.201706315073).
文摘The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal.The modification cost is measured by different norms,such asl1,l2,l∞norms and the Hamming distance,and the goal is to adjust the parameters as little as possible.In this paper,we consider the inverse maximum flow problem under the combination of the weighted l2 norm and the weighted Hamming distance,i.e.,the modification cost is fixed in a given interval and depends on the modification out of the given interval.We present a combinatorial algorithm which can be finished in O(nm)to solve it due to the minimum cut of the residual network.
文摘Given a generalized minimum cost flow problem,the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem.In this paper,we consider both types of the weighted Hamming distances for measuring the adjustment.In the sum-type case,it is shown that the inverse problem is APX-hard.In the bottleneck-type case,we present a polynomial time algorithm.
文摘In the optimization of train diagrams, selecting the arrival and departure paths of the through gains has a great impact on the dwell time at district stations. In this paper, on the basis of train paths and the through train connection time standard at district stations, we built a mathematical model aiming at minimizing dwell time of through trains at two adjacent district stations, and then converted this into a network flow model to which is added a source and a sink node. Then, we propose a new algorithm for solving the network flow model based on the minimum-cost flow algorithm. A case study for through trains from the Guiyang South Railway Station to the Chongqing West Railway Station shows that the algorithm is reliable and efficient for solving the problem of through train connections, and there is a reduction in the total dwell time that the through trains spend at two adjacent district stations.
