Abstract
The maximum flow problem is a type of network optimization problem in the flow graph theory. Many important applications used the maximum flow problem and thus it has been studied by many researchers using different methods. Ford Fulkerson algorithm is the most popular algorithm that used to solve the maximum flow problem, but its complexity is high. In this paper, a parallel Genetic algorithm is applied to find a maximum flow in a weighted directed graph, by finding the objective function value for each augmenting path from the source to the sink simultaneously in the parallel steps in every iteration. The algorithm is implemented using Message Passing Interface (MPI) library, and results are conducted from a real distributed system IMAN1 supercomputer and were compared with a sequential version of Genetic-Maxflow. The simulation results show this parallel algorithm speedup the running time by achieving up to 50% parallel efficiency.
Highlights
A flow network is a directed graph where each edge has a capacity and receives a flow
Language can measure the time with seconds only, we could not catch the enhancement in the running time when the number of nodes equals 5000 to 9000, the implementation gave an equal running time for 2 and 4 processors which could be less than the measured one if the estimated time was in millisecond
Another important result could be noticed from Table 2. It shows that using more processors in parallel to solve maximum flow problem using Genetic algorithm (GA) could not give a better enhancement
Summary
Abstract—The maximum flow problem is a type of network optimization problem in the flow graph theory. Many important applications used the maximum flow problem and it has been studied by many researchers using different methods. Fulkerson algorithm is the most popular algorithm that used to solve the maximum flow problem, but its complexity is high. A parallel Genetic algorithm is applied to find a maximum flow in a weighted directed graph, by finding the objective function value for each augmenting path from the source to the sink simultaneously in the parallel steps in every iteration. Interface (MPI) library, and results are conducted from a real distributed system IMAN1 supercomputer and were compared with a sequential version of Genetic-Maxflow. The simulation results show this parallel algorithm speedup the running time by achieving up to 50% parallel efficiency
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