Abstract
Maximum Flow Problem (MFP) is considered as one of several famous problems in directed graphs. Many researchers studied MFP and its applications to solve problems using different techniques. One of the most popular algorithms that are employed to solve MFP is Ford-Fulkerson algorithm. However, this algorithm has long run time when it comes to application with large data size. For this reason, this study presents a parallel whale optimization (PWO) algorithm to get maximum flow in a weighted directed graph. The PWO algorithm is implemented and tested on datasets with different sizes. The PWO algorithm achieved up to 3.79 speedup on a machine with 4 processors.
Highlights
In this study, a parallel algorithm for solving the maximum flow problem (MFP) based on a meta-heuristic approach called a whale optimization algorithm (WOA) by (Mirjalili & Lewis, 2016) is proposed
It has come to the attention of many researchers that the Maximum Flow Problem (MFP) involves quite a wide range of concerns all which need to be studied in different ways (Ford & Fulkerson, 1956, McHugh, 1990)
Matlab R2016a software with Parallel Toolbox was employed in order to evaluate the performance of Parallel-Whale Optimization Algorithm (WOA) for solving MF problem
Summary
A parallel algorithm for solving the maximum flow problem (MFP) based on a meta-heuristic approach called a whale optimization algorithm (WOA) by (Mirjalili & Lewis, 2016) is proposed. The main issue is to get the optimal solution for a specific directed graph wherever every edge has a capacity According to these restrictions, the aim is to find the maximum aggregate flow that directed to the sink (Goldberg & Tarjan, 1988). By assuming that the graph is the search space and that the whales are looking to get the prey, the WOA solves MFP In this setting, the sink in the network indicates to the prey and the vertices represent the whales.
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