Abstract
This study presents an algorithm for MaxFlow problem using Chemical Reaction Optimization algorithm (CRO). CRO is a recently established meta-heuristics algorithm for optimization, inspired by the nature of chemical reactions. The main concern is to find the best maximum flow value at which the flow can be shipped from the source node to the sink node in a flow network without violating any capacity constraints in which the flow of each edge remains within the upper bound value of the capacity. The proposed MaxFlow-CRO algorithm is presented, analyzed asymptotically and experimental test is conducted. Asymptotic runtime is derived theoretically. The algorithm is implemented using JAVA programming language. Results show a good performance with a complexity of O(I E2), for I iterations and E edges. The number of iterations I in the algorithm, is an important factor that will affect the results obtained. As number of iterations is increased, best possible max-Flow value is obtained.
Highlights
Imagine a material traveling without obstruction through a system from a source, where the material is produced, to a destination, where it is consumed
For initial max flow of the first parent generation, the run time complexity can be approximated by O(N E f), where N is the number of parent nodes, E is the number of edges in flow network and f is the maximum flow in the flow network graph
This study proposes a potential solution to maximum flow problem through using chemical reaction optimization algorithm
Summary
Imagine a material traveling without obstruction through a system from a source, where the material is produced, to a destination, where it is consumed. The maximum flow problem becomes one of the most well known problems for combinatorial optimization in the weighted directed graph [2]. This problem can be applied in many areas of applications such as networks, engineering, and transportations [2]. A potential solution to the maximum flow problem using a recent algorithm which is called "Chemical Reaction Optimization (CRO)" is investigated. The CRO was proposed by Lam et al in 2010, and was originally designed for solving combinatorial optimization problems. We proposed to use chemical reaction optimization algorithm to solve the maximum flow problem
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