Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Multicommodity network flows: the impact of formulation on decomposition
Mathematical Programming: Series A and B
Minimum cost capacity installation for multicommodity network flows
Mathematical Programming: Series A and B - Special issue on computational integer programming
On complexity, representation and approximation of integral multicommodity flows
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
A polyhedral approach to an integer multicommodity flow problem
Discrete Applied Mathematics
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
Metaheuristics for optimization problems in computer communications
Computer Communications
Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems
INFORMS Journal on Computing
On heuristics as a fundamental constituent of soft computing
Fuzzy Sets and Systems
Optimal multicast multichannel routing in computer networks
Computer Communications
A genetic algorithm for solving virtual source placement problem on WDM networks
Computer Communications
Algorithms of discrete optimization and their application to problems with fuzzy coefficients
Information Sciences: an International Journal
Genetic design of feature spaces for pattern classifiers
Artificial Intelligence in Medicine
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This paper treats with integral multi-commodity flow through a network. To enhance the Quality of Service (QoS) for channels, it is necessary to minimize delay and congestion. Decreasing the end-to-end delay and consumption of bandwidth across channels are dependent and may be considered in very complex mathematical equations. To capture with this problem, a multi-commodity flow model is introduced whose targets are minimizing delay and congestion in one model. The flow through the network such as packets, also needs to get integral values. A model covering these concepts, is NP-hard while it is very important to find transmission strategies in real-time. For this aim, we extend a cooperative algorithm including traditional mathematical programming such as path enumeration and a meta-heuristic algorithm such as genetic algorithm. To find integral solution satisfying demands of nodes, we generalize a hybrid genetic algorithm to assign the integral commodities where they are needed. In this hybrid algorithm, we use feasible encoding and try to keep feasibility of chromosomes over iterations. By considering some random networks, we show that the proposed algorithm yields reasonable results in a few number of iterations. Also, because this algorithm can be applied in a wide range of objective functions in terms of delay and congestion, it is possible to find some routs for each commodity with high QoS. Due to these outcomes, the presented model and algorithm can be utilized in a variety of application in computer networks and transportation systems to decrease the congestion and increase the usage of channels.