Review of Network Flow Algorithms David P. Williamson

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

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Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽

10.3390/math9151716 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1716

Author(s):

Adrian Marius Deaconu ◽

Delia Spridon

Keyword(s):

Network Flow ◽

Large Scale ◽

Random Network ◽

Minimum Cost ◽

Maximum Flow ◽

Network Flow Problems ◽

Commodity Flow ◽

Vast Number ◽

Flow Problems ◽

Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

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Opposition-based learning Multi-Verse Optimizer with disruption operator for optimization problems

10.21203/rs.3.rs-277857/v1 ◽

2021 ◽

Author(s):

Mohammad Shehab ◽

Laith Abualigah

Keyword(s):

Real World ◽

Optimization Problems ◽

Second Stage ◽

Opposition Based Learning ◽

High Fitness ◽

Fitness Value ◽

Speed Up ◽

Disruption Operator ◽

The Given ◽

Real World Problems

Abstract Multi-Verse Optimizer (MVO) algorithm is one of the recent metaheuristic algorithms used to solve various problems in different fields. However, MVO suffers from a lack of diversity which may trapping of local minima, and premature convergence. This paper introduces two steps of improving the basic MVO algorithm. The first step using Opposition-based learning (OBL) in MVO, called OMVO. The OBL aids to speed up the searching and improving the learning technique for selecting a better generation of candidate solutions of basic MVO. The second stage, called OMVOD, combines the disturbance operator (DO) and OMVO to improve the consistency of the chosen solution by providing a chance to solve the given problem with a high fitness value and increase diversity. To test the performance of the proposed models, fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems, and seven CEC 2011 real-world problems were used in both phases of the enhancement. The second step, known as OMVOD, incorporates the disruption operator (DO) and OMVO to improve the accuracy of the chosen solution by giving a chance to solve the given problem with a high fitness value while also increasing variety. Fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems and seven CEC 2011 real-world problems were used in both phases of the upgrade to assess the accuracy of the proposed models.

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