A sequential simplex algorithm for the continuous convex piecewise linear network flow problem*

2019 ◽  
Author(s):  
Zhibin Nie ◽  
Shuning Wang
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Piecewise Linear ◽  
Simplex Algorithm ◽  
Linear Network ◽  
Network Flow Problem

scholarly journals A polynomial local optimality condition for the concave piecewise linear network flow problem

2021 ◽  
Vol 6 (3) ◽  
pp. 2094-2113
Author(s):  
Zhibin Nie ◽  
◽  
Shuning Wang ◽  
Xiaolin Huang ◽  
Keyword(s):  
Optimality Condition ◽  
Network Flow ◽  
Flow Problem ◽  
Piecewise Linear ◽  
Local Optimality ◽  
Linear Network ◽  
Network Flow Problem

scholarly journals A dual exterior point simplex type algorithm for the minimum cost network flow problem

2009 ◽  
Vol 19 (1) ◽  
pp. 157-170 ◽  
Author(s):  
George Geranis ◽  
Konstantinos Paparizzos ◽  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Feasible Solution ◽  
Flow Problem ◽  
Minimum Cost ◽  
Simplex Algorithm ◽  
Network Flow Problem ◽  
Basic Point ◽  
Type Algorithm ◽  
Dual Simplex ◽  
Minimum Cost Network Flow

A new dual simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs to a special 'exterior- point simplex type' category. Similarly to the classical network dual simplex algorithm (NDSA), this algorithm starts with a dual feasible tree-solution and reduces the primal infeasibility, iteration by iteration. However, contrary to the NDSA, the new algorithm does not always maintain a dual feasible solution. Instead, the new algorithm might reach a basic point (tree-solution) outside the dual feasible area (exterior point - dual infeasible tree).

A Combined Matheuristic for the Piecewise Linear Multicommodity Network Flow Problem

2017 ◽  
Vol 34 (06) ◽  
pp. 1750033 ◽  
Author(s):  
Naoto Katayama
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Piecewise Linear ◽  
Production Lines ◽  
Network Flow Problem ◽  
Multiple Resources ◽  
Network Problems ◽  
Local Branch ◽  
Multicommodity Network Flow ◽  
Communication Lines

Multicommodity network problems appear in numerous applications, such as telecommunications, logistics, transportation, distribution and production planning networks. The piecewise linear multicommodity network flow problem is a multicommodity network flow problem with piecewise linear costs corresponding to multiple resources, such as communication lines, vehicles and production lines. In the present paper, for the piecewise linear multicommodity network continuous flow problem, we present a path-based formulation and an arc-based formulation, and develop a combined matheuristic approach, which combines capacity scaling, a column and row generation technique, restricted branch-and-bound and a local branch method.

Sign in / Sign up

Export Citation Format

Share Document