A primal–dual simplex algorithm for bi-objective network flow problems

4OR ◽  
2008 ◽  
Vol 7 (3) ◽  
pp. 255-273 ◽  
Author(s):  
Augusto Eusébio ◽  
José Rui Figueira ◽  
Matthias Ehrgott
Keyword(s):  
Network Flow ◽  
Simplex Algorithm ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Primal Dual ◽  
Dual Simplex ◽  
Dual Simplex Algorithm

A Note on the Connection Between the Primal-Dual and the A* Algorithm

2010 ◽  
Vol 1 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Xugang Ye ◽  
Shih-Ping Han ◽  
Anhua Lin
Keyword(s):  
Network Flow ◽  
Feasible Solution ◽  
Weighted Graph ◽  
Dual Algorithm ◽  
Heuristic Function ◽  
Network Flow Problems ◽  
A Algorithm ◽  
Flow Problems ◽  
Primal Dual ◽  
Initial Feasible Solution

The primal-dual algorithm for linear programming is very effective for solving network flow problems. For the method to work, an initial feasible solution to the dual is required. In this article, we show that, for the shortest path problem in a positively weighted graph equipped with a consistent heuristic function, the primal-dual algorithm will become the well-known A* algorithm if a special initial feasible solution to the dual is chosen. We also show how the improvements of the dual objective are related to the A* iterations.

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