Packing Steiner trees: a cutting plane algorithm and computational results

1996 ◽  
Vol 72 (2) ◽  
pp. 125-145 ◽  
Author(s):  
M. Grötschel ◽  
A. Martin ◽  
R. Weismantel
Keyword(s):  
Cutting Plane ◽  
Steiner Trees ◽  
Cutting Plane Algorithm ◽  
Computational Results

A Convex Cutting Plane Algorithm for Global Solution of Generalized Polynomial Optimal Design Models

1996 ◽  
Vol 118 (1) ◽  
pp. 82-88 ◽  
Author(s):  
Chihsiung Lo ◽  
P. Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Cutting Plane ◽  
Test Problems ◽  
Cutting Plane Algorithm ◽  
Computational Results ◽  
Design Models ◽  
Generalized Polynomial ◽  
Speed Reducer ◽  
Improved Performance ◽  
Search Approach

Global optimization algorithms for generalized polynomial design models using a global feasible search approach was discussed in a previous article. A new convex cutting plane algorithm (CONCUT) based on global feasible search and with improved performance is presented in this sequel article. Computational results of the CONCUT algorithm compared to one using linear cuts (LINCUT) are given for various test problems. A speed reducer design example illustrates the application of the algorithms.

scholarly journals A Strong Class of Lifted Valid Inequalities for the Shortest Path Problem in Digraphs with Negative Cost Cycles

2015 ◽  
Vol 7 (4) ◽  
pp. 162 ◽  
Author(s):  
Mamane Souleye Ibrahim
Keyword(s):  
Shortest Path ◽  
Valid Inequalities ◽  
Cutting Plane ◽  
Shortest Path Problem ◽  
Integer Solution ◽  
Linear Relaxation ◽  
Cutting Plane Algorithm ◽  
Computational Results

In this paper, we address a strong class of lifted valid inequalities for the shortest path problem in digraphs with possibly negative cost cycles. We call these lifted inequalities the $incident \ lifted \ valid \ inequalities$ ($ILI$) as they are based on the incident arcs of a given vertex.  The $ILI$ inequalities are close in spirit of the so-called \textit{simple lifted valid inequalities} ($SLI$) and $cocycle \ lifted \ valid \ inequalities$ ($CLI$) introduced in Ibrahim et al. (2015). However, as we will see the $ILI$ inequalities are stronger than the first ones in term of linear relaxation strengthening. Indeed, contrary to  $SLI$ and $CLI$ inequalities, consider the same instances, in a cutting plane algorithm, the computational results prove that the $ILI$ inequalities provide the optimal integer solution for all the considered instances within no more than three iterations except one case for which after the first strengthening iteration, there exists no generated inequality.

A Convex Cutting Plane Algorithm for Global Solution of Generalized Polynomial Optimal Design Models

1992 ◽  
Author(s):  
Chihsiung Lo ◽  
Panos Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Cutting Plane ◽  
Test Problems ◽  
Cutting Plane Algorithm ◽  
Computational Results ◽  
Design Models ◽  
Generalized Polynomial ◽  
Speed Reducer ◽  
Improved Performance ◽  
Search Approach

Abstract Global optimization algorithms for generalized polynomial design models using a global feasible search approach was discussed in a previous article. A new convex cutting plane algorithm (CONCUT) based on global feasible search and with improved performance is presented in this sequel article. Computational results of the CONCUT algorithm compared to one using linear cuts (LINCUT) are given for various test problems. Two design examples, a speed reducer and a corrugated bulkhead design, illustrate the application of the algorithms.

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