Integer Programming: Cutting Plane Algorithms

2012 ◽  
Keyword(s):  
Integer Programming ◽  
Cutting Plane ◽  
Cutting Plane Algorithms

scholarly journals Benders decomposition with adaptive oracles for large scale optimization

2020 ◽  
Author(s):  
Nicolò Mazzi ◽  
Andreas Grothey ◽  
Ken McKinnon ◽  
Nagisa Sugishita
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Optimization Problems ◽  
Cutting Plane ◽  
Computational Effort ◽  
Planning Problem ◽  
Illustrative Case ◽  
Investment Planning ◽  
Cutting Plane Algorithms ◽  
Inexact Information

AbstractThis paper proposes an algorithm to efficiently solve large optimization problems which exhibit a column bounded block-diagonal structure, where subproblems differ in right-hand side and cost coefficients. Similar problems are often tackled using cutting-plane algorithms, which allow for an iterative and decomposed solution of the problem. When solving subproblems is computationally expensive and the set of subproblems is large, cutting-plane algorithms may slow down severely. In this context we propose two novel adaptive oracles that yield inexact information, potentially much faster than solving the subproblem. The first adaptive oracle is used to generate inexact but valid cutting planes, and the second adaptive oracle gives a valid upper bound of the true optimal objective. These two oracles progressively “adapt” towards the true exact oracle if provided with an increasing number of exact solutions, stored throughout the iterations. These adaptive oracles are embedded within a Benders-type algorithm able to handle inexact information. We compare the Benders with adaptive oracles against a standard Benders algorithm on a stochastic investment planning problem. The proposed algorithm shows the capability to substantially reduce the computational effort to obtain an $$\epsilon $$ ϵ -optimal solution: an illustrative case is 31.9 times faster for a $$1.00\%$$ 1.00 % convergence tolerance and 15.4 times faster for a $$0.01\%$$ 0.01 % tolerance.

scholarly journals Volumetric Barrier Cutting Plane Algorithms for Stochastic Linear Semi-Infinite Optimization

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 4995-5008 ◽  
Author(s):  
Baha Alzalg ◽  
Asma Gafour ◽  
Lewa Alzaleq
Keyword(s):  
Cutting Plane ◽  
Cutting Plane Algorithms

A Surrogate cutting plane algorithm for all-integer programming

1985 ◽  
Vol 12 (3) ◽  
pp. 241-250 ◽  
Author(s):  
Larry M. Austin ◽  
Parviz Ghandforoush
Keyword(s):  
Integer Programming ◽  
Cutting Plane ◽  
Cutting Plane Algorithm
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