# Primal cutting plane algorithms revisited

@article{Letchford2002PrimalCP, title={Primal cutting plane algorithms revisited}, author={Adam N. Letchford and Andrea Lodi}, journal={Mathematical Methods of Operations Research}, year={2002}, volume={56}, pages={67-81} }

Abstract.Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research…

## 31 Citations

Primal Cutting Plane Methods for the Traveling Salesman Problem

- Business
- 2017

Most serious attempts at solving the traveling salesman problem (TSP) are based on the dual fractional cutting plane approach, which moves from one lower bound to the next. This thesis describes…

Integral Simplex Using Decomposition with Primal Cuts

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It is shown that MRA canonically induces a decomposition of the augmentation problem and deepens the understanding of ISUD, and characterize cuts that adapt to this decomposition and relate them to primal cuts.

A Primal Branch-and-Cut Algorithm for the Degree-Constrained Minimum Spanning Tree Problem

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A primal branch-and-cut algorithm that solves instances of the degree-constrained minimum spanning tree problem to optimality and turns out to be competitive with other methods known in the literature.

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A possible implementation of a finite ABC algorithm that differs from standard branch-and-cut in several important ways, including the terms separation, branching, and fathoming take on new meanings in the primal context.

Primal separation algorithms

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The complexity of primal separation for several well-known classes of inequalities for various important combinatorial optimization problems, including the knapsack, stable set and travelling salesman problems are examined.

Integral Column Generation for Set Partitioning Problems with Side Constraints

- Computer ScienceINFORMS Journal on Computing
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A new integral column generation algorithm that can solve efficiently large-scale set partitioning problems with side constraints is developed and the latter alter the quasi-integrality property needed for primal integral algorithms.

Integral simplex using double decomposition for set partitioning problems

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- 2019

Influence of the normalization constraint on the integral simplex using decomposition

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Integral simplex using double decomposition

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An integral simplex using double decomposition (ISU2D) is proposed, which uses an innovative disjoint vertical decomposition to find in parallel orthogonal descent directions leading to an integer solution with a larger improvement.

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