Using the primal-dual interior point algorithm within the branch-price-and-cut method

Authors:
Pedro Munari;Jacek Gondzio
Affiliations:
Instituto de Ciências Matemáticas e de Computação, University of São Paulo, Av. Trabalhador, São-carlense, 400 - Centro, Cx. Postal 668, CEP 13560-970, São Carlo ...;School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
Venue:
Computers and Operations Research
Year:
2013

Citing 30
Cited 0

A new polynomial-time algorithm for linear programming

Combinatorica
Algorithms for the vehicle routing and scheduling problems with time window constraints

Operations Research
Solving combinatorial optimization problems using Karmakar's algorithm

Mathematical Programming: Series A and B
Multiple centrality corrections in a primal-dual method for linear programming

Computational Optimization and Applications
Warm start of the primal-dual method applied in the cutting-plane scheme

Mathematical Programming: Series A and B
An Interior Point Algorithm for Minimum Sum-of-Squares Clustering

SIAM Journal on Scientific Computing
Generalized Bundle Methods

SIAM Journal on Optimization
Computational Experience with an Interior Point Cutting Plane Algorithm

SIAM Journal on Optimization
Warm-Start Strategies in Interior-Point Methods for Linear Programming

SIAM Journal on Optimization
Reoptimization With the Primal-Dual Interior Point Method

SIAM Journal on Optimization
2-Path Cuts for the Vehicle Routing Problem with Time Windows

Transportation Science
Exact Algorithm for Minimising the Number of Setups in the One-Dimensional Cutting Stock Problem

Operations Research
Optimal Integer Solutions to Industrial Cutting-Stock Problems: Part 2, Benchmark Results

INFORMS Journal on Computing
The integration of an interior-point cutting plane method within a branch-and-price algorithm

Mathematical Programming: Series A and B
An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems

Networks
Vehicle routing problem with elementary shortest path based column generation

Computers and Operations Research
Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms

Transportation Science
An exact primal---dual penalty method approach to warmstarting interior-point methods for linear programming

Computational Optimization and Applications
Comparison of bundle and classical column generation

Mathematical Programming: Series A and B
New dynamic programming algorithms for the resource constrained elementary shortest path problem

Networks
Implementation of warm-start strategies in interior-point methods for linear programming in fixed dimension

Computational Optimization and Applications
Further development of multiple centrality correctors for interior point methods

Computational Optimization and Applications
On the choice of explicit stabilizing terms in column generation

Discrete Applied Mathematics
Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows

Operations Research
Tabu Search, Partial Elementarity, and Generalized k-Path Inequalities for the Vehicle Routing Problem with Time Windows

Transportation Science
A New Unblocking Technique to Warmstart Interior Point Methods Based on Sensitivity Analysis

SIAM Journal on Optimization
A proximal trust-region algorithm for column generation stabilization

Computers and Operations Research
On Interior-Point Warmstarts for Linear and Combinatorial Optimization

SIAM Journal on Optimization
Cutting planes for branch-and-price algorithms

Networks
An improved column generation algorithm for minimum sum-of-squares clustering

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.01

Visualization

Abstract

Branch-price-and-cut has proven to be a powerful method for solving integer programming problems. It combines decomposition techniques with the generation of both columns and valid inequalities and relies on strong bounds to guide the search in the branch-and-bound tree. In this paper, we present how to improve the performance of a branch-price-and-cut method by using the primal-dual interior point algorithm. We discuss in detail how to deal with the challenges of using the interior point algorithm with the core components of the branch-price-and-cut method. The effort to overcome the difficulties pays off in a number of advantageous features offered by the new approach. We present the computational results of solving well-known instances of the vehicle routing problem with time windows, a challenging integer programming problem. The results indicate that the proposed approach delivers the best overall performance when compared with a similar branch-price-and-cut method which is based on the simplex algorithm.