Tight compact models and comparative analysis for the prize collecting Steiner tree problem

Authors:
Mohamed Haouari;Safa Bhar Layeb;Hanif D. Sherali
Affiliations:
Department of Industrial Engineering, Faculty of Engineering, Ozyegin University, Istanbul, Turkey and Princess Fatimah Alnijris Research Chair for AMT, College of Engineering, King Saud Universit ...;Department of Industrial Engineering, Ecole Nationale d'ingénieurs de Tunis, University of El Manar, Tunisia;Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, USA
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 21
Cited 0

A hierarchy of relaxation between the continuous and convex hull representations

SIAM Journal on Discrete Mathematics
A note on the prize collecting traveling salesman problem

Mathematical Programming: Series A and B
A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems

Discrete Applied Mathematics
The primal-dual method for approximation algorithms and its application to network design problems

Approximation algorithms for NP-hard problems
Integer Programming Formulation of Traveling Salesman Problems

Journal of the ACM (JACM)
The prize collecting Steiner tree problem: theory and practice

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The asymmetric travelling salesman problem: on generalizations of disaggregated Miller-Tucker-Zemlin contraints

Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
A comparison of Steiner tree relaxations

Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems

Operations Research
On Tightening the Relaxations of Miller-Tucker-Zemlin Formulations for Asymmetric Traveling Salesman Problems

Operations Research
Strong lower bounds for the prize collecting Steiner problem in graphs

Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
On extended formulations for the precedence constrained asymmetric traveling salesman problem

Networks
The prize-collecting generalized minimum spanning tree problem

Journal of Heuristics
The prize collecting Steiner tree problem: models and Lagrangian dual optimization approaches

Computational Optimization and Applications
Models and branch-and-cut algorithms for the Steiner tree problem with revenues, budget and hop constraints

Networks - Special Issue on Trees
A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem

Computers and Operations Research
Prize collecting Steiner trees with node degree dependent costs

Computers and Operations Research
A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints

Discrete Optimization
Algorithmic expedients for the Prize Collecting Steiner Tree Problem

Discrete Optimization
Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints

Operations Research Letters
New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints

Operations Research Letters

Quantified Score

Hi-index	0.04

Visualization

Abstract

We investigate a generalized version of the prize collecting Steiner tree problem (PCSTP), where each node of a given weighted graph is associated with a prize as well as a penalty cost. The problem is to find a tree spanning a subset of nodes that collects a total prize not less than a given quota Q, such that the sum of the weights of the edges in the tree plus the sum of the penalties of those nodes that are not covered by the tree is minimized. We formulate several compact mixed-integer programming models for the PCSTP and enhance them by appending valid inequalities, lifting constraints, or reformulating the model using the Reformulation-Linearization Technique (RLT). We also conduct a theoretical comparison of the relative strengths of the associated LP relaxations. Extensive results are presented using a large set of benchmark instances to compare the different formulations. In particular, a proposed hybrid compact formulation approach is shown to provide optimal or very near-optimal solutions for instances having up to 2500 nodes and 3125 edges.