Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
Memetic algorithms: a short introduction
New ideas in optimization
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Optimization of Steiner Trees Using Genetic Algorithms
Proceedings of the 3rd International Conference on Genetic Algorithms
A Genetic Algorithm for the Rectilinear Steiner Problem
Proceedings of the 5th International Conference on Genetic Algorithms
Strong lower bounds for the prize collecting Steiner problem in graphs
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
A hybrid genetic algorithm and bacterial foraging approach for global optimization
Information Sciences: an International Journal
The prize collecting Steiner tree problem: models and Lagrangian dual optimization approaches
Computational Optimization and Applications
Computers and Industrial Engineering
A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs
Discrete Applied Mathematics
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We consider the version of prize collecting Steiner tree problem (PCSTP) where each node of a given weighted graph is associated with a prize and where the objective is to find a minimum weight tree spanning a subset of nodes and collecting a total prize not less that a given quota Q. We present a lower bound and a genetic algorithm for the PCSTP. The lower bound is based on a Lagrangian decomposition of a minimum spanning tree formulation of the problem. The volume algorithm is used to solve the Lagrangian dual. The genetic algorithm incorporates several enhancements. In particular, it fully exploits both primal and dual information produced by Lagrangian decomposition. The proposed lower and upper bounds are assessed through computational experiments on randomly generated instances with up to 500 nodes and 5000 edges. For these instances, the proposed lower and upper bounds exhibit consistently a tight gap: in 76% of the cases the gap is strictly less than 2%.