A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Improved solutions for the traveling purchaser problem
Computers and Operations Research
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A dynamic programming approach to sequencing problems
ACM '61 Proceedings of the 1961 16th ACM national meeting
A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem
Operations Research
Filtering Algorithms for the NValue Constraint
Constraints
The Optimal Diversity Management Problem
Operations Research
Models for a traveling purchaser problem with additional side-constraints
Computers and Operations Research
Improving the held and karp approach with constraint programming
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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We present a novel approach to the Traveling Purchaser Problem (TPP), based on constraint programming and Lagrangean relaxation. The TPP is a generalization of the Traveling Salesman Problem involved in many real-world applications. Given a set of markets providing products at different prices and a list of products to be purchased, the problem is to determine the route minimizing the sum of the traveling and purchasing costs. We propose in this paper an efficient approach when the number of markets visited in an optimal solution is low. We believe that the real-world applications of this problem often assume a bounded number of visits when they involve a physical routing. It is an actual requirement from our industrial partner which is developing a web application to help their customers' shopping planning. The approach is tested on academic benchmarks. It proves to be competitive with a state of the art branch-and-cut algorithm and can provide in some cases new optimal solutions for instances with up to 250 markets and 200 products.