Authors:
Kamyar Khodamoradi
and
Ramesh Krishnamurti
Affiliation:
Simon Fraser University, Canada
Keyword(s):
Prize Collecting TSP, Linear Programming, Generalized Subtour Elimination Constraints, Primitive Comb Inequalities, Integrality Gap, Shrinking Heuristic.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Artificial Intelligence
;
e-Business
;
Enterprise Information Systems
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Linear Programming
;
Logistics
;
Methodologies and Technologies
;
Operational Research
;
Optimization
;
OR in Transportation
;
Pattern Recognition
;
Routing
;
Software Engineering
;
Symbolic Systems
Abstract:
The Prize Collecting Travelling Salesman Problem (PCTSP) is an important generalization of the famous Travelling Salesman Problem. It also arises as a sub problem in many variants of the Vehicle Routing Problem. In this paper, we provide efficient methods to solve the linear programming relaxation of the PCTSP. We provide efficient heuristics to obtain the Generalized Subtour Elimination Constraints (GSECs) for the PCTSP, and compare its performance with an optimal separation procedure. Furthermore, we show that a heuristic to separate the primitive comb inequalities for the TSP can be applied to separate the primitive comb inequalities introduced for the PCTSP. We evaluate the effectiveness of these inequalities in reducing the integrality gap for the PCTSP.