The multiobjective vending problem: a generalization of the travelling salesman problem

A generalization of the travelling salesman problem is introduced. Each node has an associated reward, and a penalty is incurred by travelling between nodes. In the multiobjective vending problem, the subset of nodes and associated tour which will minimize penalty and maximize reward is sought. The problem is placed within the context of multi-objective programming. A heuristic is proposed and evaluated, and it is found to give satisfactory performance when applied to a problem with twenty-five nodes. Further generalizations are suggested.