An Improved Augmented $\varepsilon$ -Constraint and Branch-and-Cut Method to Solve the TSP With Profits

In this paper, a novel approach is presented to solve the traveling salesman problem with profits (TSPP). This problem is an extension of the famous traveling salesman problem (TSP) in which a prize is associated with each vertex. The aim here is to find a route that simultaneously minimizes the tour length and maximizes the collected prize. A new method, AUGMECON2-BC, was developed incorporating an improved version of the augmented ε-constraint and a Branch and Cut algorithm. This method transforms a multi-objective problem into a mono-objective problem by optimizing one of the objective functions and converting the others into constraints. The Branch and Cut algorithm is then proposed to solve the generated subproblems. Computational results are taken on TSP Library instances. The performance of this approach is slightly better than what is already found from previous works and it is able to produce the exact Pareto front for the TSPP.