JUREMA , A NEW BRANCH & BOUND ANYTIME ALGORITHM FOR THE ASYMMETRIC TRAVELLING SALESMAN PROBLEM

In many different ways to solve combinatorial optimization problems, the Branch-and-Bound (BnB) method is one that performs implicit and complete enumeration of the solution space, and is one of the most popular methods because of its inherent optimality proof when in its termination. We show a new way to do Branch-and-Bound, evaluated to the Asymmetrical Traveling Salesman Problem (ATSP), called JUREMA. Jurema is an abundant tree from the Brazilian semi-arid, which topology in dry seasons looks like the BnB tree of the related method. The method Jurema showed to be of high performance for the very difficult ATSP instances, comparatively superior to traditional BnB-DFS commonly used for this propose. The method can be extended for other NP-Hard problems, once it can be combined with heuristic and metaheuristics with great success. Jurema is an Anytime BnB. We present the details of the method and the results for the difficult instances form the literature.

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