Abstract
TSP (Traveling Salesman Problem) are widely applied to engineering problems, and they have been solved by using meta-heuristic methods, combinatorial search methods and the other methods. In this paper, we formulated the TSP as a MILP (Mixed Integer Linear Programming) and applied a method to solve TSP numerically by introducing nonconvex ADMM. The main idea of the proposed method is that the nonconvex integer constraints can be expressed as a set inclusion problem. To be more specific, the rows of the decision variables are being included in the set of the unit vectors, and the proximal mapping step in the ADMM procedures can easily handle the set inclusion problem by computing the projection onto the finite set of the unit vectors. The convergence of the proposed method is investigated by computing the primal residuals and the dual residuals. The performance of the proposed algorithm is verified via a series of numerical simulations of well-known TSP examples.
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