Abstract
The availability of an LP routine where we can add constraints and reoptimize, makes it possible to adopt an integer programming approach to the travelling-salesman problem.
Starting with some of the constraints that define the problem we use either a branching process or a cutting planes routine to eliminate fractional solutions. We then test the resulting integer solution against feasibility and if necessary we generate the violated constraints and reoptimize until a “genuine” feasible solution is achieved.
Usually only a small number of the omitted constraints is generated.
The generality of the method and the modest solution times achieved leads us to believe that such an LP approach to other combinatorial problems deserves further consideration.
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Miliotis, P. Integer programming approaches to the travelling salesman problem. Mathematical Programming 10, 367–378 (1976). https://doi.org/10.1007/BF01580682
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DOI: https://doi.org/10.1007/BF01580682