If you modify "If it's worse, discard the change, and swap again" to sometimes accepting "unfavorable" moves depending on a random number and a parameter that decreases during the simulation (usually called "temperature"), you have the simulated annealing algorithm, which has been applied to this problem. See for example,

• http://en.wikipedia.org/wiki/Simulated_annealing
• S. Kirkpatrick and C. D. Gelatt and M. P. Vecchi, Optimization by Simulated Annealing, Science, Vol 220, Number 4598, pages 671-680, 1983.
• V. Cerny, A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm. Journal of Optimization Theory and Applications, 45:41-51, 1985

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