Parallel algorithm for traveling salesman problem on SIMD machines using simulated annealing

The authors present a fast parallel simulated annealing algorithm for solving the traveling salesman problem (TSP) on single-instruction multiple-data (SIMD) machines with linear interconnections among processing elements. In the algorithm for TSP, it is shown that with the proper data distribution and movement schemes, the generation of a new configuration and the calculation of energy difference can be done in constant time, and the whole time complexity of the move operation is proportional to the time taken to broadcast one bit information on an acceptance decision to all the other processing elements (PEs) on a linear class computer with the same number of PEs as of cities. Therefore, if a control unit has the broadcasting capability, as is often the case with the SIMD machine, the move operation can be done in constant time and the whole simulated annealing algorithm has a time complexity only proportional to the number of moves.