Fast parallel simulated annealing for traveling salesman problem

The authors present a fast parallel simulated annealing (SA) algorithm for solving the traveling salesman problem (TSP) on single instruction stream, multiple data stream (SIMD) machines with linear interconnections among processing elements. The whole simulated annealing algorithm has been sped up by implementing the move operation in parallel. A generation scheme which can be efficiently adapted to parallel implementation and achieve the balanced permutation has been designed. 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 1 b of information on acceptance decision to all the other PEs (processing elements) on a linear class computer with the same number of PEs as that of cities. Therefore, if the control unit has the capability of broadcasting 1 b in one PE to all the other PEs, as is often the case with the SIMD machine, the time complexity of the whole SA algorithm can be reduced to the order of the number of the moves.