Complex optimisation problems with many degrees of freedom are often characterised by the enormously large configuration space, typically O(eN) or O(N!). The idea of simulated annealing (SA) proposed by Kirkpatrick has been applied to the complex optimisation problems, which can be treated as annealing a statistical mechanical system from high temperature to low temperature; however, the SA is terribly slow for large problem sizes in typically O(N3lnN) time. We discover the hybrid algorithm (HA), which is based on a hybrid mechanism which combines conventional heuristics with low temperature simulated annealing (LTSA), which could be parallelised easily. The HA is a new approach of resolving optimisation problems with O(N) complexity where information propagation can be inhibited by restraining the range of searches in the configuration space. We use the HA to resolve several famous combinatorial optimisation problems, including the travelling salesman problem (TSP) of large sizes up to 1 000 000 cities within 3 to 5 percent of the optimal value in linear time and other nonuniformly distributed TSPs as well. We shall also discuss the applicability of the HA to the optimisation problems in general.
Relation:
Physica A: Statistical Mechanics and its Applications 205(1-3), pp.367-374
