A genetic algorithm for the multiple destination routing problems

The multiple destination routing (MDR) problem can be formulated as finding a minimal cost tree which contains designated source and multiple destination nodes so that certain constraints in a given communication network are satisfied. This is a typical NP-hard problem, and therefore only heur istic algorithms are of practical value. As a first step, a new genetic algorithm is developed to solve the MDR problems without constraints. It is based on the transformation of the underlying network of an MDR problem into its distance complete form, a natural chromosome representation of a minimal spanning tree (an individual), and a completely new computation of the fitness of individual. Compared with the known genetic algorithms and heuristic algorithms for the same problem, the proposed algorithm has several advantages. First, it guarantees convergence to an optimal solution with probability one. Second, not only are the resultant solutions all feasible, the solution quality is also much higher than that obtained by the other methods (indeed, in almost every case in our simulations, the algorithm can find the optimal solution of the problem). Third, the algorithm is of low computational complexity, and this can be decreased dramatically as the number of destination nodes in the problem increases. The simulation studies for the sparse and dense networks all demonstrate that the proposed algorithm is highly robust and very efficient in the sense of yielding high-quality solutions.