Genetic local search for multicast routing with pre-processing by logarithmic simulated annealing

Over the past few years, several local search algorithms have been proposed for various problems related to multicast routing in the off-line mode. We describe a population-based search algorithm for cost minimisation of multicast routing. The algorithm utilises the partially mixed crossover operation (PMX) under the elitist model: for each element of the current population, the local search is based upon the results of a landscape analysis that is executed only once in a pre-processing step; the best solution found so far is always part of the population. The aim of the landscape analysis is to estimate the depth of the deepest local minima in the landscape generated by the routing tasks and the objective function. The analysis employs simulated annealing with a logarithmic cooling schedule (logarithmic simulated annealing—LSA). The local search then performs alternating sequences of descending and ascending steps for each individual of the population, where the length of a sequence with uniform direction is controlled by the estimated value of the maximum depth of local minima. We present results from computational experiments on three different routing tasks, and we provide experimental evidence that our genetic local search procedure that combines LSA and PMX performs better than algorithms using either LSA or PMX only.