Searching Randomly for Maximum Matchings

Many real-world optimization problems in, e. g., engineering or biology have the property that not much is known about the function to be optimized. This excludes the application of problem-specific algorithms. Simple randomized search heuristics are then used with surprisingly good results. In order to understand the working principles behind such heuristics, they are analyzed on combinatorial optimization problems whose structure is well-studied. The idea is to investigate when it is possible to “simulate randomly” clever optimization techniques and when this random search fails. The main purpose is to develop methods for the analysis of general randomized search heuristics. The maximum matching problem is well suited for this approach since long augmenting paths do not allow local improvements and since our results on randomized local search and simple evolutionary algorithms can be compared with published results on the Metropolis algorithm and simulated annealing.