Evolutionary Algorithms, Randomized Local Search, and the Maximum Matching Problem

The design and analysis of problem-specific algorithms for combinatorial optimization problems is a well-studied subject. It is accepted that randomization is a powerful concept for theoretically and practically efficient problem-specific algorithms. Randomized search heuristics like randomized local search, tabu search, simulated annealing, and variants of evolutionary algorithms can be combined with problem-specific modules. The subject of this paper are general and not problem-specific search heuristics. Practitioners report surprisingly good results which they have obtained with such search heuristics. Nevertheless, one cannot doubt that problem-specific algorithms outperform general search heuristics – if they exist. So the area of applications of general search heuristics is limited to situations where good problem-specific algorithms are not known. This may happen if one quickly needs an algorithm for some subproblem in a large project and there are not enough resources (time, money, or experts) available to develop an efficient problem-specific algorithm. In many real-life applications, especially in engineering disciplines, there is no possibility to design a problem-specific algorithm. E.g., we may have the rough draft of a machine but we still have to choose between certain alternatives to obtain an explicit description of the machine. If we have m binary decisions to take, the search space (the space of all possible solutions) equals {0, 1}m. Then there exists a function f : {0, 1}m → R such that f(a) measures the quality of the machine if the vector of alternatives a = (a1, . . . , am) is chosen. However, often no closed form of f is known and we obtain f(a) only by an experiment (or its simulation).