Eine neue Methodik zur Erhöhung der Leistungsfähigkeit evolutionärer Algorithmen durch die Integration lokaler Suchverfahren

Evolutionary Algorithms form a procedure upon the pattern of the principals of biological evolution for improving solutions iteratively by means of heredity, selection and survival of the fittest. Their main area of application are complex optimization problems, for which no mathematical solutions or suitable heuristics exist or are too costly to develop. Examples for these tasks are design optimization problems, scheduling, resource optimization or sequencing problems. As the global searching Evolutionary Algorithm shows a poor convergence close to the optimum, nearly all successful real world applications use so called hybrids, where Evolutionary Algorithms are supported by, in most cases, problem-specific local searchers. This results in a considerable acceleration (frequently in the magnitude of factors) but turns the general applicable Evolutionary Algorithm into a domain specific tool. The goal of the work on hand is the creation of a generally applicable hybrid procedure, which combines the advantages of both classes of algorithms, i.e. the robustness and globality of the search on the one hand and the speediness on the other, while maintaining the generality and the convergence reliability. The new method consists of two elements: The usage of generally applicable local searchers instead of problem-specific ones and second, the development of a convergence-based control procedure for distributing the computational power between the basic algorithms involved. This procedure is based on new methods for calculating the genotypic difference between individuals and for determining established niches within a population. Great importance was attached to the applicability of the new method to all population based Evolutionary Algorithms. To verify the two goals of the preservation of the convergence reliability and the raise of the convergence velocity a test implementation was performed. The Evolutionary Algorithm GLEAM combining aspects of the Evolution Strategy and the real-coded Genetic Algorithms was chosen together with two approved derivation-free local search procedures, namely the Rosenbrock algorithm and the COMPLEX procedure. Five mathematical benchmark functions and three real world problems (design optimization, resource optimization in conjunction with scheduling and collision-free robot path planning) served as test cases. Four basic kinds of hybridization were investigated, pre-optimization of the initial population, post-optimization of the GLEAM results and (delayed) direct integration of the local search into the offspring production of the Evolutionary Algorithm. Based on combinations and modifications of these kinds and the two alternatively used local searchers this adds up to 13 hybrids. The experiments were based on 100 runs per hybrid and parameterization and for a success all runs had to accomplish the given target qualities. Summarizing the results it can be stated that the goal of improving the velocity was achieved: The most impressive speed-up was yielded by the resource optimization task and Fletcher’s function which needed about 90 and 100 times less evaluations on average than the average of best GLEAM run. The (delayed) direct integration turned out to be the best kind of hybridization. Unfortunately no common parameterization could be extracted from the experiments. For direct integration the Rosenbrock procedure worked always but the COMPLEX algorithm delivered better results in those cases were it worked at all. The text concludes with a recommendation for practical applications of the results and with a new concept for an adaptive direct integration to overcome the parameterization problems. Inhaltsverzeichnis i