Statistical analysis of control parameters in evolutionary map L-systems-based topology optimization

Abstract

Map L-systems-based parametrization, also referred to as the cellular division method, is a generative encoding, suitable for topology optimization. The parametrization is compact due to its ability to reuse its elements, and therefore capable of covering a large design space with relatively few design variables. Map L-systems are often evolved using genetic algorithms (GAs). A key implementation detail of such procedures, as with most GA-based geometry searches, is the choice of parameters controlling the operation of the evolutionary process. The optimal choice of these in conventional optimization formulations is highly problem-specific -- far less so, however, when the GA evolves an L-systems encoding and does not act directly on the geometry. This is because the L-system encoding is, itself, independent of the geometry. We study the effects of different control parameters by conducting a statistical test of over 400 parameter combinations on five test cases, for which the global optima are known. The best-performing parameter combinations are reported as a Pareto front of the average number of objective function evaluations and ranking based on the average of optimized fitnesses. Finally, three Pareto-optimal parameter combinations are selected and applied to an optimization problem of maximizing the fundamental natural frequency of an integrally stiffened aluminum panel. The best of the resulting designs has a higher fundamental natural frequency than the baseline design by a margin of 11.2%.

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Identifiers

ORCID for Teemu, Johannes Ikonen: orcid.org/0000-0001-7413-9310

ORCID for Andras Sobester: orcid.org/0000-0002-8997-4375

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