GA kryžminimo operatoriaus modifikacija pamatų optimizavimo uždaviniams

Abstract

Šiame dokumente pateikiama klasikinio genetinio algoritmo modifikacija, kurioje individų atranka ir kryžminimas atliekamas pagal iš anksto nustatytas taisykles, taip atsisakant atsitiktinio individų kryžminimo. Kryžminimo taisyklė parinkta taip, kad kryžminimo metu visų geriausių individų genai būtų plačiai paskirstyti visoje populiacijoje. Taip pat atliekant kryžminimą bei atranką, naudojami ne tik naujausios kartos individai, bet ir dviejų ankstesnių kartų geriausių individų genai. Siūlomo metodo efektyvumas ištirtas sprendžiant realaus gyvenimo civilinės statybos globalios optimizacijos problemą: rostverko tipo pamatų optimizavimas. Ši problema yra geras rodiklis dėl to, kad minimali tikslo funkcijos reikšmė yra žinoma, todėl galima tiksliai įvertinti optimizavimo efektyvumą ir paklaidas.

Modified genetic algorithm with special phenotypes’ selection and crossover operators with default specified rules is proposed in this paper thus refusing the random crossover. The suggested crossover operator enables wide distribution of genes of the best phenotypes over the whole population. During selection and crossover, the best phenotypes of the newest population and additionally the genes of the best individuals of two previous populations are involved. The effectiveness of the modified algorithm is shown numerically on the real-life global optimization problem from civil engineering – the optimal pile placement problem under grillage-type foundations. This problem is a fair indicator for global optimization algorithms since the ideal solutions are known in advance but with unknown magnitudes of design parameters. Comparison of the proposed algorithm with 6 other stochastic optimization algorithms clearly reveals its advantages: at similar accuracy level the algorithm requires less time for tuning of genetic parameters and provides narrower confidence intervals on the results than other algorithms. In rather simple configurations of grillages where the optimal distribution of piles due to the geometry and given loadings is more or less even, the proposed method MCGA outperforms other popular stochastic optimization algorithms. Additionally, this algorithm requires less effort in tuning of algorithm parameters. The crossover and selection parameters are forecasted in advance by recursive crossover rules. Also the confidence intervals for results of MCGA are always narrower than those of BAcoor. Thus, the proposed method can be treated as a new global optimization algorithm that is simpler to use as the classical genetic algorithm but providing better or similar level of accuracy.