Uma abordagem para avaliar o desempenho de algoritmos baseada em simulações automáticas de modelos de Petri coloridas hierárquicas

Abstract

Among the various approaches established for analyzing the performance of algorithms in terms of runtime, one can highlight as examples, the asymptotic analysis, recurrence techniques, and probabilistic analysis. However, there are algorithms that present certain peculiarities, which make the use of these purely mathematical performance evaluation techniques inadequate or excessively difficult. This is the case of algorithms for which the runtime varies significantly for the same input data, due to its execution dynamics. The same happens in the case of distributed algorithms, where depending on the complexity of the distribution policy being used, the evaluation by means of analytical methods concerning the effect of a gradual increase in processors on runtime can become impractical. In situations such as these, in order to avoid the high mathematical complexity involved in the performance analysis, researchers have adopted alternatives based on empirical methods or visual modeling. However, both alternatives have drawbacks: in the case of empirical methods, they require the implementation of analyzed algorithms, which has a perverse effect especially in the case of distributed algorithms. This occurs, as they demand the acquisition beforehand of expensive multiprocessing hardware resources before knowing if the distribution proposal under investigation is in fact viable. On the other hand, those approaches based on visual models currently under use (based on graphs, automata and Unified Modeling Language) one notes that does not contain the necessary dynamic resources for dealing with the runtime evaluation of algorithms. In this scenario, the present study proposes a formal visual approach, in order to evaluate the algorithm runtime based on automatic simulations of Hierarchical Colored Petri Net models in the CPN Tools graphic environment. The proposed approach is validated through the calculation of the following parameters associated with the algorithms being used as a case study: the complexity function, real runtime, and in the case of distributed algorithms, speedup and efficiency. The cases studies were based on three relevant search algorithms used in the agents of the Artificial Intelligence, with the aim of defining the most appropriate actions that these agents need to execute in order to fulfil their objective, in an environment where the opponent tries to minimize their chances of success. The algorithms under consideration were the serial algorithms Minimax and Alpha-Beta; and the PVS distributed algorithm. The obtained results confirm the correction of the proposed approach.