Otimização para simulação com Krigagem: uma aplicação em alocação de ambulâncias

Abstract

Metamodeling is a common subject in Optimization for Simulation literature. Its applicability is focused on the optimization of functions defined over simulators or simulation models, so that the evaluation of an unknown point requires considerable computational effort. The use of metamodels aims to estimate the actual value (simulated) even before the point is evaluated by the simulation model. However, most publications do not apply the method to models with real world complexity and size. This dissertation sought to apply Kriging to minimize the response time of the Serviço de Atendimento Móvel de Urgência (SAMU) of Belo Horizonte, while allocating ambulances throughout all city bases. Kriging is considered the state-of-art technique in metamodeling as it provides, in addition to the new point estimation, the level of prediction uncertainty (estimation variance), which is proportional to the covariance between samples of its training set. The optimization process followed the Efficient Global Optimization algorithm (EGO), which explores Kriging by using the performance criterion Expected Improvement (EI), and, in the stochastic case, it was used the Reinterpolation Procedure (RI). Also, a new estimation criterion, called KOIC, was proposed with the motivation of taking into account the whole response variable confidence interval. To allocate the ambulances, a Simulated Annealing heuristic has been specified in order to deal with the discrete variables of the model. Finally, RI and KOIC were compared and the best technique was used to obtain a curve that reflected the relationship between the minimum response time and the total number of ambulances allocated to the city, a very relevant information to health-care public systems managers and designers.