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Proceedings of GO 2005, pp. 47 – 52.Calibration of a Gravity–Opportunity Modelof Trip Distribution by a HybridProcedure of Global OptimizationEdson Tadeu Bez, 1 Mirian Buss Gonçalves, 2 and José Eduardo Souza de Cursi 31 Universidade do Vale do Itajaí - UNIVALI, São José, Brasil, edsonbez@univali.br2 Universidade Federal de Santa Catarina - UFSC, Florianópolis, Brasil, mirian@mtm.ufsc.br3 Laboratoire de Mécanique de Rouen (INSA - Rouen), Saint-Etienne du Rouvray, France, souza@insa-rouen.frAbstractKeywords:In this work, we present a hybrid global optimization method of evolutionary type. The procedureuses random perturbations of descent methods in the mutation step and generates the initialpopulation by using a Representation Formula of the global optimum. The method is applied toa relevant inverse problem: the calibration of a gravity–opportunity model for trip distribution intransportation theory.Global Optimization, Hybrid Methods, Gravity–Opportunity Model1. IntroductionTransportation planning is a field where the calibration of models is often used. In typicalsituations, the mathematical model to be used contains parameters to be determined fromempiric data by identification procedures. Generally, these procedures lead to non convexoptimization problems and robust numerical methods are needed in the calibration process.We consider in this work the calibration of a gravity–opportunity model which is derived byapplying the Maximum Likelihood Principle to the experimental data, such as, for instance,measurements of O-D (origin-destination) trips (see, for instance, [5]). Such a model leads tofunction exhibiting the typical behaviour shown in Figure 1. Previous works [3, 6, 7] properlyaddressed the numerical difficulties in the calibration procedure, which are essentially connected,on the one hand, to the nonconvexity and, on the other hand, to the wide sensibility ofthe objective function with respect to the parameters to be determined: large desequilibratedgradients are involved. We present here a hybrid global optimization procedure for solvingthe problem. The method has been tested on classical functions such as Rastringin’s one (Figure2) [4] and it is applied here to the calibration of a gravity–opportunity model from O-Dsources [5]. In this field, the standard procedures are difficulty to use, request high computationaleffort and uses optimization parameters specially defined for a given data set. Amongour objectives, we look for the definition of a calibration procedure less dependent on the dataset and saving computational cost.2. The Trip Distribution ModelBy limitation of the room, we do not give more detailed derivation of the model: the readerinterested in this aspect is invited to refer to [5]. Let us denote by T ij the number of trips going