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48 Edson Tadeu Bez, Mirian Buss Gonçalves, and José Eduardo Souza de CursiFigure 1. Function defined by the Maximum Likelihood criteria ( [2]).Figure 2.Rastringin’s test function.from origin number i to destination number j, O i the number of departures from origin numberi, D j the number of arrivals at destination j, W ij a quantity measuring the opportunitiesfound between origin i and destination j, c ij a quantity connected to the cost of the trip fromorigin i to destination j. The gravity – opportunity model doubly restricted reads asT ij = A i O i B j D j e −(λW ij +βc ij ), i, j = 1, 2, ..., n. (1)Parameters A i , B j , λ, β are usually unknown and must be determined. Usually, the mainparameters are λ and β, since the coefficients A i and B j must verify nonlinear relations connectedto the equilibrium of the fluxes between destinations and origins. For given λ and β,A i and B j may be determined by solving the nonlinear equations establishing the equilibriumof the fluxes. One of the most popular methods for this determination is Furness balancingmethod, which will not be developed here.Let us assume that a set of measurements Tij ∗ is given. Then, we have (see, for instance, [5]):