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however, is focused on concepts and models that are relevant for current GSM frequency planning and not on simpli ed models of the abstract problem In GSM, a network operator has usually a small number of frequencies (few dozens) available to satisfy the demand of several thousands of TRXs A reuse of these frequencies is therefore unavoidable However, reusing frequencies is limited by interferences that could lead the quality of service (QoS) for subscribers to be reduced down to unsatisfactory levels The automatic generation of frequency plans in real GSM networks [5] is a very important task for present GSM operators not only in the initial deployment of the system, but also in the subsequent expansions or modi cations of the network, solving unpredicted interference reports, and/or handling anticipated scenarios (eg, an expected increase in the traf c demand in some areas).

This optimization problem is a generalization of the graph coloring problem, and thus it is an NP-hard problem [10] As a consequence, using exact algorithms to solve real-sized instances of AFP problems is not practical, and therefore other approaches are required Many different methods have been proposed in the literature [1], and among them, metaheuristic algorithms have proved to be particularly effective Metaheuristics [3,8] are stochastic algorithms that sacri ce the guarantee of nding optimal solutions for the sake of (hopefully) getting accurate (also optimal) ones in a reasonable time This fact is even more important in commercial tools, in which the GSM operator cannot wait very long times for a frequency plan (eg, several weeks) Among the existing metaheuristic techniques, evolutionary algorithms (EAs) [2] have been widely used [6] EAs work iteratively on a population of individuals.

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Open a browser and enter the following URL: http://localhost:8080/ Figure C-5 shows what you should see on your screen.

Every individual is the encoded version of a tentative solution to which a tness value is assigned indicating its suitability to the problem The canonical algorithm applies stochastic operators such as selection, crossover (merging two or more parents to yield one or more offsprings), and mutation (random alterations of the problem variables) on an initial population in order to compute a whole generation of new individuals However, it has been reported in the literature that crossover operators do not work properly for this problem [4,17] In this scenario, our algorithmic proposal is a fast and accurate (1 + 10) EA (see the work by Schwefel [16] for details on this notation) in which recombination of individuals is not performed The main contributions of this chapter are the following: We have developed and analyzed a new (1 + 10) EA.

as C1 (S) = area(S) . area(CH(S))

Several seeding methods as well as several mutation operators have been proposed The evaluation of the algorithm has been performed by using a real-world instance provided by Optimi CorpTM This is a currently operating GSM network in which we are using real traf c data, accurate models for all the system components (signal propagation, TRX, locations, etc), and actual technologies such as frequency hopping This evaluation of the tentative frequency plans is carried out with a powerful commercial simulator that enables users to simulate and analyze those plans prior to implementation in a real environment Results show that this simple algorithm is able to compute accurate frequency plans, which can be directly deployed in a real GSM network..

Step 1. Initialize the weights and threshold as small random numbers. Step 2. Input the training vector [x1, x2, . . ., xn]T and evaluate the output of the neuron. Step 3. Adjust the weights with equation (B.4) as y wj t 1 wj t l ^ y xj B:4

ditional on the present value of the portfolio loss value being equal to some target portfolio capital amount. In PM v. 2.0, there are two methods to calculate this: one where loss is in excess of expected loss (EL) and one where loss is in excess of total spread (TS). In general, the weighted sum of the tail risk contributions will equal the portfolio capital. In its implementation of tail risk contribution, Portfolio Manager v. 2.0 requires the user to specify a capital interval upon which to perform the calculations. If we de ne CLB to be the lower bound and CUB to be the upper bound of this interval, then the tail risk contribution is given by V V LP C P H C LB < < C UB = E LP H V0 (1 + rH )H V0 (1 + rH )

can apply Markov s inequality to estimate the probability that Zj 1, obtaining Pr[Zj 1] F0 E[Zj ] = j, 1 2 (8.2)

typedef struct tagDISPPARAMS { [size_is(cArgs)] VARIANTARG *rgvarg; //Array of arguments [size_is(cNamedArgs)] DISPID *rgdispidNamedArgs; //arg dispIDs unsigned int cArgs; //Number of total arguments unsigned int cNamedArgs; //Number of named arguments } DISPPARAMS; interface IDispatch : IUnknown { ... HRESULT GetIDsOfNames([in] REFIID riid, //reserved

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