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Ho, Intermetallic Compounds of Al and Transitions Metals: Effect of Electromigration in 1 2 mm Wide Lines, J Appl Phys, vol 49, no 7, p 4083, July 1978 28 S S Iyer and C Y Ting, Electromigration study of the Al-Cu/Ti/Al-Cu Systems, Proc 1984 Int Reliability Physics Symp, Apr 1984 29 J P Tardy and K N Tu, Interdiffusion and Marker Analysis in Aluminum Titanium Thin Film Bilayers, in Proceedings of the Electronic Materials Conference, T C Harman, Ed, Metallurgical Society of AIME, June 1984, p 12..

The units of the marginal cost curve are dollars per MWH. Both X and Y are quantities of energy in MWH. For those familiar with calculus, the marginal cost curve is the derivative of the cost curve. In our context, Y is small: Y = 1 MWH. An interpretation of the marginal cost curve is that it is the cost of producing one additional MWH of power beyond X MWH. Components that make up the costs of the marginal cost curve include fuel and VOM. Fuel is the predominant component. The fuel component of the marginal cost curve is the incremental heat rate multiplied by the fuel price. In this example we assume the following cost curves for Venus I, C1(X), and Venus II, C2(X): C1(X) = .000001X3 .0033X2 + 40X + 10,000 C2(X) = .0000004X3 .0012X2 + 38X + 8000 450 X 1200 400 X 1100

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11 LISTING ALL INSTANCES OF A COMBINATORIAL OBJECT The design of algorithms to generate combinatorial objects has long fascinated mathematicians and computer scientists Some of the earliest papers on the interplay between mathematics and computer science are devoted to combinatorial algorithms Because of its many applications in science and engineering, the subject continues to receive much attention In general, a list of all combinatorial objects of a given type might be used to search for a counterexample to some conjecture, or to test and analyze an algorithm for its correctness or computational complexity This branch of computer science can be de ned as follows: Given a combinatorial object, design an ef cient algorithm for generating all instances of that object For example, an algorithm may be sought to generate all n-permutations Other combinatorial objects include combinations, derangements, partitions, variations, trees, and so on.

In ( + ) EAs, the perturbation (or mutation) operator largely determines the search capabilities of the algorithm. The mutation mechanisms proposed are based on modifying the channels allocated to a number of transceivers. Therefore, two steps must be performed: 1. Selection of the transceivers. The perturbation has rst to determine the set of transceivers to be modi ed. 2. Selection of channels. Once a list of TRXs have been chosen, a new channel allocation must be performed. 9.3.5.1 Strategies for Selecting Transceivers This is the rst decision to be made in the perturbation process. It is a major decision because it determines how explorative the perturbation is; that is, how different the resulting plan is from its original solution. Several strategies have been developed, which consist of reallocating channels on neighborhoods of TRXs. These neighborhoods are de ned based on the topological information of the network:

When analyzing the ef ciency of an algorithm, we distinguish between the cost of generating and cost of listing all instances of a combinatorial object By generating we mean producing all instances of a combinatorial object, without actually outputting them Some properties of objects can be tested dynamically, without the need to check each element of a new instance In case of listing, the output of each object is required The lower bound for producing all instances of a combinatorial object depends on whether generating or listing is required In the case of generating, the time required to create the instances of an object, without actually producing the elements of each instance as output, is counted Thus, for example, an optimal sequential algorithm in this sense would generate all n-permutations in (n!) time, that is, time linear in the number of instances.

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In the case of listing, the time to actually output each instance in full is counted For instance, an optimal sequential algorithm generates all n-permutations in (nn!) time, since it takes (n) time to produce a string..

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