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(This ensures that no single elementary move may cause B1 or B2 to become the empty set) 2 B1 B2, and at least two elementary moves are needed to make B1 and B2 equal We then obviously have f (B) = f (m(B)) for all m M(B) In effect, if B occurs as an intermediate result of a TS search, the cost function f gives no hint how TS should proceed, for all possible transitions would appear equally valuable We have found that the situation described above, even though it appears to be a rather extreme case, actually arises very frequently Experiments have shown that given a problem instance of EPP, for many ensemble assignments B we have f (B) f (m(B)) for all elementary moves m M(B) and thus no achievable improvement in the cost function.

Furthermore, for many ensemble assignments B we even have f (B) = f (m(B)) for most elementary moves m M(B) and thus no change in the cost function at all This problem-specific phenomenon makes the cost function as is absolutely unsuitable for any kind of guidance of TS A way to overcome this dilemma is to develop an alternative system for evaluating the elementary moves m M(B) Such a system will rely on characteristic features of the problem at hand, but only those aspects will be considered that appear to be relevant for guiding TS into promising directions.

server: some users request several orders of magnitude more documents/data than do other users; accesses from wireless clients also reveal a similar property. Thus, service providers can consider designing different pricing plans that cater to the widely varying needs of different users. 5.4.2.2 Distribution of Wireless User Sessions To model the behavior of wireless users, it is important to understand how long users stay connected for Web browsing. We use the notion of a session to model such a sequence of interactions initiated by a user on his or her microbrowser (i.e., a browser on a cell phone or a PDA). A wireless service provider can utilize information about the number of sessions and length of sessions for effective pricing, capacity planning, and for providing service differentiation between users with different usage characteristics. A Web server administrator can classify users as short-session or long-session users and utilize this information for better load balancing (e.g., a uniform mix of long-session users and short-session users may result in fewer resource bottlenecks) and prefetching/caching strategies (e.g., cache or prefetch time-insensitive information for long-session users). Since it was not possible for us to instrument client microbrowsers for demarcating when a user sessions starts and ends, we approximate session times using a heuristic: if a user is idle for a suf ciently long time, called the session inactivity period, we say that the session has ended. We now describe our heuristic to determine the session inactivity period.

One of these characteristic features of EPP is that for any v, w V, v w, and any B Bv , C Bw, not only may we use the same frequency f (v, B) = f (w, C) in the case that vw E (which, in an analogous form, applies to virtually all kinds of frequency assignment problems), but also in the case that vw E but B = C Let us call this latter case the SFN property (SFN = single frequency network) Now, knowing from GFF, which takes exhaustive advantage of the SFN property by oversupplying vertices v V with services s S not explicitly required, that use of this property may lead to significant reduction in frequency demand, this gives us an idea how to proceed 1254 Heuristic Move Evaluation Before going into the details, let us give an overview of where we are heading.

We will introduce an equivalence relation and an order relation for the elementary moves.

1. L. F. Pau, Failure Diagnosis and Performance Monitoring. New York: Marcel Dekker, 1981. 2. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. New York; Plenum Press, 1981. 3. F. H ppner, F. Klawonn, R. Kruse, Fuzzy-Klusteranalyse. Verfahren f r die Bilderkennung, o u Klassi kation und Datenanalyse. Braunschweig: Vieweg, 1996. 4. F. Klawonn, R. Kruse, H. Timm, Fuzzy Shell Cluster Analysis, In Learning, Networks and Statistics (G. Della Riccia, H. J. Lenz, R. Kruse, eds.). Wien: Springer-Verlag, 1997, pp. 105 120. 5. C. G. Looney, A Fuzzy Clustering and Fuzzy Merging Algorithm, Technical Report, Computer Science Department, University of Nevada, Reno, NV, 1999. Available at http:// sherry.i .unizh.ch/looney99fuzzy.html. 6. C. G. Looney, A Fuzzy Classi er Network with Ellipsoidal Epanechnikovs, Technical Report, Computer Science Department, University of Nevada, Reno, NV, 2001. Available at http://sherry.i .unizh.ch/looney01fuzzy.html. 7. F. L. Chung, T. Lee, Fuzzy Competitive Learning, Neural Networks, Vol. 7, pp. 539 552, 1994. 8. D. C. Park, I. Dagher, Gradient Based Fuzzy C-Means (GBFCM) Algorithm, Proc. IEEE Int. Conf. on Neural Networks, 1984, pp. 1626 1631.

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