Tối ưu hóa viễn thông và thích nghi Kỹ thuật Heuristic P1
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Tối ưu hóa viễn thông và thích nghi Kỹ thuật Heuristic P1
Optimization Issues in Telecommunications The complexity and size of modern telecommunications networks provide us with many challenges and opportunities. In this book, the challenges that we focus on are those which involve optimization. This simply refers to scenarios in which we are aiming to find something approaching the ‘best’ among many possible candidate solutions to a problem. For example, there are an intractably large number of ways to design the topology of a private data network for a large corporation....
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 Telecommunications Optimization: Heuristic and Adaptive Techniques. Edited by David W. Corne, Martin J. Oates, George D. Smith Copyright © 2000 John Wiley & Sons Ltd ISBNs: 0471988553 (Hardback); 047084163X (Electronic) 1 Heuristic and Adaptive Computation Techniques in Telecommunications: an Introduction David Corne, Martin Oates and George Smith 1.1 Optimization Issues in Telecommunications The complexity and size of modern telecommunications networks provide us with many challenges and opportunities. In this book, the challenges that we focus on are those which involve optimization. This simply refers to scenarios in which we are aiming to find something approaching the ‘best’ among many possible candidate solutions to a problem. For example, there are an intractably large number of ways to design the topology of a private data network for a large corporation. How can we find a particularly good design among all of these possibilities? Alternatively, we may be trying to find a good way to assign frequency channels to the many users of a mobile network. There are a host of complex constraints involved here, but it still remains that the number of possible candidate solutions which meet the main constraints is still too large for us to hope to examine each of them in turn. So, again, we need some way of finding good solutions among all of these possibilities. These challenges present opportunities for collaboration between telecommunications engineers, researchers and developers in the computer science and artificial intelligence Telecommunications Optimization: Heuristic and Adaptive Techniques, edited by D.W. Corne, M.J. Oates and G.D. Smith © 2000 John Wiley & Sons, Ltd
 2 Telecommunications Optimization: Heuristic and Adaptive Techniques communities. In particular, there is a suite of emerging software technologies specifically aimed at optimization problems which are currently underused in industry, but with great potential for profitable and effective solutions to many problems in telecommunications. Much of this book focuses on these optimization techniques, and the work reported in the forthcoming chapters represents a good portion of what is currently going on in terms of applying these techniques to telecommunicationsrelated problems. The techniques employed include socalled ‘local search’ methods such as simulated annealing (Aarts and Korst, 1989) and tabu search (Glover, 1989; 1989a), and ‘populationbased’ search techniques such as genetic algorithms (Holland, 1975; Goldberg, 1989), evolution strategies (Schwefel, 1981; Bäck, 1996), evolutionary programming (Fogel, 1995) and genetic programming (Koza, 1992). Section 1.3 gives a brief and basic introduction to such techniques, aimed at one type of reader: the telecommunications engineer, manager or researcher who knows all too much about the issues, but does not yet know a way to address them. Later chapters discuss their use in relation to individual problems in telecommunications. 1.2 Dynamic Problems and Adaptation A fundamental aspect of many optimization issues in telecommunications is the fact that they are dynamic. What may be the best solution now may not be the ideal solution in a few hours, or even a few minutes, from now. For example, the provider of a distributed database service (such as videoondemand, webcaching services, and so forth) must try to ensure good quality of service to each client. Part of doing this involves redirecting clients’ database accesses to different servers at different times (invisibly to the client) to effect appropriate loadbalancing among the servers. A good, modern optimization technique can be used to distribute the load appropriately across the servers, however this solution becomes invalid as soon as there is a moderate change in the clients’ database access patterns. Another example is general packet routing in a large essentially pointtopoint network. Traditionally, routing tables at each node are used to look up the best ‘next hop’ for a packet based on its eventual destination. We can imagine an optimization technique applying to this problem, which looks at the overall traffic pattern and determines appropriate routing tables for each node, so that general congestion and delay may be minimized, i.e. in many cases the best ‘next hop’ might not be the next node on a shortest path, since this link may be being heavily used already. But, this is clearly a routine which needs to be run over and over again as the pattern of traffic changes. Iterated runs of optimization techniques are one possible way to approach dynamic problems, but it is often a rather inappropriate way, especially when good solutions are needed very fast, since the environment changes very quickly. Instead, a different range of modern computational techniques are often appropriate for such problems. We can generally class these as ‘adaptation’ techniques, although those used later in this book are actually quite a varied bunch. In particular, later chapters will use neural computation, fuzzy logic and game theory to address adaptive optimization in dynamic environments, in some cases in conjunction with local or populationbased search. Essentially, whereas an optimization technique provides a fast and effective way to find a good solution from a huge space of possibilities, an adaptive technique must provide a good solution almost
 Heuristic and Adaptive Computation Techniques in Telecommunications: An Introduction 3 instantly. The trick here is that the methods usually employ ‘offline’ processing to learn about the problem they are addressing, so that, when a good, quick result is required, it is ready to deliver. For example, an adaptive approach to optimal packet routing in the face of changing traffic patterns would involve some continual but minimal processing which continually updates the routing tables at each node based on current information about delays and traffic levels. In the remainder of this chapter, we will briefly introduce the optimization and adaptation techniques which we have mentioned. More is said about each of these in later chapters. Then, we will say a little about each of the three parts of this book. Finally, we will indicate why we feel these techniques are so important in telecommunications, and will grow more and more with time. 1.3 Modern Heuristic Techniques There are a range of wellknown methods in operations research, such as Dynamic Programming, Integer Programming, and so forth, which have traditionally been used to address various kinds of optimization problems. However, a large community of computer scientists and artificial intelligence researchers are devoting a lot of effort these days into more modern ideas called ‘metaheuristics’ or often just ‘heuristics’. The key difference between the modern and the classical methods is that the modern methods are fundamentally easier to apply. That is, given a typical, complex realworld problem, it usually takes much less effort to develop a simulated annealing approach to solving that problem than it does to formulate the problem in such a way that integer linear programming can be applied to it. That is not to say that the ‘modern’ method will outperform the ‘classical’ method. In fact, the likely and typical scenarios, when both kinds of method have been applied, are: • A metaheuristics expert compares the two kinds of technique: the modern method outperforms the classical method. • A classical operations research expert compares the two kinds of technique: the classical method outperforms the modern method. Although tongueincheek, this observation is based on an important aspect of solving optimization problems. The more you know about a particular technique you are applying, the better you are able to tailor and otherwise exploit it to get the best results. In this section we only provide the basic details of a few modern optimization algorithms, and hence do not provide quite enough information for a reader to be able to tailor them appropriately to particular problems. However, although we do not tell you how to twiddle them, we do indicate where the knobs are. How to twiddle them depends very much on the problem, and later chapters will provide such information for particular cases. What should become clear from this chapter, however, is that these techniques are highly general in their applicability. In fact, whenever there is some decent way available to evaluate or score candidate solutions to your problem, then these techniques can be applied. The techniques essentially fall into two groups: local search and populationbased search. What this means is discussed in the following.
 4 Telecommunications Optimization: Heuristic and Adaptive Techniques 1.3.1 Local Search Imagine you are trying to solve a problem P, and you have a huge set S of potential solutions to this problem. You don’t really have the set S, since it is too large to ever enumerate fully. However, you have some way of generating solutions from it. For example, S could be a set of connection topologies for a network, and candidate solutions s, s′, s′′, and so on, are particular candidate topologies which you have come up with somehow. Also, imagine that you have a fitness function f(s) which gives a score to a candidate solution. The better the score, the better the solution. For example, if we were trying to find the most reliable network topology, then f(s) might calculate the probability of link failure between two particularly important nodes. Strictly, in this case we would want to use the reciprocal of this value if we really wanted to call it ‘fitness’. In cases where the lower the score is, the better (such as in this failure probability example), it is often more appropriate to call f(s) a cost function. We need one more thing, which we will call a neighbourhood operator. This is a function which takes a candidate s, and produces a new candidate s′ which is (usually) only slightly different to s. We will use the term ‘mutation’ to describe this operator. For example, if we mutate a network toplogy, the resulting mutant may include an extra link not present in the ‘parent’ topology, but otherwise be the same. Alternatively, mutation might remove, or move, a link. Now we can basically describe local search. First, consider one of the simplest local search methods, called hillclimbing, which amounts to following the steps below: 1. Begin: generate an initial candidate solution (perhaps at random); call this the current solution, c. Evaluate it. 2. Mutate c to produce a mutant m, and evaluate m. 3. If f(m) is better than or equal to f(c), then replace c with m. (i.e. c is now a copy of m). 4. Until a termination criterion is reached, return to step 2. The idea of hillclimbing should be clear from the algorithm above. At any stage, we have a current solution, and we take a look at a neighbour of this solution – something slightly different. If the neighbour is fitter (or equal), then it seems a good idea to move to the neighbour; that is, to start again but with the neighbour as the new current solution. The fundamental idea behind this, and behind local search in general, is that good solutions ‘congregate’. You can’t seriously expect a very reliable topology to emerge by, for example, adding a single extra link to a very unreliable topology. However, you can expect that such a change could turn a very reliable topology into a slightly more reliable one. In local search, we exploit this idea by continually searching in the neighbourhood of a current solution. We then move to somewhere reasonably fit in that neighbourhood, and reiterate the process. The danger here is that we might get stuck in what is called a ‘local optimum’, i.e. the current solution is not quite good enough for our purposes, but all of its neighbours are even worse. This is bad news for the hillclimbing algorithm, since it will simply be trapped there. Other local search methods distinguish themselves from
 Heuristic and Adaptive Computation Techniques in Telecommunications: An Introduction 5 hillclimbing, however, precisely in terms of having some way to address this situation. We will look at just two such methods here, which are those in most common use, and indeed, are those used later on in the book. These are simulated annealing and tabu search. Simulated Annealing Simulated annealing is much like hillclimbing. The only differences are the introduction of a pair of parameters, an extra step which does some bookkeeping with those parameters, and, which is the main point, step 3 is changed to make use of these parameters: 1. Begin: generate and evaluate an initial candidate solution (perhaps at random); call this the current solution, c. Initialize temperature parameter T and cooling rate r (0 < r < 1). 2. Mutate c to produce a mutant m, and evaluate m. 3. If test(f(m), f(c), T) evaluates to true, then replace c with m. (ie: c is now a copy of m). 4. Update the temperature parameter (e.g. T becomes rT) 5. Until a termination criterion is reached, return to step 2. What happens in simulated annealing is that we sometimes accept a mutant even if it is worse than the current solution. However, we don’t do that very often, and we are much less likely to do so if the mutant is much worse. Also, we are less likely to do so as time goes on. The overall effect is that the algorithm has a good chance of escaping from local optima, hence possibly finding better regions of the space later on. However, the fundametal bias of moving towards better regions is maintained. All of this is encapsulated in the test function in step 3. An example of the kind of test used is first to work out: e ( f ( m ) − f ( c )) / T This assumes that we are trying to maximize a cost (otherwise we just switch f(m) and f(c)). If the mutant is better or equal to the current solution, then the above expression will come to something greater or equal to one. If the mutant is worse, then it will result to something smaller than 1, and the worse the mutant is, the closer to zero it will be. Hence, the result of this expression is used as a probability. A random number is generated, rand, where 0 < rand < 1, and the test in step 3 simply checks whether or not the above expression is smaller than rand. If so (it will always be so if the mutant is better or equal), we accept the mutant. T is a ‘temperature’ parameter. It starts out large, and is gradually reduced (see step 4) with time. As you can tell from the above expression, this means that the probabilities of accepting worse mutants will also reduce with time. Simulated annealing turns out to be a very powerful method, although it can be quite difficult to get the parameters right. For a good modern account, see Dowsland (1995). Tabu Search An alternative way to escape local optima is provided by tabu search (Glover 1989; 1989a; Glover and Laguna, 1997). There are many subtle aspects to tabu search; here we will just indicate certain essential points about the technique. A clear and full introduction is provided in Glover and Laguna (1995; 1997).
 6 Telecommunications Optimization: Heuristic and Adaptive Techniques Tabu search, like some other local search methods which we do not discuss, considers several neighbours of a current solution and eventually chooses one to move to. The distinguishing feature of tabu search is how the choice is made. It is not simply a matter of choosing the fittest neighbour of those tested. Tabu search also takes into account the particular kind of mutation which would take you there. For example, if the best neighbour of your current solution is one which can be reached by changing the other end of a link emerging from node k, but we have quite recently made such a move in an earlier iteration, then a different neighbour may be chosen instead. Then again, even if the current best move is of a kind which has been used very recently, and would normally be disallowed (i.e. considered ‘taboo’), tabu search provides a mechanism based on ‘aspiration criteria’, which would allow us to choose that more if the neighbour in question was sufficiently better than the (say) current solution. Hence, any implementation of tabu search maintains some form of memory, which records certain attributes of the recently made moves. What these attributes are depends much on the problem, and this is part of the art of applying tabu search. For example, if we are trying to optimize a network topology, one kind of mutation operator would be to change the cabling associated with the link between nodes a and b. In our tabu search implementation, we would perhaps record only the fact that we made a ‘changecabling’ move at iteration i, or we might otherwise, or additionally, simply record the fact that we made a change in association with node a and another in association with node b. If we only recorded the former type of attribute, then nearfuture possible ‘changecabling’ moves would be disallowed, independent of what nodes were involved. If we recorded only the latter type of attribute, then nearfuture potential changes involving a and/or b might be disallowed, but ‘changecabling’ moves per se would be acceptable. Artful Local Search Our brief notes on simulated and tabu search illustrate that the key aspect of a good local search method is to decide which neighbour to move to. All local search methods employ the fundamental idea that local moves are almost always a good idea, i.e. if you have a good current solution, there may be a better one nearby, and that may lead to even better ones, and so forth. However, it is also clear that occasionally, perhaps often, we must accept the fact that we can only find improved current solutions by temporarily (we hope) moving to worse ones. Simulated annealing and tabu search are the two main approaches to dealing with this issue. Unfortunately, however, it is almost never clear, given a particular problem, what is the best way to design and implement the approach. There are many choices to make; the first is to decide how to represent a candidate solution in the first place. For example, a network topology can be represented as a list of links, where each link is a pair of nodes (a,b). Decoding such a list into a network topology simply amounts to drawing a pointto point link for each nodepair in the list. Alternatively, we could represent a network topology as a binary string, containing as many bits as there are possible links. Each position in the bit string will refer to a particular potential pointtopoint link, So, a candidiate solution such as ‘10010…’ indicates that there is a pointtopoint link between nodes 1 and 2, none between nodes 1 and 3, or 1 and 4, but there is one between nodes 1 and 5, and so forth.
 Heuristic and Adaptive Computation Techniques in Telecommunications: An Introduction 7 Generally, there are many ways of devising a method to represent solutions to a problem. The choice, of course, also affects the design of neighbourhood operators. In the above example, removing a link from a topology involves two different kinds of operation in the two representations. In the nodepair list case, we need to actually remove a pair from the list. In the binary case, we change a 1 to a 0 in a particular position in the string. Devising good representations and operators is part of the art of effectively using local search to solve hard optimization problems. Another major part of this art, however, is to employ problem specific knowledge or existing heuristics where possible. For example, one problem with either of the two representations we have noted so far for network topology is that a typical randomly generated topology may well be unconnected. That is, a candidate solution may simply not contain paths between every pair of nodes. Typically, we would only be interested in connected networks, so any algorithmic search effort spent in connection with evaluating unconnected networks seems rather wasteful. This is where basic domain knowledge and existing heuristics will come in helpful. First, any good network designer will know about various graph theoretic concepts, such as spanning trees, shortest path algorithms, and so forth. It is not difficult to devise an alteration to the node pair list representation, which ensures that every candidate solution s contains a spanning tree for the network, and is hence connected. One way to do this is involves interpreting the first few nodepairs indirectly. Instead of (a, b) indicating that this network contains a link between a and b, it will instead mean that the ath connected node will be linked to the bth unconnected node. In this way, every next node pair indicates how to join an as yet unused node to a growing spanning tree. When all nodes have been thus connected, remaining nodepairs can be interpreted directly. Better still, the problem we address will probably involve cost issues, and hence costs of particular links will play a major role in the fitness function. Domain knowledge then tells us that several well known and fast algorithms exits which find a minmalcost spanning tree (Kruskal, 1956; Prim, 1957). It may therefore make good sense, depending on various other details of the problem in hand, to initialize each candidate solution with a minimal cost tree, and all that we need to represent are the links we add onto this tree. There are many, many more ways in which domain knowledge or existing heuristics can be employed to benefit a local search approach to an optimization problem. Something about the problem might tell us, for example, what kinds of mutation have a better chance of leading to good neighbours. An existing heuristic method for, say, quickly assigning channels in a mobile network, might be used to provide the initial point for a local search which attempts to find better solutions. 1.3.2 PopulationBased Search An alternative style of algorithm, now becoming very popular, builds on the idea of local search by using a population of ‘current’ solutions instead of just one. There are two ways in which this potentially enhances the chances of finding good solutions. First, since we have a population, we can effectively spend time searching in several different neighbourhoods at once. A populationbased algorithm tends to share out the computational effort to different candidate solutions in a way biased by their relative fitness. That is, more time will be spent searching the neighbourhoods of good solutions than moderate solutions.
 8 Telecommunications Optimization: Heuristic and Adaptive Techniques However, at least a little time will be spent searching in the region of moderate or poor solutions, and should this lead to finding a particularly good mutant along the way, then the loadbalancing of computational effort will be suitably revised. Another opportunity provided by populationbased techniques is that we can try out recombination operators. These are ways of producing mutants, but this time from two or more ‘parent’ solutions, rather than just one. Hence the result can be called a recombinant, rather than a mutant. Recombination provides a relatively principled way to justify large neighbourhood moves. One of the difficulties of local search is that even advanced techniques such as simulated annealing and tabu search will still get stuck at local optima, the only ‘escape’ from which might be a rather drastic mutation. That is, the algorithm may have tried all of the possible local moves, and so must start to try nonlocal moves if it has any chance of getting anywhere. The real problem here is that there are so many potential nonlocal moves. Indeed, the ‘nonlocal’ neighbourhood is actually the entire space of possibilities! Recombination is a method which provides a way of choosing good nonlocal moves from the huge space of possibilities. For example, if two parent solutions are each a vector of k elements, a recombination operator called uniform crossover (Syswerda, 1989) would build a child from these two parents by, for each element in turn, randomly taking its value from either point. The child could end up being 50% different from each of its parents, which is vastly greater than the typical difference between a single parent solution and something in its neighbourhood. Below are the steps for a generic population based algorithm. 1. Begin: generate an initial population of candidate solutions. Evaluate each of them. 2. Select some of the population to be parents. 3. Apply recombination and mutation operators to the parents to produce some children. 4. Incorporate the children into the population. 5. Until a termination criterion is reached, return to step 2. There are many ways to perform each of these steps, but the essential points are as follows. Step 2 usually employs a ‘survival of the fittest’ strategy; this is where the ‘load sharing’ discussed above comes into play. The fitter a candidate solution is, the more chance it has of being a parent, and therefore the more chances there are that the algorithm will explore its neighbourhood. There are several different selection techniques, most of which can be parameterised to alter the degree to which fitter parents are preferred (the selection pressure). Step 3 applies either recombination or mutation operators, or both. There are all sorts of standard recombination and mutation operators, but – as we hinted above – the real benefits come when some thought has been put into designing specific kinds of operator using domain knowledge. In step 4, bear in mind that we are (almost always) maintaining a fixed population size. So, if we have a population of 100, but 20 children to incorporate, then 20 of these 120 must be discarded. A common approach is to simply discard the 20 least fit of the combined group, but there are a few other approaches; we may use a technique called ‘crowding’, e.g. De Jong (1975), in which diversity plays a role in the decision about what candidate solutions to discard. For example, we would
 Heuristic and Adaptive Computation Techniques in Telecommunications: An Introduction 9 certainly prefer to discard solution s in favour of a less fit solution t, if it happens to be the case that s already has a duplicate in the population, but t is ‘new’. Finally, we should point out some terminological issues. There are many population based algorithms, and in fact they are usually called evolutionary algorithms (EAs). Another common term employed is genetic algorithms, which strictly refers to a family of such methods which always uses a recombination operator (Holland, 1965; Goldberg, 1989), while other families of such algorithms, called evolutionary programming (Fogel, 1995) and evolution strategies (Bäck, 1996), tend to use mutation alone, but are quite clever about how they use it. In all cases, a candidate solution tends to be called a chromosome and its elements are called genes. 1.4 Adaptive Computation Techniques To address the optimization needs inherent in constantly changing telecommunications environments, direct use of local or population based optimization techniques may sometimes be quite inappropriate. This might be because it may take too long to converge to a good solution, and so by the time the solution arrives, the problem has changed! What we need instead in this context is a way to make very fast, but very good, decisions. For example, to decide what the best ‘next hop’ is for a packet arriving at node a with destination d, we could perhaps run a simulation of the network given the current prevailing traffic patterns and estimate the likely arrival times at the destination for given possible next hops. The result of such a simulation would provide us with a wellinformed choice, and we can then send the packet appropriately on its way. Now, if we could the above in a few microseconds, we would have a suitable and very profitable packet routing strategy. However, since it will probably take several hours to do an accurate simulation using the sort of processing power and memory typically available at network switches, in reality it is a ridiculous idea! Instead, we need some way of making good decisions quickly, but where the decision will somehow take into account the prevailing circumstances. Ideally, we are looking for a ‘black box’ which, when fed with a question and some environmental indicators, provides a sensible and immediate answer. One example of such a black box is a routing table of the sort typically found in packetswitched networks. The question asked by a communication packet is: ‘eventually I want to get to d, so where should I go next?’. The routing table, via a simple lookup indexed by d, very quickly provides an answer and sends it on its way. The trouble with this, of course, is that it is fundamentally nonadaptive. Unless certain advanced network management protocols are in operation, the routing table will always give the same answer, even if the onward link from the suggested next hop to d is heavily congested at the moment. Our black boxes must therefore occasionally change somehow, and adapt to prevailing conditions. In fact, chapters eight and nine both discuss ways of doing this involving routing tables in packet switched networks. So, adaptive techniques in the context of telecommunications tends to involve black boxes, or models, which somehow learn and adapt ‘offline’ but can react very quickly and appropriately when asked for a decision. In some of the chapters that involve adaptation, the techniques employed are those we have discussed already in section 1.3, but changed appropriately in the light of the need for fast decisions. Though, in others, certain other important modern techniques are employed, which we shall now briefly introduce. These
 10 Telecommunications Optimization: Heuristic and Adaptive Techniques are neural computation, fuzzy logic and game theory. The role of neural computation in this context is to develop a model offline, which learns (by example) how to make the right decisions in varied sets of circumstances. The resulting trained neural network is then employed online as the decision maker. The role of fuzzy logic is to provide a way of producing robust rules which provide the decisions. This essentially produces a black box decisionmaker, like a neural network, but with different internal workings. Finally, game theory provides another way of looking at complex, dynamic network scenarios. Essentially, if we view certain aspects of network management as a ‘game’, a certain set of equations and well known models come into play, which in turn provide good approximations to the dynamics of real networks. Hence, certain network management decisions can be supported by using these equations. 1.4.1 Neural Computation Neural computation (Rumelhart and MacClelland, 1989; Haykin, 1998) is essentially a pattern classification technique, but with vastly wider application possibilities than that suggests at first sight. The real power of this method lies in the fact that we do not need to know how to distinguish one kind of pattern from another. To build a classical rulebased expert system for distinguishing patterns, for example, we would obviously need to acquire rules, and build them into the system. If we use neural computation, however, a special kind of black box called a ‘neural network’ will essentially learn the underlying rules by example. A classic application of the technique is in credit risk assessment. The rules which underlie a decision about who will or will not be a good credit risk, assuming that we disregard clear cases such as those with preexisting high mortgages but low salaries (i.e. one of the coeditors of this book), are highly complex, if indeed they can be expressed at all. We could train a neural network to predict bad risks, however, simply by providing a suite of known examples, such as ‘person p from region r with salary s and profession y … defaulted on a loan of size m; person q with salary t …’ and so forth. With things like p, r, s, and so forth, as inputs, the neural network gradually adjusts itself internally in such a way that it eventually produces the correct output (indication the likelihood of defaulting on the loan) for each of the examples it is trained with. Remarkably, and very usefully, we can then expect the neural network to provide good (and extremely fast) guesses when provided with previously unseen inputs. Internally, a neural network is a very simple structure; it is just a collection of nodes (sometimes called ‘artificial neurons’) with input links and output links, each of which does simple processing: it adds up the numbers arriving via its input links, each weighted by a strength value (called a weight) associated with the link it came through, it then processes this sum (usually just to transform it to a number between 0 and 1), and sends the result out across its output links. A socalled ‘feedforward’ neural network is a collection of such nodes, organised into layers. The problem inputs arrive as inputs to each of the first layer of nodes, the outputs from this layer feed into the second layer, and so on, although usually there are just three layers. Obviously, the numbers that come out at the end depend on what arrives at the input layer, in a way intimately determined by the weights on the links. It is precisley these weights which are altered gradually in a principled fashion by the training process. Classically, this is a method called backpropagation (Rumelhart and MacClelland,
 Heuristic and Adaptive Computation Techniques in Telecommunications: An Introduction 11 1989), but there are many modern variants. Indeed, the kind of network we have briefly described here is just one of many types available (Haykin, 1999). 1.4.2 Fuzzy Logic In some cases we can think of decent rules for our problem domain. For example, ‘if traffic is heavy, use node a’, and ‘if traffic is very heavy, use node b’. However, such rules are not very useful without a good way of deciding what ‘heavy’ or ‘very heavy’ actually mean in terms of link utilization, for example. In a classical expert system approach, we would adopt predetermined thresholds for these socalled ‘linguistic variables’, and decide, for example, that ‘traffic is heavy’ means that the utilization of the link in question is between 70% and 85%. This might seem fine, but it is not difficult to see that 69.5% utilization might cause problems; in such a scenario, the rule whose condition is ‘moderate traffic’ (55% to 70%, perhaps) would be used, but it may have been more appropriate, and yield a better result, to use the ‘heavy traffic’. Fuzzy logic provides a way to use linguistic variables which deals with the thresholds issue in a very natural and robust way. In fact, it almost rids us of a need for thresholds, instead introducing things called ‘membership functions’. We no longer have traffic which is either heavy or moderate. Instead, a certain traffic value is to some extent heavy, and to some other extent moderate. The extents depend upon the actual numerical values by way of the membership functions, which are often simple ‘triangular functions’. For example, the extent to which traffic is heavy might be 0 between 0% and 35% utilization, it may then rise smoothly to 1 between 35% and 75%, and then drop smoothly to 0 again between 75% and 90%, being 0 from then on. The membership function for the linguistic variable ‘very heavy’ will overlap with this, so that a traffic value of 82.5% might be ‘heavy’ to the extent 0.5, and ‘very heavy’ to the extent 0.7. Given certain environmental conditions, different rules will therefore apply to different extents. In particular, fuzzy logic provides ways in which to determine the degree to which different rules are applicable when the condition parts of the rules involve several linguistic variables. Chapter 8, which uses fuzzy logic, discusses several such details. The main strength of fuzzy logic is that we only need to ensure that the membership functions are intuitively reasonable. The resulting system, in terms of the appropriateness of the decisions that eventually emerge, tends to be highly robust to variations in the membership functions, within reasonable bounds. We may have to do some work, however, in constructing the rules themselves. This is where the ‘offline’ learning comes in when we are using fuzzy logic in an adaptive environment. Sometimes, genetic algorithms may be employed for the task of constructing a good set of rules. 1.4.3 Game Theory Finally, game theory provides another way to look at certain kinds of complex, dynamic commuicationsrelated problems, especially as regards network management and service provision. Consider the complex decision processes involved in deciding what tariff to set for call connection or data provision service in a dynamic network environment, involving competition with many other service providers. Under certain sets of assumptions, the
 12 Telecommunications Optimization: Heuristic and Adaptive Techniques dynamics of the network, which includes, for example, the continual activity of users switching to different service providers occasionally based on new tariffs being advertised, will bear considerable resemblance to various models of competition which have been developed in theoretical biology, economics, and other areas. In particular, certain equations will apply which enable predictions as to whether a proposed new tariff would lead to an unstable situation (where, for example, more customers would switch to your new service than you could cope with). Especially in future networks, many quite complex management decisions might need to be made quickly and often. For example, to maintain market share, new tariffs might need to be set hourly, and entirely automatically, on the basis of current activity in terms of new subscriptions, lapsed customers, and news of new tariffs set by rival providers. The game theoretic approaches being developed by some of the contributors to this book will have an ever larger role to play in such scenarios, perhaps becoming the central engine in a variety of adaptive optimization techniques aimed at several service provision issues. 1.5 The Book Heuristic and adaptive techniques are applied to a variety of telecommunications related optimization problems in the remainder of this book. It is divided into three parts, which roughly consider three styles of problem. The first part is network design and planning. This is, in fact, where most of the activity seems to be in terms of using modern heuristic techniques. Network design is simple to get to grips with as an optimization problem, since the problems involved can be quite well defined, and there is usually no dynamicity involved. That is, we are able to invest a lot of time and effort in developing a good optimization based approach, perhaps using specialized hybrid algorithms and operators, which may take quite a while to come up with a solution. Once a solution is designed, it might be gradually implemented, built and installed over the succeeding weeks or months. In contrast, routing and protocols, which are the subject of Part Two, involve optimization issues which are almost always dynamic (although two of the chapters in Part Two sidestep this point by providing novel uses for timeconsuming optimization method – see below). The bulk of this part of the book considers various ways to implement and adapt the ‘black box’ models discussed earlier. In one case, the black box is a neural network; in another, it is a fuzzy logic ruleset and in another it is a specialized form of routing table, adapted and updated via a novel algorithm reminiscent of a genetic algorithm. Part Three looks at a range of issues, covering software, strategy, and various types of traffic management. Software development is a massive and growing problem in the telecommunications industry; it is not a telecommunications problem per se, but good solutions to it will have a very beneficial impact on service providers. The ‘problem’ is essentially the fact that service provision, network equipment, and so forth, all need advanced and flexible software, but such software takes great time and expense to develop. The rising competition, service types and continuing influx of new technologies into the telecommunications arena all exacerbate this problem, and telecommunications firms are therefore in dire need of ways to speed up and economize the software development process. One of the chapters in Part Three addresses an important aspect of this problem. Part Three also addresses strategy, by looking at the complex dynamic network
 Heuristic and Adaptive Computation Techniques in Telecommunications: An Introduction 13 management issues involved in service provision, and in admission and flow control. In each case, an approach based on game theory is adopted. Finally, Part Three also addresses traffic management, in both static and mobile networks. We therefore cover a broad range of telecommunications optimization issues in this book. This is, we feel, a representative set of issues, but far from complete. The same can be said in connection with the range of techniques which are covered. The story that emerges is that heuristic and adaptive computation techniques have gained a foothold in the telecommunications arena, and will surely build on that rapidly. The emerging technologies in telecommunications, not to mention increasing use of the Internet by the general public, serve only to expand the role that advanced heuristic and adaptive methods can play.
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