Tối ưu hóa viễn thông và thích nghi Kỹ thuật Heuristic P14 pot

This scenario is shown schematically in Figure 14.2 and, with the basic ‘least worst performing server’ evaluation function, isfound to have many different solutions with the same global

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The Internet is a large scale distributed file system, where vast amounts of highlyinterconnected data are distributed across many number of geographically dispersed nodes.

It is interesting to note that even individual nodes are increasingly being implemented as acluster or ‘farm’ of servers These ‘dispersed’ systems are a distinct improvement overmonolithic databases, but usually still rely on the notion of fixed master/slave relationships(mirrors) between copies of the data, at fixed locations with static access configurations For

‘fixed’ systems, initial file distribution design can still be complex and indeed evolutionary

Telecommunications Optimization: Heuristic and Adaptive Techniques, edited by D Corne, M.J Oates and G.D Smith

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algorithms have been suggested in the past for static file distribution by March and Rho(1994, 1995) and Cedano and Vemuri (1997), and for Video-on Demand like services byTanaka and Berlage (1996) However as usage patterns change, the efficiency of theoriginal distribution can rapidly deteriorate and the administration of such systems, beingmainly manual at present, can become labour intensive as an alternative solution, Bichevand Olafsson (1998) have suggested and explored a variety of automated evolutionarycaching techniques However, unless such a dispersed database can dynamically adjustwhich copy of a piece of data is the ‘master’ copy, or indeed does away with the notion of a

‘master copy’, then it is questionable whether it can truly be called a ‘distributed’ database.The general objective is to manage varying loads across a distributed database so as toreliably and consistently provide near optimal performance as perceived by clientapplications Such a management system must ultimately be capable of operating over arange of time varying usage profiles and fault scenarios, incorporate considerations formultiple updates and maintenance operations, and be capable of being scaled in a practicalfashion to ever larger sized networks and databases To be of general use, the system musttake into consideration the performance of both the back-end database servers, and thecommunications networks, which allow access to the servers from the client applications.Where a globally accessible service is provided by means of a number of distributed andreplicated servers, accessed over a communications network, the particular allocation ofspecific groups of users to these ‘back-end’ servers can greatly affect the user perceivedperformance of the service Particularly in a global context, where user load variessignificantly over a 24 hour period, peak demand tends to ‘follow the sun’ from Europethrough the Americas and on to the Asia Pacific region Periodic re-allocation of groups ofusers to different servers can help to balance load on both servers and communications links

to maintain an optimal user-perceived Quality of Service Such allocation can also be usefully applied under server node or communications link failureconditions, or during scheduled maintenance

re-configuration/re-The management of this dynamic access configuration/load balancing in near real timecan rapidly become an exceedingly complex task, dependent on the number of nodes, level

of fragmentation of the database, topography of the network and time specific loadcharacteristics Before investigation of this problem space can be contemplated, it isessential to develop a suitable model of the distributed database and network, and a method

of evaluating the performance of any particular access and data distribution given aparticular loading profile is required This model and evaluation method can then be usedfor fitness function calculations within an evolutionary algorithm or other optimisationtechnique, for investigating the feasibility and effectiveness of different accessconfigurations based on sampled usage and other data Armed with such a ‘performancepredicting’ model, an automated load balancing system can be devised which uses anoptimiser to determine ideal access configurations based on current conditions, which canthen be used to apply periodic database self-adaption in near real time

Figure 14.1 shows a block diagram of such an automated, self adapting, load balancing,distributed database The system employs a performance predicting model of the servers

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Figure 14.1 Schematic of an automated, self-adapting, load-balancing distributed database.

and communication links, and an optimiser which produces possible allocations of groups

of users to ‘back-end’ servers These ‘allocations’ (solution vectors) are evaluated by themodel, which uses them to determine how to combine respective workloads onto selectedservers and predicts the degraded performance of each server and communication link usingtwo key formulae based on the principles of Little’s Law and MM1 queuing These are:

)TAR)BTT/1((

1Time

ResponseDegraded

−

where BTT is the server Base Transaction Time and TAR is Transaction Arrival Rate, and:

i S i i S i S

i

i maxTR maxTRTR

CVCTR

where CTR stands for Combined Transaction Rate, taking into account individual

transaction rates TR from a range of sources S, and where CV is a Contention Value

representing a measure of the typical degree of collision between transactions

Each node can be considered to be both a client (a source of workload) and a potentialserver As a client, the node can be thought of as a ‘Gateway’ or ‘Portal’ aggregating userload for a particular geographical sub-region or interest group This is referred to as the

‘Client node’ loading and is characterised for each node by a Retrieval rate and Update ratetogether with a transaction overlap factor As a server, each node’s ability to store dataand/or perform transactions is characterised by its Base Transaction Time (the latencyexperienced by a solitary transaction on the server – this then degrades as work load

OPTIMISER

MODEL

CONFIGURATIONS USAGE DATA

PREDICTED PERFORMANCE

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increases) and a resource contention factor Workload retrievals from a particular node areperformed on the server, specified in a solution vector supplied by the optimiser, withupdates applied to all active servers Each nodal point-to-point communications link is alsocharacterised by a Base Communications Time which deteriorates with increased load.Specified as a matrix, this allows crude modelling of a variety of different interconnectiontopologies.

The optimiser runs for a fixed number of evaluations in an attempt to find aconfiguration giving the least worst user transaction latency, moderated by a measure ofoverall system performance (variants of this will be described in due course) As the system

is balancing worst server performance, communications link performance and overallsystem performance, this effectively becomes a multi-objective minimisation problemwhich can be likened to a rather complex bin-packing problem Experiments described hereutilise 10 node ‘scenarios’ for the problem space which are described later

A typical solution vector dictates for each client node load, which server node to use forretrieval access as shown below :

This solution vector is generated by the optimiser using a chromosome of length 10 and

an allelic range of the integers 1 through 10 – and is manipulated as a direct 10-aryrepresentation rather than in a binary representation more typical of a cannonical geneticalgorithm (see Bäck, 1996; Goldberg, 1989; Holland, 1975) Previous publications by theauthor and others have demonstrated differential algorithmic performance betweenHillClimbers, Simulated Annealers and differing forms of GA on this problem set (see

Oates et al 1998; 1998a; 1998b), under different tuning values of population size and mutation rates (see Oates et al., 1998c), on different scenarios (Oates et al., 1998b) and using different operators (Oates et al 1999) Some of these results are reviewed over the

next few pages

The scenarios investigated typically vary the relative performance of each node withinthe system and the topography of the communications network Two such scenarios were

explored in (Oates et al., 1998b) where the first, Scenario A, consists of all servers being of

similar relative performance (all Base Transaction Times being within a factor of 2 of eachother) and similar inter-node communication link latency (again all within a factor of 2).The communications link latency for a node communicating with itself is obviously setsignificantly lower than the latency to any other node This scenario is shown schematically

in Figure 14.2 and, with the basic ‘least worst performing server’ evaluation function, isfound to have many different solutions with the same globally optimum fitness value.Scenario B considers the case where the 10 nodes are split into two regions, all nodes ineach region being connected by a high speed LAN and the two LANs being interconnected

by a WAN, the WAN being 10 times slower than the LANs This is represented by highcommunication latencies for clients accessing servers outside their region, medium latenciesfor access within their region, and the lowest latencies for access to themselves One node ineach region is considered a Supernode, with one tenth the Base Transaction Time of theother nodes in its region This scenario, shown in Figure 14.3, has only one optimal solution

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under most load conditions, where all nodes in a region access their own region’ssupernode.

Figure 14.2 Logical topology of Scenario A.

Figure 14.3 Logical topology of Scenario B.

S e r v e r C

l i e n t

Node 1

2800

Node 3 3100

Node 4 2900

Node 5 4000 Node 6

Node 4

500 Node 55000

Node 6 5000

High Speed LAN

Lower Speed WAN

Node 7

500

Node 9 5000

Node 10 5000

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Several different optimisation algorithms have been explored, and selected results fromthese experiments are presented and compared below As a baseline, a simple randommutation ‘Hill Climber’ was used, where the neighbourhood operator changed a singlerandom gene (Client) to a new random allele value (representing the server choice for thatclient) If superior, the mutant would then become the current solution, otherwise it would

be rejected This optimisation method is later referred to as HC A Simulated Annealer (SA)was also tried, using the same neighbourhood operator, with a geometric cooling scheduleand start and end temperatures determined after preliminary tuning with respect to theallowed number of iterations

Three types of genetic algorithm were also tried, each of these maintaining a population

of potential solution vectors, intermixing sub-parts of these solutions in the search for everbetter ones Firstly a ‘Breeder’ style GA (see Mühlenbein and Schlierkamp-Voosen, 1994)was used employing 50% elitism, random selection, uniform crossover and uniformlydistributed allele replacement mutation Here, each member of the population is evaluatedand ranked according to performance The worst performing half are then deleted, to bereplaced by ‘children’ generated from randomly selected pairs of parent solutions from thesurviving top half of the population These are created, for each client position, by choosingthe nominated server from either of the two parent solutions at random This process isknown as Uniform Crossover (see Syswerda, 1989) These ‘children’ are then all evaluatedand the entire population is re-ranked and the procedure repeated The population sizeremains constant from one generation to the next This is later referred to as ‘BDR’

The results from a simple ‘Tournament’ GA (Bäck, 1994) were also compared, usingthree way single tournament selection, where 3 members of the population were chosen atrandom, ranked, and the best and second best used to create a ‘child’ which automaticallyreplaces the third member chosen in the tournament This GA also used uniform crossoverand uniformly distributed allele replacement mutation and is later referred to as ‘TNT’.Finally, another ‘Tournament’ style GA was also used, this time using a specialisedvariant of two point crossover With this method the child starts off as an exact copy of thesecond parent but then a random start position in the first parent is chosen, together with arandom length (with wrap-around) of genes, and these are overlaid into the child starting atyet another randomly chosen position This is then followed by uniformly distributed allelereplacement mutation This gives a ‘skewing’ effect as demonstrated below and is laterreferred to as ‘SKT’

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Figure 14.4 The ‘Basic’ model evaluation function.

The basic model was devised by Derek Edwards as part of the Advanced Systems andNetworks Project at British Telecommunications Research Labs, and is demonstrated inFigure 14.4 It assumes that all nodes can act as both clients and servers For each clientnode, its Effective Transaction Rate (ETR = combined Retrieval and Update rates) iscalculated using equation 14.2, and this is entered into the left hand table of Figure 14.4under the server entry denoted for this client by the solution vector The update rate fromthis client is entered into all other server positions in that row This is then repeated for eachclient In the example shown (with only 6 nodes) the solution vector would have been 1, 4,

3, 4, 3, 1 Reading down the columns of the left hand table and using equation 14.2 with theappropriate server resource contention value, the Combined Transaction Rate (or aggregateload) is then calculated for each server Using equation 14.1 for each server, this is thenconverted into a Degraded Response Time (DRT) using the server’s specified BTT

Using equation 14.1 the degraded response time for each point-to-point link is nowcalculated and entered into the right hand table using the appropriate base communicationstime and the traffic rate specified in the corresponding entry in the left hand table

The highest entry in each communications table column is now recorded, denoting theslowest response time to that server seen by any client Each of these communications times

is then added to the corresponding server’s DRT to produce the worst overall response time

C ETR UR UR UR UR UR C RespTi me

Resp

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Ti me

l UR UR UR ETR UR UR ⇒ l RespTi me

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i UR UR ETR UR UR UR i RespTi me

Resp

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e UR UR UR ETR UR UR e RespTi me

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t ETR UR UR UR UR UR t RespTi me

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Worst Seen Per for mance ↑

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as seen by any client to each server The highest value in this row now represents the worstoverall response time seen by any client to any server and it is this value that is returned bythe evaluation function It is the optimisers job to minimise this, leading to the concept of

‘least worst’ performance Checks are made throughout to ensure that any infinite ornegative response time is substituted by a suitably large number

Figure 14.5 The ‘Plus Used’ model evaluation function.

Several variants of this ‘basic’ evaluation function have been explored The first of these(plus avg) again assumes that all nodes are potential servers It therefore applies updates toall nodes, however this time 10% of the average performance of all nodes is added to theperformance of the worst transaction latency seen by any user

Another variant restricts updates only to those servers considered to be ‘active’, i.e.appear in the solution vector and are therefore ‘in use’ This variant is termed ‘just used’and has been investigated but is not reported on here Yet another variant starts from the

‘just used’ position but this time adds a usage weighted average to the worstcommunications time as shown in Figure 14.5 This the ‘plus used’ variant and is seen as agood overall reflection of user perceived quality of service It is the basis of many resultspresented here Previous publications have shown how different combinations of thesescenarios and evaluation functions produce radically different fitness landscapes which vary

dramatically in the difficulty they present to Genetic Search (see Oates et al., 1998b; 1999).

X Resp

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Resp

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Worst Seen Perfor mance ↑

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14.4 Initial Comparative Results

For each optimiser and each scenario, 1000 trials were conducted, each starting withdifferent, randomly generated initial populations For each trial, the optimisers were firstallowed 1000 and then 5000 iterations (evaluations) before reporting the best solution theyhad found For the SA, cooling schedules were adjusted to maintain comparable start andend temperatures between the 1000 iteration and 5000 iteration runs For the BDR GA, thenumber of ‘generations’ used was adjusted with respect to population size

Of the 1000 trials it is noted how many trials found solutions with the known globallyoptimal fitness value These are referred to as being ‘on target’ It was also noted how manytimes the best solution found was within 5% of the known globally optimal fitness value, asthis was deemed acceptable performance in a real-time industrial context Finally it wasnoted how many times out of the 1000 trials, the best solution found was more than 30%worse than the known globally optimal fitness value – this was deemed totally unacceptableperformance The results of these trials for Scenario A with the ‘plus average’ fitness modelare shown in Figure 14.6

Figure14 6 Scenario A with the ‘plus average’ fitness model.

Here it can be seen in the left-hand set of columns that at only 1000 evaluations (theforeground row), very few trials actually found the global optimum solution The Breeder(BDR) and Skewed Tournament (SKT) genetic algorithms actually perform worst howeverneither Hillclimber (HC) nor Simulated Annealing (SA) nor Tournament Genetic Algorithm(TNT) deliver better than a 3% success rate Still at only 1000 evaluations, Hillclimber can

be seen to totally fail (right hand set of columns) around 5% of the time, with all othertechniques never falling into this category At 5000 evaluations (the background row), the

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performance of the genetic algorithms improves significantly with Skewed Tournamentdelivering around 30% ‘on target’ hits For best results falling within 5% of the globaloptimum fitness value (the middle set of columns), there is little to choose betweenSimulated Annealing, Breeder or Skewed Tournament GA, all delivering success ratesabove 99% The third set of columns at 5000 evaluations shows the failure rate where bestfound solutions were more than 30% adrift of the global optimum fitness value OnlyHillclimber has any significant entry here Interestingly it is only Hillclimber that fails toshow any significant improvement in its performance when given five times the number ofevaluations This implies the fitness landscape must have some degree of multi-modality (or

‘hanging valleys’) which Hillclimber quickly ascends but becomes trapped at

Figure 14.7 shows similar performance charts for the five optimisers on Scenario B withthe ‘plus used’ evaluation function Here it is clear that only the Skewed TournamentGenetic Algorithm gives any degree of acceptable performance, and even this requires 5000evaluations In terms of best solutions found being worse than 30% more than the globaloptimum, even at 5000 evaluations all techniques, with the exception of SkewedTournament, are deemed to fail over 75% of the time Skewed Tournament gives on targethits 99.7% of the time with no complete failures

Figure 14 7 Scenario B with the ‘plus used’ fitness model.

These results and others are summarised in Table 14.1 with respect to the performance

of simulated annealing In this table, the difficulty with which simulated annealing was able

to find the best result on various scenario/evaluation function pairings is classified roughly

as either ‘Very Easy’, ‘Easy’, ‘Moderate’, ‘Fairly Hard’ or ‘Very Hard’ One clear trend isthat the imposition of the ‘plus used’ evaluation function on Scenario B produces alandscape that makes optimal solutions particularly difficult to find However it is intriguing

SKT 1K ev als 5K evals 0

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that the ‘plus average’ model yields an easier problem in the Scenario B case than withScenario A.

Table 14.1 Summary of search space difficulty.

Model Scenario A Scenario BBasicVery Easy ModerateJust used Very Easy Fairly HardPlus avg Easy Very EasyPlus used Very Easy Very Hard

Wright (1932) introduced the concept of a ‘fitness landscape’ as a visual metaphor todescribe relative fitness of neighbouring points in a search space To try to discover moreabout those features of our ADDMP search space landscapes that cause difficulties toevolutionary search, a number of investigations were carried out exploring thecharacteristics of the landscape around the ‘global optimum’ solution to Scenario B usingthe ‘plus used’ model This ‘neighbourhood analysis’ focused on the average evaluationvalues of 100 ‘n-distance nearest neighbours’ to try and determine whether a ‘cusp’ likefeature existed immediately surrounding the ‘globally optimal solution’ Such a feature inthe 10 dimensional landscape, would make it difficult to ‘home in’ on the globally optimalsolution, as the nearer the solution got in terms of Hamming distance, the worse the returnedevaluation value would be, and this would generate negative selection pressure within theGAs This technique is similar to that of Fitness Distance Correlation which is describedand demonstrated in detail by Jones and Forrest (1995)

The left-hand edge of Figure 14.8 shows the average evaluation value of 100 randomlychosen, single mutation neighbours of the ‘globally optimum solution’ to both the ‘plusaverage’ and ‘plus used’ models both against Scenario B (the global optimum evaluationvalue being less than 9000 in both cases) The plot continues from left to right, nextintroducing the average evaluation value of 100 randomly chosen, dual mutationneighbours This continues up to the final two points showing the average evaluation value

of 100 points in the search space, each different from the globally optimal solution in eightgene positions It was hoped to see a significant difference between the two plots, but this isclearly not the case Indeed, in the case of the ‘plus used’ plot, it was hoped to see a peakvalue at 1 mutation, dropping off as Hamming distance increased This would havesupported a hypothesis of a ‘cusp’ in the 10 dimensional search space which would haveprovided a degree of negative selection pressure around the global optimum solution, hencemaking it ‘hard’ to find

An examination of the distribution of evaluation values of the 100 points at eachHamming distance however, on close examination, does provide some supporting evidence.Figure 14.9 shows the distribution of these points for ‘plus avg’ on Scenario B Clearly asHamming distance increases, evaluation values in excess of 100,000 become more frequent(however it must be borne in mind that each point shown on the plot can represent 1 or

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many instances out of the 100 samples, all with the same evaluation value Figure 14.10gives the same plot for ‘plus used’.

Figure 14.8 Neighbourhood analysis.

Figure 14.9 Distribution for ‘plus avg’.

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Figure 14.10 Distribution for ‘plus used’.

Taking a closer look at the high evaluation value groupings in these figures shows thatfor ‘plus avg’ (in Figure 14.11), high evaluation value points decrease in evaluation value asHamming distance decreases However, for ‘plus used’ (in Figure 14.12), there is a repeatedtrend implying an increase in evaluation value as Hamming distance decreases Bearing inmind this is a minimisation problem, this feature would act as a deterrent to ‘homing in’ onthe global optimum, providing negative selection pressure the closer the search came to theedge of the ‘cusp’ Although this requires many assumptions on the nature of associationbetween points on the plot, it is nonetheless an interesting result which requires furtherinvestigation

The possibility of the ‘cusp’ is also explainable by examining the evaluation functionitself Considering a single deviation from the global optimum solution for Scenario B using

‘plus used’ could simply incur a greater communications overhead to access an existingused server (if the deviation simply causes a client to access the wrong region’s activeserver) Alternatively, the deviation could introduce a ‘new used server’ This would add tothe list of ‘used servers’ and would mean the application of a single ‘retrieval rate’ and acombined ‘update rate’ to an inappropriate node This will almost certainly give a new

‘worst server’ result, significantly worse than the global optimum A second deviation couldadd another ‘new used server’ to the list which, whilst probably no worse than the precedingeffect, increases the number of ‘used servers’, and hence reduces the bias, as the evaluationfunction divides this by the number of used servers which has now increased further Thiswould cause the first deviation to produce a radically worst first nearest neighbour, but withthe effect reducing with increased Hamming distance, and would produce exactly the

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negative selection pressure postulated The fact that more ‘used servers’ are performingworse is irrelevant to this model as it considers the average of client access to the worstserver, not the average of the ‘used servers’.

By contrast, increasing deviations from the global optimum with ‘plus avg’ on Scenario

B, whilst still likely to introduce ‘new used servers’, will see an increasingly worseningeffect as the ‘average server performance’ is influenced by an increasing number of poorlyperforming servers

Figure 14.11 ‘Many evaluation’ fitness distribution for ‘plus avg’.

The ‘cusp’ hypothesis is not as directly applicable in the case of Scenario A In Scenario

A, not only are there several solutions attainable which share the ‘best known fitness value’,but these solutions usually contain a wide genotypic diversity That is, there are multipleoptimal solutions which are quite distinct in terms of the ‘servers’ used by clients.Deviations from these solutions will have a far less marked effect than in a case when thebest known solution is a unique vector, or perhaps a small set containing very littlediversity However, such potential shallow multimodality will produce a degree ofruggedness which, as already demonstrated by Figure 14.6, is seen to be sufficient toprevent a basic hillclimbing algorithm from finding the global optimum

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‘dominant’ gene positions, but there is little guarantee that this would cover any interestinglandscape feature Secondly, even if two gene positions could be determined, the order inwhich the alleles were plotted would have a significant bearing on the 3D landscapevisualised With our examples from the Adaptive Dynamic Database Management Problem(ADDMP), allele values range as integers from 1 to 10 but with no ordinal significance, i.e.

‘1’ is as different from ‘2’ as it is from say ‘7’ It is effectively a symbolic representation

As such, a feature in the landscape which for some reason exploited a commoncharacteristic from the allele values ‘2’, ‘5’, ‘7’ and ‘9’ would appear as a rugged zig-zag in

a visualisation which plotted allele values in ascending numerical order In this case,plotting the fitness of solutions with the odd valued alleles followed by the even valued onesmight expose more of a ‘clustered’ feature Clearly, it would not be practical to explore allpossible permutations in both dimensions

Tiêu đề	Tối ưu hóa viễn thông và thích nghi Kỹ thuật Heuristic P14 pot
Tác giả	Martin J.. Oates, David Corne
Trường học	John Wiley & Sons Ltd
Chuyên ngành	Telecommunications Optimization
Thể loại	Tài liệu hướng dẫn, bài báo
Năm xuất bản	2000

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Số trang	30
Dung lượng	0,97 MB