CN107105052A - Heuristic web service composition method based on figure planning - Google Patents

Heuristic web service composition method based on figure planning Download PDF

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CN107105052A
CN107105052A CN201710343392.5A CN201710343392A CN107105052A CN 107105052 A CN107105052 A CN 107105052A CN 201710343392 A CN201710343392 A CN 201710343392A CN 107105052 A CN107105052 A CN 107105052A
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service
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CN107105052B (en
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刘杰
印桂生
韩启龙
董宇欣
王燕
张艳平
姚甄
张立国
邹子靖
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Harbin Engineering University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/01Protocols
    • H04L67/02Protocols based on web technology, e.g. hypertext transfer protocol [HTTP]
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/50Network services
    • H04L67/51Discovery or management thereof, e.g. service location protocol [SLP] or web services
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/50Network services
    • H04L67/60Scheduling or organising the servicing of application requests, e.g. requests for application data transmissions using the analysis and optimisation of the required network resources

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The present invention is to provide a kind of heuristic web service composition method based on figure planning.Services Composition problem is modeled first, its corresponding relation with intelligent planning problem is elaborated;In order to solve the shortcoming of the blind search based on the Service Combination Algorithm for scheming planning, it is proposed that the concept of state distance, its effect in approachability analysis is analyzed and demonstrated, the construction method of state distance matrix is given;According to state distance matrix, design heuristic function is estimated the accessibility of service, trims unnecessary service, reduces the scale of planning chart, improves the solution efficiency of algorithm.

Description

Heuristic web service composition method based on figure planning
Technical field
The present invention relates to a kind of heuristic web service composition method.
Background technology
Nowadays, Services Composition problem obtains the concern of numerous researchers, wherein, it is directed generally to that group will be serviced in industrial quarters It is main by the way of process modeling and the engine performed in terms of the method and theory of conjunction are applied to engineering practice, it there is spirit The defect of activity and autgmentability difference.In academia, researcher focuses on the theoretical research of the automatic combination method of service, in order to The Automatic Combined of service is realized, generally describes to service by semantic service, so that computer is capable of the semanteme of automatic understanding service Information, and then the correlation theory of intelligent planning is combined, solve the problems, such as Services Composition.But the correlation theory of automatic combination method is simultaneously It is immature, it tends to be difficult to be applied in Practical Project.Services Composition problem can obtain different points from different angles Class result, is divided into static method and dynamic approach according to the difference of combination opportunity;Difference according to the technology of support is classified as figure and searched Method, the method for business flow control and the method for intelligent planning theory control of rope control;Services Composition problem is divided into reality When task solving scheme and the scheme of business-driven
The assembled scheme of Flow driving is realized by binding service node in flow definition figure, shows as participant Taken action according to pre-defined rule and realize function.Because workflow has been widely used, therefore the assembled scheme of Flow driving There are the theoretical foundation and technology application background of maturation.The combination of Flow driving is using workflow as technical foundation, with business Template is core, and user is used it can be readily appreciated that improving the manageability during performing.Its shortcoming is that automaticity is poor, Most of work must be adopted manually, and need domain expert to design service template, it is difficult to which reply is extensive, complicated Operation flow.
The scheme that real-time task is solved is the assembled scheme based on AI planning theories, using the think of of classical artificial intelligence Think, Services Composition problem is mapped as planning problem, solved by intelligent planning reasoning, i.e., in known initial state and target The situation of state, searches an optimal Perform sequence to realize the progressively evolution between the two states from Web service candidate storehouse. The assembled scheme planned based on AI, i.e., portray combinatorial problem, and automatic calculation according to the associated description method of intelligent planning.Therefore Services Composition problem can be with abstract for intelligent planning problem, and numerous achievements in research in intelligent planning field are applied to service Combination.
Figure planning algorithm is the process of an iteration, by iteration each time, and planning chart can extend new service and obtain To new proposition.After the extension of continuous iteration, if proposition layer contains target complete proposition or planning chart is entered not Dynamic layer then terminates expansion process.If planning chart enters motionless layer, illustrate the service solution for not meeting demand.Otherwise, planning chart Into the solution extraction stage, the stage planning chart need to look for each dbjective state one group of service to meet the state, and form new mesh Mark state, untill all dbjective states are both present in original state, then obtains the planning solution of the problem.
If so planning chart of the planning problem without solution will not return to solution;Otherwise, it will return to a solution The action sequence set of problem scheme.In addition, each planning chart has a number of plies k, and it is complete to only need to polynomial time The extension of paired planning chart.And scheming the algorithm of planning has reliability, integrality and terminability.
In the Service Combination Algorithm based on figure planning:
(1) service ws can be mapped as the action a in planning problem;
(2) the input parameter I of service can be mapped as precondition preconds (a);
(3) the action effect effects (a) that the output parameter O of service can be mapped as;
(4) r in user's requestinThe original state s that can be mapped as0
(5) r in user's requestoutThe dbjective state g that can be mapped as;
(6) G=<SL1,AL1,SL2,AL2,...,SLi-1,ALi-1,SLi>:The planning being made up of action layer and state layer Figure.
In classic map planning problem, there is good effect and point of negative effect in action, however, in Services Composition problem In, Web service only exists good effect, therefore proposes simple planning chart in order to apply in Services Composition problem, in letter It is separate in single planning chart, between action, in the absence of the mutex relation of action and action, proposition and proposition.For ease of Description, the present invention will continue simple planning chart being referred to as planning chart.Service Combination Algorithm based on figure planning is divided into extension phase Conciliate the extraction stage.
Extension phase:
(1) the primitive proposition set provided according to user builds first layer state layer
(2) the service ws for the condition that meets is extended according to service library and forms planning chart action layer ALi
(3) by the new state layer SL of effects (ws) formationi+1
(4) repeat step (2) and (3), until dbjective state is all appeared in state layer, or reach motionless layer.
(5) continuous iteration Expansion Planning figure, until then being obtained in planning chart comprising target complete state by solving extraction algorithm To a Services Composition scheme, if planning chart reaches motionless layer, illustrate to meet user's request in the absence of one group of service.
Solve the extraction stage:
(1) to each dbjective state g, one group of service WS is found, its enable exports and obtain state g
(2) effects (WS) is constituted to new dbjective state set;
(3) above procedure is repeated, until reaching initial shape state layer, then one is obtained and reaches dbjective state from original state Group
Conjunction solution ResultWS (<WS1,WS2,...,WSi>)。
Fig. 2 show service relation illustrated example, and wherein A, B and C is the original state of the combinatorial problem, and H and J are target-like State, W1、W2、W3、W4And W5For existing service in service library.First proposition layer is constituted by original state A, B and C, in service Searched in storehouse and choose all services that can be performed and constitute first element layer, the service W in layer will be acted1Output D and E It is added in second layer proposition layer, forms new proposition layer, the like, until dbjective state G and H are integrally incorporated in proposition layer In, now enter the solution extraction stage.In the stage, for sub-goal H and I, in previous action layer selecting one group can reach Target H and I service W4, and the input D and F of the service are constituted into new dbjective state, the like, until reaching initial shape State, then obtain one group of solution W1、W2、W4Enable and dbjective state H and J are reached by original state A, B and C.
Based on the service combining method of figure planning, in time complexity with having relative to other method on space complexity Some superiority, but still there is deficiency:Breadth First is similar on the expansion process of Service Combination Algorithm based on figure planning Algorithm, blind search, time complexity is high, easily occurs multiple shot array, it is difficult to applied to magnanimity services set.
The content of the invention
It is an object of the invention to propose a kind of opening based on figure planning that can be reduced planning map space, improve solution efficiency Hairdo web service composition method.
The object of the present invention is achieved like this:
Step 1:Input the service that user is asked in summed data storehouse;
Step 2:Structure state distance matrix M (i, j);
Step 3:Calculate heuristic function value h (wsi), the accessibility to service is estimated, trims unnecessary service;
Step 4:Judge that planning chart enters fixed point layer, then perform step 5, otherwise perform step 6;
Step 5:Planning is without solution, and algorithm terminates;
Step 6:Judge that planning chart some state layer occurs and includes target complete state, then perform step 7, otherwise return to step Rapid 3;
Step 7:Perform solution extraction algorithm;
Step 8:Combined result is exported, is terminated.
The present invention can also include:
The state distance matrix and heuristic function value are:
(1) service with triple ws (ID, a Sin,Sout) represent, wherein SinRepresenting one group is used to describe input state Semantic concept set, SoutRepresent one group of semantic concept set for being used to describe output state;
(2) semantic state is apart from D (si,sj) represent semantic state siWith semantic state sjCorrelation degree:
(3) semantic state distance matrix M, is the matrix for representing the relation between semantic state, is specially:
M (i, j)=D (si,sj);
State distance describes the always too high estimation service solution of the weak accessibility between state and state, i.e. state distance Accessibility, it is if the state distance between state A and state B is infinitely great, i.e., unreachable, then in the absence of one group of planning solution cause from State A reaches state B;
(4) if original state is rin=(i1,i2...in), dbjective state rout=(o1,o2...on), service WS=(ws1, ws2...wsn), N (S) represents the number of state contained by state set S, wherein gs(p) it is from state s to dbjective state p estimation Value is state distance matrix M (s, p) value, then services wsiInspiration value h (wsi) be:
h(wsi) accessibility of current service and dbjective state set is have estimated using the value of the output state distance of service, The value describes the average of the state distance between the output state of service and dbjective state, h (wsi) always in state in Choose minimum value to be estimated, h (wsi) value for it is infinitely great when, service wsiDo not appear in solution.
The present invention analyzes the defect of the Service Combination Algorithm based on figure planning, and it is improved proposes figure planning framework Under heuristic Web service combination algorithm (SDSC-GP).Services Composition problem is modeled first, itself and intelligence is elaborated The corresponding relation of planning problem;In order to solve the shortcoming of the blind search based on the Service Combination Algorithm for scheming planning, it is proposed that shape The concept of state distance, analyzes and demonstrates its effect in approachability analysis, give the construction method of state distance matrix; According to state distance matrix, design heuristic function is estimated the accessibility of service, trims unnecessary service, reduces planning The scale of figure, improves the solution efficiency of algorithm.
Due to being similar to breadth first algorithm on the expansion process of the Service Combination Algorithm based on figure planning, there is extension effect The problem of rate is low, the present invention carries out beta pruning by evaluation services and the accessibility of dbjective state to planning chart.Propose state away from From concept, to assess the correlation degree and accessibility of current service and dbjective state, and inaccessible service is cut Branch, so as to reduce planning chart scale, improves the expansion efficiency of planning chart.Rule will not be destroyed by the Pruning strategy by finally demonstrating Draw the solution of figure.This method possesses lower space consuming and Geng Gao solution efficiency on the basis of not influenceing to solve success rate.
In heuritic approach, in order to avoid the node that blind search is unnecessary, in order to reduce solution space, generally using base In the heuristic strategies of loose problem.In the strategy, generally the constraints of former problem is reduced, simplifies problem scale, By the cost under computational short cut problem, the target cost of the former problem of estimation.Its state distance proposed, passes through state distance Computational algorithm, the State Reachability in former problem is estimated by the State Reachability in loose problem, and then to each action (service) is estimated, and deletion does not have the service of facilitation to dbjective state accessibility.Under normal circumstances, with loosening degree Reduction, simplify problem with former problem closer to loose estimation is also more accurate.
With reference to Fig. 4, according to the calculating of state range formula in figure, D (A, G)=2, D (B, H)=2, D (C, K)=2.It is right For state A, state G state is reached apart from D (A, G)=2, due to service W4Lack input state C, and in the absence of one group Service causes state A to reach state G, and state A to state G actual distance is 0;And for state B, its state is apart from D (B, H)=2, while in the presence of one group of service (W2,W3,W5) such that state B reaches state H, i.e. state B reach state H it is true away from From for 3.For state C, there is one group of service (W in its state apart from D (C, K)=26,W7) cause state C to reach state K, That is the actual distance that state C reaches state K is 2.It is possible thereby to know, state is reachable between always too high estimated state Property.
From the building process of state matrix it is seen that, state matrix describe it is stateful between correlation degree and can Up to property.
The Pruning strategy of the present invention, can avoid the blindness of planning chart from extending, the effective size for reducing planning chart, lifting Solution efficiency, and inspiration value h (wsi) computation complexity it is very low, if assume wsiOutput parameter maximum number be c, mesh The number of parameters for marking state set is k, then h (wsi) computation complexity be O (k*c), c and k are one and are less than under normal circumstances 3 number, therefore h (wsi) computational efficiency height.
Brief description of the drawings
Fig. 1 is the service relation illustrated example of the Service Combination Algorithm based on figure planning.
Fig. 2 is the planning illustrated example of the Service Combination Algorithm based on figure planning.
Fig. 3 is the flow chart of the present invention.
Fig. 4 is the service relation figure of the present invention.
Fig. 5 is the service relation figure of the present invention.
Fig. 6 is state matrix example.
Fig. 7 is beta pruning effect exemplary plot.
Fig. 8 is the overview flow chart of the embodiment of the present invention.
Fig. 9 is the state distance matrix block diagram of the present invention.
Figure 10 be three kinds of methods in the case of different pieces of information scale, combine success rate situation of change.
Figure 11 be three kinds of methods in the case of different pieces of information scale, the situation of change of service request handling time.
Figure 12 is planning chart scale comparison diagram.
Embodiment
Illustrate below and the present invention is described in more detail.
With reference to Fig. 8, the heuristic Web service combination algorithm of the invention based on figure planning includes:
Step 1:Input the request (r of userin,rout) and service library in service;
Step 2:Structure state distance matrix M (i, j);
Step 3:Init state layer SL1
Step 4:The service in traverse service storehouse;
Step 5:Judge that current state layer, whether comprising parameter is fully entered needed for service, performs step 6 if meeting, Otherwise return to step 4;
Step 6:Inspiration value h (ws are calculated according to formula 2-3i);
Step 7:If h (wsi) be not maximum, i.e., critical value is not arrived, then step 8 is performed, otherwise it is assumed that current service is not A part for planning solution, return to step 4 can be turned into;
Step 8:The service is added to first layer action layer AL1, the output state of service is added to new state layer SL2
Step 9:Judge whether to have traveled through the service in service library, then perform step 10, otherwise return to step 4;
Step 10:Produce complete new state layer SL2
Step 11:Judge all dbjective state routState layer is appeared in, then performs step 12, step 14 is otherwise performed;
Step 12:Perform solution extraction algorithm;
Step 13:Combined result is exported, algorithm terminates;
Step 14:Judge that planning chart enters fixed point layer, then perform step 15, otherwise return to step 4;
Step 15:Planning is without solution, and algorithm terminates.
With reference to Fig. 9, the present invention builds state distance matrix in the expansion process of planning chart, builds state distance matrix Method is as follows:
Step 1:Input user's request (rin,rout) and service library in service;
Step 2:Initialize matrix M, M (i, j)=∞;
Step 3:Each service in traverse service storehouse;
Step 4:Service M (i, j) comprising original state and dbjective state is entered as 1;
Step 5:Ergodic Matrices M each value;
Step 6:It is not 0 to judge service M (i, j), M (j, k), then performs step 7, otherwise return to step 5;
Step 7:Carry out calculating M (i, k);
Step 8:Judge k<J, then perform step 9, otherwise performs step 10;
Step 9:Labeled as true, return to step 5;
Step 10:Labeled as vacation;
Step 11:Complete state distance matrix.
It is terminable that planning chart, which is discussed below, and fixed point layer is provided first and is defined as follows:
The motionless layer for defining 1. planning chart G is kth layer, then rightLow i layers of G are constantly equal to kth layer.That is SLi= SLk,ALi=ALk
2. each planning chart G are defined in the presence of a minimum fixed point layer k so that SLk-1=SLk
Defined from two above, due in the expansion process of planning chart, the state number in proposition layer must be Monotonic increase, i.e. the scale of proposition layer constantly increases, and proposition number is limited in classical planning problem, therefore planning nomography Certainly exist fixed point layer k.Therefore, if request is without planning solution, the algorithm one surely reaches fixed point layer, and terminates the calculation Method.
Experimental verification:
To verify the validity of SDSC-GP methods, measurement is used as using combination success rate, planning chart scale, assembly time Index, contrast test is carried out with PGSGA methods and ACSWS-PG methods.
The software environment and hardware environment of test are as follows:
CPU:Intel(R)Core(TM)2 Quad CPU
Physical memory:1.96GB
Dominant frequency:2.66GHz
Operating system:Windows XP Professional
Database:MySQL
Software tool:Prot é g é have the characteristics such as free download, graphic interface, abundant plug-in unit, therefore this problem is selected Prot é g é are selected as ontology editor, Semantic Web Services description is carried out using the OWL-S Editor plug-in units under Prot é g é The editor of OWL-S documents.OWL-S API are a set of Java API for being developed and being safeguarded by University of Maryland, for OWL-S files Establishment, read-write and perform.This experiment obtains the input of OWL-S services using OWL-S API class libraries parsing OWL-S files The result that intelligent planning is produced, is converted into the OWL-S files of composite services, performs the destination service by the information such as output afterwards.
Experimental data:OWLS-TC4 data sets are increased income, and can arbitrarily be used by personal and group, the data set by Benedikt Fries, MahboobAlam Khalid, Martin Vasileski joint developments, include 1083 Semantic Webs Service, is related to traffic, economy, education, food, geography, medicine, emulation, nine fields of tourism and weapon.
Test program is realized using java language.For the validity of measure algorithm, this problem in OWL S-TC4 with Machine chooses 5 service libraries of different scales, respectively 200,400,600,800,1000.This problem and PGSCA algorithms and ACSWS-PG algorithms are contrasted, and evaluation criterion is used as with request processing time using combination success rate.
Experimental result and analysis:
5 groups of service requests are generated for experiment, every group contains 100 service requests.Submitted respectively on 5 service libraries This 5 groups of service requests, compare PGSCA, ACSWS-PG and SDSC-GP these three methods and are serviced on the service library of different scales The success rate of combination.
Figure 10 be three kinds of methods in the case of different pieces of information scale, combine success rate situation of change.With data set The increase of middle quantity of service, the combination success rate of PGSCA, ACSWS-PG and SDSC-GP method rises appreciably, this table It is bright, with the increase of data set scale, the possibility increase that planning solution is present, this is consistent with actual conditions.ACSWS- PG and SDSC-GP methods, in the case of service scale identical, it combines success rate and is above PGSCA methods, and this is due to The matching way based on keyword that PGSCA is used when processing parameter is matched, it is impossible to match the body ginseng of equivalence class each other Number, causes the reduction of Services Composition success rate.
Figure 11 be three kinds of methods in the case of different pieces of information scale, the situation of change of service request handling time.From figure In can easily find out, the solution time of PGSCA, ACSWS-PG and SDSC-GP method, be in the increase of quantity of service The combination request processing time of ascendant trend, wherein ACSWS-PG methods is less than PGSCA methods, and the combination of SDSC-GP methods please Processing is asked to be significantly lower than ACSWS-PG methods, but with the increase of quantity of service, the combination request processing time of SDSC-GP methods Start to level off to PGSCA methods.ACSWS-PG methods set up inverted index to the output parameter of service and optimize PGSCA methods, Therefore the treatment effeciency of ACSWS-PG methods is rational higher than PGSCA methods.The solution time of SDSC-GP methods is less than ACSWS-PG methods and PGSCA methods illustrate that SDSC-GP carries out beta pruning by setting up state distance matrix to planning chart Method can effectively point out programming evaluation efficiency.But with the increase of quantity of service, the combination request of SDSC-GP methods is handled Time starts to level off to PGSCA methods, and this explanation is with the increase of quantity of service, the correlation degree increase between semantic state, The beta pruning effect of PGSCA methods is caused to die down.
In order to verify that SDSC-GP methods can reduce the scale of planning chart, experiment 100 requests of random generation, and advising Carry out solution statistical rules figure on the service library that mould is 200,400,600,800,1000 with SDSC-GP and PGSCA methods respectively The average value of the quantity of service of extension.Experimental configuration is as shown in figure 11.
As shown in Figure 12, the scale of the planning chart built with the increase of service scale, SDSC-GP and PGSCA methods increases Greatly, the ratio of the difference station PGSCA methods of SDSC-GP and PGSCA methods scale is gradually reduced, the rule that SDSC-GP methods are built Draw the planning chart scale that figure scale is consistently less than PGSCA methods structure.Two methods with service library increase planning chart scale Increase, the planning chart scale that the planning chart scale that SDSC-GP methods are built is consistently less than PGSCA methods structure demonstrates SDSC- The beta pruning effect of GP methods.The ratio of the difference station PGSCA methods of SDSC-GP and PGSCA method scales is gradually reduced, this explanation With the increase of quantity of service, the correlation degree between state increases, and causes the beta pruning effect of PGSCA methods to die down.

Claims (3)

1. a kind of heuristic web service composition method based on figure planning, it is characterized in that:
Step 1:Input the service that user is asked in summed data storehouse;
Step 2:Structure state distance matrix M (i, j);
Step 3:Calculate heuristic function value h (wsi), the accessibility to service is estimated, trims unnecessary service;
Step 4:Judge that planning chart enters fixed point layer, then perform step 5, otherwise perform step 6;
Step 5:Planning is without solution, and algorithm terminates;
Step 6:Judge that planning chart some state layer occurs and includes target complete state, then perform step 7, otherwise return to step 3;
Step 7:Perform solution extraction algorithm;
Step 8:Combined result is exported, is terminated.
2. it is according to claim 1 based on figure planning heuristic web service composition method, it is characterized in that build state away from Method from matrix is:
Step 1:Input user's request (rin,rout) and service library in service;
Step 2:Initialize matrix M, M (i, j)=∞;
Step 3:Each service in traverse service storehouse;
Step 4:Service M (i, j) comprising original state and dbjective state is entered as 1;
Step 5:Ergodic Matrices M each value;
Step 6:It is not 0 to judge service M (i, j), M (j, k), then performs step 7, otherwise return to step 5;
Step 7:Carry out calculating M (i, k);
Step 8:Judge k<J, then perform step 9, otherwise performs step 10;
Step 9:Labeled as true, return to step 5;
Step 10:Labeled as vacation;
Step 11:Complete state distance matrix.
3. it is according to claim 2 based on figure planning heuristic web service composition method, it is characterized in that the state away from It is from matrix and heuristic function value:
(1) service with triple ws (ID, a Sin,Sout) represent, wherein SinRepresent one group of semanteme for being used to describe input state Concept set, SoutRepresent one group of semantic concept set for being used to describe output state;
(2) semantic state is apart from D (si,sj) represent semantic state siWith semantic state sjCorrelation degree:
(3) semantic state distance matrix M, is the matrix for representing the relation between semantic state, is specially:
M (i, j)=D (si,sj);
State distance describes the weak accessibility between state and state, i.e., the always too high estimation service solution of state distance can It is if the state distance between state A and state B is infinitely great, i.e., unreachable up to property, then cause in the absence of one group of planning solution from state A reaches state B;
(4) if original state is rin=(i1,i2...in), dbjective state rout=(o1,o2...on), service WS=(ws1, ws2...wsn), N (S) represents the number of state contained by state set S, wherein gs(p) it is from state s to dbjective state p estimation Value is state distance matrix M (s, p) value, then services wsiInspiration value h (wsi) be:
<mrow> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>ws</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>&amp;Sigma;</mi> <mrow> <mi>s</mi> <mo>&amp;Element;</mo> <mi>e</mi> <mi>f</mi> <mi>f</mi> <mi>e</mi> <mi>c</mi> <mi>t</mi> <mrow> <mo>(</mo> <msub> <mi>ws</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>p</mi> <mo>&amp;Element;</mo> <msub> <mi>r</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </mrow> </munder> <mi>min</mi> <mo>(</mo> <mrow> <msub> <mi>g</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>/</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>e</mi> <mi>f</mi> <mi>f</mi> <mi>e</mi> <mi>c</mi> <mi>t</mi> <mo>(</mo> <mrow> <msub> <mi>ws</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
h(wsi) accessibility of current service and dbjective state set, the value are have estimated using the value of the output state distance of service Describe the average of the state distance between the output state of service and dbjective state, h (wsi) always chosen in state distance Minimum value estimated, h (wsi) value for it is infinitely great when, service wsiDo not appear in solution.
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