IACSIT International Journal of Engineering and Technology, Vol.3, No.1, February 2011 ISSN: 1793-8236
85
Implementing a Decision Support Module in
Distributed Multi-Agent System for Task
Allocation Using Granular Rough Model
Abstract—A Multi-Agent System (MAS) is a branch of distributed artificial intelligence, composed of a number of distributed and autonomous agents. In MAS, an effective coordination is essential for autonomous agents to reach their goals. Any decision based on a foundation of knowledge and reasoning can lead agents into successful cooperation, so to achieve the necessary degree of flexibility in coordination, an agent requires making decisions about when to coordinate and which coordination mechanism to use. The performance of any MAS depends directly with the right decisions that the agents made. Therefore the agents must have the ability of making right decisions. In this paper, we propose a decision support module in a distributed multi-agent system, which enables any agent to make decisions needed for Task allocation problem; we propose an algorithm for Task Allocation Decision Maker (TADM) based on Granular Rough Model (GRM). Furthermore, a number of experiments were performed to validate the effectiveness of the proposed algorithm (TADM)); we compare the efficiency of our algorithms with recent frameworks. The preliminary results demonstrate the efficiency of our algorithms
Index Terms—Decision Making, Task allocation, Coordination Mechanism, Multi-Agent System (MAS), Rough Set, Granular Computing
I. INTRODUCTION
The notion of distributed intelligent systems (DIS) [1] has been a subject of interest for number of years. A Multi-Agent system (MAS) is one of the main areas in the DIS. Any Multi-agent system consists of several agents capable of mutual interaction, with heterogeneous capabilities, that cooperate with each others to pursue some set of goals, or to complete a specific task. MAS used to solve problems which are difficult or impossible for an individual agent or monolithic system to solve. Agents are autonomous programs which can understand an environment, take actions depending upon the current status of the environment using its knowledge base and also learn so as to act in the future. In order to solve complex problems agents have to cooperate and exhibit some level of autonomy. Agents cooperate with each other to solve large and complex collaborative problems. Because the majority of work is completed through distributing the tasks among
Sally M. El-Ghamrawy is with the Computers and Systems Department,Faculty of Engineering,Mansoura University, Egypt(email: [email protected])
Ali I. El-Desouky is with the Computers and Systems Department,Faculty of Engineering,Mansoura University, Egypt(email: [email protected])
MostafaSaleh is with the Computers and Systems Department,Faculty of Engineering,Mansoura University, Egypt
the cooperative agents, the decision support module is responsible on the most of the work. So the pros and cons in decision support module directly affect on the success of tasks completion and problem solving. In [2], we proposed a Distributed Multi-Agent Intelligent System (DMAIS,) a general purpose agent framework, in which several interacting intelligent agents cooperate with some auxiliary agents to pursue some set of goals or tasks that are beyond their individual capabilities. There are some modules must be considered in designing the Distributed Multi-Agent Intelligent System (DMAIS) that help in developing in the agent systems. There are many researches considered some modules when designing multi-agent systems (MAS) in different ways. Each autonomous agent in DMAIS must be able to decide how to behave in various situations, so in this paper our main concern is to propose an efficient decision support module that helps in the improvement of DMAIS performance.
Agents have attractive characteristics like: autonomy, reactivity, reasoning capability and social ability. These characteristics ensure that agent-based technologies are responsible for enhancing the decision support system capabilities beyond the capabilities of the old model. Any active decision support can be facilitated by the autonomy, reactivity and social ability of agents. Furthermore, the artificial view of agents can contribute towards stronger collaborative relationships between a human and a decision support system. These enormous interests of researchers in investigating the decision support in Multi-Agent Systems is due to the great benefits of combining the decision support technology and Agent-based technology with taking the advantage of the agent characteristics. In this sense, many researches [3-7] recognized the promise that agent -based technologies holds for enhancing DSS capabilities.
IACSIT International Journal of Engineering and Technology, Vol.3, No.1, February 2011 ISSN: 1793-8236
86 extended the work done in DMAIS [2] by proposing a Decision support module in it, this module is concerned about taking the right decisions needed to allocate a specific task to a specific agent, by using the Task Allocation Decision Maker sub-module (TADM). So we spotted on these decisions due to the great importance for them in the improvement of agents’ coordination in DMAIS framework. The rest of the paper is organized as following. Section 2 demonstrates the proposed decision support module. Section 3 discusses the related work on task allocation in Multi-agent Systems. An algorithm for the Task Allocation Decision Maker (TADM) is proposed in section 4, showing the scenario of our algorithm in allocating tasks to specific agent/s. section 5 shows the proposed granular rough model that used in TADM. Section 6shows the experimental evaluation and the results obtained after implementing the proposed algorithm. Section 7 summarizes major contribution of the paper and proposes the topics for future research.
II. DECISION SUPPORT MODULE
In the DMAIS framework [2], the decision support module takes the information collected in the coordination and negotiation module, as shown in fig 1, so that it can help in the decision support process.
Figure 1. The Decision Support Module in DMAIS Framework
Figure 2. Architecture of the Decision Support Module
The Decision support module is activated when a decision is needed from the agent, we concerned about two main decisions that the agent may face: (1) the decision needed to allocate a specific task to a specific agent, making an effective decision for the task allocation problem is a critical job for any multi-agent system; it helps our DMAIS framework to complete its tasks and missions through cooperation among agents. The Task Allocation Decision Maker sub-module (TADM) is responsible for making this decision. (2) The decision needed to select appropriate coordination mechanism, when agents need to coordinate with another agent/s to accomplish a specific task.
The decision support module contains four main phases,
as shown in figure 2, first is the decision knowledge management that contains:
• The database: contains the data that directly related to the decision problem (i.e. the performance measures, the values of nature states).
• The knowledge base: contains the descriptions for roles and structures of document and some knowledge of the problem itself, (i.e. Guide for how to select decision alternatives or how to interpret outputs).
• The knowledge modeling: is a repository contains the decision problem formal models and the algorithms and methodologies for developing outcomes from the formal models. Also contains different process models,
Decision knowledge Management Knowledge
Modeling
Knowledge Base
Database
Action Taker Result Evaluator
Ta
sk
Allo
cation
Decision
Ma
ker
Data Interpreter Decision making method identifier
Proper Action Selection Building the representation model
Calculating the expected utilities of all possiblealternative solutions
Data
Or
ganizer
Agent State Evaluator Attributes estimator
Capabilities estimator
Dependency estimator Behaviors
Task State Evaluator
Urgency degree estimator Demandsestimator
Importance degree estimator Relevant data
from agents
Relevant data from Tasks
C . M Selection
Decision Maker
Probability of success estimator C.M list
Cost Estimator
BonusEstimator
Calculate Maximum values Switch procedure
Module Evaluator
Reasoning Module
Communication Module Decision Support
Module
Planning Module Negotiation Module
Scheduling Module
M
anage
me
nt Module
IACSIT International Journal of Engineering and Technology, Vol.3, No.1, February 2011 ISSN: 1793-8236
87 each model is represented as a set of process and event objects.
Second phase is the data organizer, which organizes agent’s attributes using the agent state evaluator and organizes task’s preferences by using task state evaluator The agent state evaluator estimates the attributes and capabilities of agents, in our work we concerned on specific attributes and characteristics of the agent that will help in the decision making procedure, as shown in fig 3, where:
Figure 3. Attributes, Capabilities and behaviors of Agents Agent attributes is defined as a tuple
<AgentID(A), Addrs(A)> (1)
Where AgentID(A) is the identity of the agent, Addrs(A) records the IP address of agent A.Agent Capability is defined as a tuple
<Availability(A), Ability(A), Intensity(A)> (2)
Where Availability(A) is the ratio of total number of successful agents, capable of accomplishing the task, to the total number of agents in the system,
AVLB(T)= SUC(A) / TOT (A) (3)
Ability(A) indicates number of agents capable of fulfilling the task.Intensity(A) refers to the number of tasks that the agents can accomplish per time unit.
Agent Behaviors is defined as a tuple
< Task History(A), Active degree(A), Dependency(A)> (4)
Where task history(A) stores the number of accomplished tasks that the agent(A) performed. Active degree(A) indicates the activity degree of a specific agent, this degree varies from agent to another according to many parameters (e.g. number of finished tasks, number of cooperation process).Agent Dependency(A) is concerned with the Cooperation Degree of an Agent(A) with respect to other agents in the system.
Third phase is divided into two main Sub-modules: (1)The Task Allocation Decision Maker (TADM) ,this sub-module will be discussed in details in the next sections, and (2) The Coordination Mechanism Selection Decision Maker (CMSDM), that takes the decision needed to select appropriate coordination mechanism, when agents need to coordinate with another agent/s to accomplish a specific task, it will be discussed in our future work. Both of them are responsible on making the proper decisions according to the input obtained from the Data organizer phase. The module evaluator phase is the fourth phase, it has two main goals: first, take the action that the third phase decided to be taken. Second, evaluate the results of taking this action.
III. RELATED WORK
The task allocation in Multi-Agent Systems represent a problem which occupied to a large extends the researchers
of decision support and artificial intelligence until our days. Tasks allocation is defined, in [8], as the ability of agents to self-organize in groups of agents in order to perform one or more tasks which are impossible to perform individually. In our context, it is a problem of assigning responsibility and problem solving resources to an agent. There are two main benefits for Minimizing task interdependencies in the coordination process between the agents: First, improving the problem solving efficiency by decreasing communication overhead among the agents. Second, improving the chances for solution consistency by minimizing potential conflicts. The issue of task allocation was one of the earliest problems to be worked on in Distributed Artificial Intelligence (DAI) research. In this sense, several authors studied the problem related to Task Allocation especially in MAS. The researches in task allocation can be classified in to two main parts, centralized and distributed, based on utility/cost functions.
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IACSIT International Journal of Engineering and Technology, Vol.3, No.1, February 2011 ISSN: 1793-8236
90 information granulation. Missing or null values will increase the uncertainty of information system and the induced rules will not be trusted. These missing values are represented by the set of all possible values for the attribute. To indicate such a situation, a distinguished value, a so-called null value is usually assigned to those attributes. Let , , is the information system, for every a
∈
A, there is a mappinga, a:U→ , where is called the value set of a. If
a∈Acontains a null value (will be denoted as *) for at least one attribute a ∈A, then is called an IIS, otherwise it is complete information systems. Recently, the researchers presented many ways to handle the IIS; these researches can be classified into two main approaches :(1) Indirectly handle the IIS(Data Reparation): This approach is to transforming an IIS to a complete system using estimation methods (probabilistic and statistical techniques). These estimation methods mainly work as estimating the null value based on the appearing frequency of other values with same attribute. The value gained by these methods maybe not archive the best efficiency to the classification of decision attribute because it changes the original information and lead to a lower support degree and confidence degree. That is to say, this approach is to replace unknown value of attributes by either specific subsets of values or statistical values [28-30]. (2) Directly handle the IIS (Model Extension): This approach is to extend the concepts of RST on complete information systems for handling IIS. It does not require the changes in the original system and still is capable of reducing dispensable knowledge efficiently. By using knowledge reduction that eliminates only the information which is not essential from the point of view of classification or decision making or by relaxing the requirement of indiscernibility relation of reflexivity, symmetry and transitivity, i.e., the indiscernibility relation is extended to inequivalence relations that can process IISs directly [31-35]. A Missing Value Estimator (MVE) algorithm is proposed, as shown in figure 7, to handle the IIS based on information granulation. Suppose that
, , is the IIS and let the attribute set isR ⊆C. Based on Kryszkiewicz , in order to deal directly with IIS we can define the tolerance relation as follows:
, ∈ |
∀
c ∈ R, c u c vc u c v . . . (4)
Let SIMR U express the information granular for the
biggest object satisfy the condition.Divide the information table into granules to i condition attributes. If the one of the i condition attribute values of the object is *, it will not be divided into any granules. Information granularity means we can observe and analysis the same problem from very different granularities. GQR is called the information
granularity of information system , , for the R ⊆C.
SIM U , SIM U , … . SIMR U| | . . . (5)
Then the definition of information granularity GQR will be:
GQR | | ∑| | |SIMR U | . . . (6)
Missing Value Estimator (MVE) Algorithm Based on Information Granulation
Input: Associate R c c c
I=1,2,……n where n is the number of condition attributes of information table
I c , c , … . . c
Output: Fill the missing values in the information table. 1. R R , R , … . . R
2. xx:
3. Calculate SIMR U
4. Calculate GQR
5. Foreach c in c
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7. Select c= c
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9. Next
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18. Next
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26. I I c
27. IfI then
28. Exit
29. Else
30. Go to mm
31. End if
Figure 7: The Pseudo Code of MVE Based on Information Granulation
2.Set Approximation
As mentioned in the introduction of RST, set approximation is the kernel concept in RST. The starting point of RST is the indiscernibility relation, generated by information about objects of interest. The indiscernibility relation is intended to express the fact that due to the lack of knowledge we are unable to discern some objects employing the available information. That means that, it is a must to consider clusters of indiscernible objects, as fundamental concepts of RST because there is no ability to deal with single objects. The equivalence classes of the indiscernibility relation are the basic building blocks from which sets of cases or objects can be assembled. Sets of interest to assemble in a supervised learning setting would typically be the sets of cases with the same value for the outcome variable. The set approximation concept add a great benefit in applying it in the decision support module , this is because any decision about the presence or absence of a given category is approximated by lower and upper approximation of decision concept.
In this extension, a notion of granulation order is introduced by using the Granular rough theory, in third phase of GRM model, to propose a Lower approximation Generator (LAG) algorithm and Upper approximations Generator (UAG) algorithm, these approximations of a target set under a granulation order is defined in an incomplete information system. Suppose that , ,
is IIS and R
⊆
C. And as showed in the previous sub-section,SIMR U is a tolerance relation on U, It can be easily shown that:
SIMR U ∈ SIMR c . . . (7)
IACSIT International Journal of Engineering and Technology, Vol.3, No.1, February 2011 ISSN: 1793-8236
91
MaxR U is the maximal set of objects which are possibly indistinguishable by R with u. Let / denote the family sets | ∈ , the classification or the knowledge induced by R. A member MaxR U from
/ will be called a tolerance class or a granule of information. It should be noticed that, in general the tolerance classes in U/SIMR U do not constitute a partition of U, but they constitute a cover of U, i.e.,MaxR U for every u ∈ U , and ∈UMaxR U U .In an incomplete information system, a cover /SIMR U of U induced by the tolerance relation SIMR U , provides a granulation world
for describing a concept X. So a sequence of attribute sets
∈ 2 (n = 1, 2... N)can determine a sequence of granulation worlds, from the most rough one to the most fine one. Based on RST approximations, lower and upper approximations are generated under a granulation order in IIS in the proposed LAG and UAG algorithms, as shown in figure 8(a) and 8 (b), respectively.
Figure 8 (a): LAG algorithm Figure 8(b): UAG algorithm
Let Q is subset of U, Q
⊆
U , ∈ C, and /SIMR c ,thatdenote classification under granulation in IIS ,is defined as: /SIMR c= MaxR u , MaxR u … . , MaxR| | u|U| . . . (8)
The lower and upper approximation to Q fromU/SIMR c
is defined as:
lower R Q u ∈ U|MaxR u ⊆ Q . . . ……(9)
Upper R Q u ∈ U|MaxR u Q . . . (10)
The R-boundary region of Q from U/SIMR c equals the
difference between the upper and lower approximations.
R Q R Q . . . (11)
3. Data Reduction Phase
Attribute reduction can be viewed as the strongest and most characteristic results in RST to distinguish itself from other theories. Since, in real world it is difficult to identify all possible causal attributes, it will be necessary to establish a methodology to identify the critical attributes by eliminating redundant attributes using feature reduction or knowledge compression methods in rough set knowledge systems. This can be achieved by removing the attributes whose removal will not change the indiscernibility relation. Attribute reduction aims to find minimal subsets of attributes, each one of them has the same discrimination power as the entire attributes. A minimal subset of attributes that enables the same classification of elements of the universe as the whole set of attributes is called a reduction, if it cannot be further reduced without affecting the essential
information [36]. The RST provides different methods for finding which attributes separates one class or classification from another. RST generates reduced information table, which implies that the number of evaluation criteria is reduced with no information loss through rough set approach. And then, this reduced information is used to develop classification rules.
The main objective of this section is to propose an Attribute Reducts Generator algorithm ARG, based on information granulation, to be embedded in the fourth phase of GRM model. Based on RST, a lot of attributes reduction algorithms has been developed recently [37], which can be classified into two categories: (1) Attribute reduction from the view of algebra [38,39]. (2)Attribute reduction from the view of information [40,41]. Algebra view only focuses on the positive region of a decision system, while information view also tries to keep the distribution of inconsistent instances in attribute space besides that. In other words, information view restricts attribute reduction more rigorously. Therefore, a reducible attribute in information view is also reducible in algebra view, but not vice versa. The challenging issues of these methods are multiple computations for equivalent classes and huge number of objects.
Although algebra and information view’s definitions are different [39], both of them need to compute equivalent classes. To compute the equivalent classes, let the decision table is DT= (U, C ∪{D}, V) where d c is a distinguished attribute called decision. The value set of conditions c is
c , c , … . . c , the value set of decisions d is d , d , … . . d ,
and The value set of objects o is o , o , … . . o .The notation c o is used to represent the value of a condition attribute ci ∈ C for an object o ∈ U. Similarly, the notation
d o ) represents the value of the decision attribute d for an object o . The concept of indiscernibility relation is adopted to partition the object set U into disjoint subsets, this partition that includes o is denoted by o R, denoted by
U/R or INDR, as shown:
INDR U/R= o R/ ∈ U . . ………….. (12)
Where
o R/ o | c ∈ R c o . . . (13)
The equivalence classes based on the decision attribute are denoted byU/ d , as shown:
IND U/ d = o |o ∈ U . . . (14)
As described in equation (9) and (10), the objects in R Q
can be classified with certainty as members of Q on the basis of knowledge in R, while the objects in R Q can be only classified as possible members of Q on the basis of knowledge in R. Pos d is the positive region of the partition U/ d with respect to C, it can be defined as the set of all elements of U that can be uniquely classified to blocks of the partition U/ d .
Pos d Q∈U/ R Q . . …..…(15)
A reduct is a minimal subset of attributes from C that preserves the positive region and the ability to perform classifications as the entire attributes set C. A subset R ⊆ C is a reduct of C with respect to d, iff R is minimal, and:
PosR d PosC d . . …... ….... (16)
The core is the most important subset of attributes; it is
Input /SIMR c
LA
i=1
i=|U| True
False
i+=1
MaxRU ⊆ True
LA LA u
False
Generate LA
Input /SIMR c
HA
i=1
i=|U| True
False i+=1
MaxRU True
HA HA u
False
IACSIT International Journal of Engineering and Technology, Vol.3, No.1, February 2011 ISSN: 1793-8236
92 included in every reduct. The Core corresponding to this part of information cannot be removed without loss in the knowledge that can be derived from it, it can be defined as:
Core A, d RED A, d . . .………. (17)
Where RED A, d is the set of all reducts of A relative to
d.Decision Table DT=(U, C∩D), where U is a non-empty, finite set called the universal, C is condition attributes set, D is decision attributes set, R U’, C D , U’ U, R is called sub-decision table of DT. Let p DT denote the set of all sub-decision system of DT, F ⊆ DT is called aF family of decision tableDT, RED DT denotes the set which contains all reducts of decision table DT, and RED R denotes the set which includes allreducts of sub-decision table R.
A decision system at least exists one reduct, which is just itself, so the set of reduct is not empty. In many cases, a given decision table may exist several reducts, as it the case in our decision tables (table2). Each reduct can product a rule set, and it is difficult to justify which is the best rule set. Therefore it is a important to search the most stable reduct, dynamic reduct is proposed in this case. The Dynamic reduct of decision table DT, DR (DT, F), is describes as:
DR DT, F RED DT, d R∈FRED R, d . . . (18)
Any element of DR(DT, F) is called an F-dynamic reduct of DT, which describes the most stable reducts in decision table. From the definition of dynamic reducts, it follows that a relative reduct of DT is dynamic if it is also a reduct of all sub-tables from a given family F. This notation can be sometimes too restrictive, so there is a more general notion of dynamic reduct is applied, it is called (F, ε)-dynamic reducts, Where ε is the dynamic reduct threshold and it ranges 1 ≥ε≥ 0. The set DRε(A, F) of all (F, ε)-dynamic
reducts is defined by:
DR DT, F R ∈ RED DT, d : R∈F:R∈RED R,|F| 1 ε . . . (19) Significance of an attribute can be evaluated by measuring effect of removing the attribute from decision table. Let C and D be sets of condition and decision attributes respectively and let a be a condition attribute, i.e.,
C
a ∈ . The number γ(C,D) expresses a degree of
consistency of the decision table, or the degree of dependency between attributes C and D, or accuracy of approximation of U/D by C. If the attribute a removed, the coefficient γ (C ,D) must changes. The difference between
) ,
(C D
γ and γ (C −{a}, D) is normalized and the
significance of the attribute a, is defined as:
) , (
) }, { ( 1 )
, (
)) }, { ( ) , ( ( ) (
) ,
( C D
D a C D
C
D a C D C a
SigF CD γ
γ γ γ
γ − − = − −
=
. . . (20) It can be denoted by SigF a and it ranges
1 SigF(a)
0 ≤ ≤ . The more important is the attribute a, the
greater is the number SigF a . SigF DTJ, a denotes the
significance factor of attribute a within all attributes in sub-decision table DTJ. The Attribute Reducts Generator
algorithm ARG, shown in figure 9, used to generate reducts for our decision tables. The scenario of using this algorithm is: First, the reducts for the whole decision table DT are calculated by this algorithm. Then this decision table is randomly divided into new sub-systemDT , and the dynamic reducts are computed for each sub-table DT , using ARG algorithm too.
Figure 9: The Attribute Reducts Generator Algorithm (ARG) The above algorithm generates RED A, d , is the set of all reducts of A relative to d by incrementally removing the least informative attribute from it till there is no change in the value of dependency function. The positive region of c with respect to d, Pos d , is also calculated to help in generating the reducts of our decision tables.
4. Rule Generation Phase
The basic notations of rule generation concept are introduced in the fifth phase of the GRM model. The rules generation based on granular rough theory, is the output of this model. According to the condition attributes of decision table, the rules are generated. However, not all condition attributes may need to be checked in the sense that some condition attributes are essential to classify and the other attributes are redundant. When the reduced decision table = {U, C ∪D, V} is obtained from the previous phase. Once reducts are found, generating a set of decision rules from this decision table can be an easy process. Every reduced decision table describes some decisions (actions, results etc.), when some conditions are satisfied. In other words, each row of the decision table specifies a decision rule which determines decisions in terms of conditions [41]. A decision rule expressed as a logical statement: IF
conjunction of elementaryconditionsTHEN disjunction of elementary decisions. The decision rule constructed is denoted from a subset B ⊆ C of condition attribute, the set D of decision attributes and an object x ∈ U by (B, x) → (D, x), or in short B D. Decision table is a finite set of “if ... Then” decision rules. With every decision rule three coefficients are associated: the certainty, the coverage, and the strength factors of the rule. These factors are well-known criteria for evaluating decision rules. The
Supp B D) is the support of the decision rule B D
and defined as:
Supp B D | x B d | . . . (21)
False True
True False
Input =(U A) DT=(U C D)
Select random afrom
A
Let , d , A=C
CalculateSigF DT, a , a∈
Ascend |SigF DT, a |
PosRED
Calculate Pos d
Pos d PosRED d
A= , d
, d , d ai Select Max(SigF DT, a
A=A-{a}
Calculate PosRED d
Pos d PosRED d
, d = , d a
Output , d
0 0
False True
Pos d Pos d c
Input IND = o |o ∈ U IND = o |o ∈
IND IND c
Select random c from c
Temp=IND
Let Pos d
Output
P d IND
Temp
Temp Temp d
Select random dfrom d
Ψ=c + d
Ψ
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CONCLUSIO
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decisions: fir cific task to ded to sele And a survey Multi-agent Sy for the Task roposed show
c agent/s. a G
IT International
30 and the a task is also 3
on different numb
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average numb 30. The numb
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nt’s team and same time red h lead to dec ng task alloc ter Run Time
URE WORK
odule is prop ns needed, foc ecision neede agent. Second iate coordin lgorithms in cussed. In add n Decision M nario of alloc
h Model (GR
gineering and Te ISSN: 1793-823 94 ber of ber of am io of GDAP cause urs of mance t, but higher these ferent ously P. As from e the AP is which g task d also duces crease cation e that posed cused ed to d, the nation task dition Maker cating RM) is prop of T cond scala plan mech we i fram [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] echnology, Vol.3 36
posed to gener TADM.Finall ducted, in abilityadvanta to propose hanism select ntend to prop mework.
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