《系统工程》课程教学资源（英文文献）Multi-Agent Model for a distributed Logistic System

Multi-Agent Model for a distributed LogisticSystemGuide Words: Distributed logistic system, multi-agent system.Abstract:Problems approached by logistic system are typically complex in particular the planningof a distributed logistic system which is a complex process implying several constraints. Among theseconstraints we can mention: cooperation between the different organizational entities of the system,the hold in consideration of the diversity of the nature of the product routed and the category of theclient targeted. This paper introduces a new Multi-Agent modeling approach; our model represents adistributed logistic system. Flows are forwarded from a zone to the other one by way of a strategictransport. The needs in flows (medicines flow, clothes flow, foods flow...) are indicated by informationsystem placed in every zone. We want to optimize the routing of these flows from one zone to anotheras well as to satisfy the needs in every zone, knowing that these needs are different according toseveral criteria among which we mention: features of the geographic zone, the nature of the stocks, thestricken individuals in every zone. Indeed, these problems bring us to study several approaches:i Multi-Agent systemii Optimization methodsili Fuzzy logic approachiv Statistics Estimators.In this paper we propose the Multi-Agent technology and the fuzzy estimators as potentialsolutions for the resolution of thiskind of problemsI.INTRODUCTIONMilitary origin concept, the logistics made its entry in the enterprises, about thirty year ago. Itfirst appeared in the sector of the big distribution and the automobile industry. First attached to thetransport or the production, it became a fully-fledged function in the middle of the years 1970 [6],[8]The introduction ofthelogistics within the production system is born out of a need of structuringand supervision of these systems through the organization, the rationalization, hierarchization and thecoordination of the set of its flows.Nowadays, logistic companies must stand in a constant gait ofevolution to remain competitive, inorder to answer to waits and to client's needs. Systems corresponding of such exigencies must

Multi-Agent Model for a distributed Logistic System Guide Words：Distributed logistic system, multi-agent system. Abstract： Problems approached by logistic system are typically complex in particular the planning of a distributed logistic system which is a complex process implying several constraints. Among these constraints we can mention: cooperation between the different organizational entities of the system, the hold in consideration of the diversity of the nature of the product routed and the category of the client targeted. This paper introduces a new Multi-Agent modeling approach; our model represents a distributed logistic system. Flows are forwarded from a zone to the other one by way of a strategic transport. The needs in flows (medicines flow, clothes flow, foods flow.) are indicated by information system placed in every zone. We want to optimize the routing of these flows from one zone to another as well as to satisfy the needs in every zone, knowing that these needs are different according to several criteria among which we mention: features of the geographic zone, the nature of the stocks, the stricken individuals in every zone. Indeed, these problems bring us to study several approaches: i Multi-Agent system ii Optimization methods iii Fuzzy logic approach iv Statistics Estimators. In this paper we propose the Multi-Agent technology and the fuzzy estimators as potential solutions for the resolution of this kind of problems. I. INTRODUCTION Military origin concept, the logistics made its entry in the enterprises, about thirty year ago. It first appeared in the sector of the big distribution and the automobile industry. First attached to the transport or the production, it became a fully-fledged function in the middle of the years 1970 [6],[8]. The introduction of the logistics within the production system is born out of a need of structuring and supervision of these systems through the organization, the rationalization, hierarchization and the coordination of the set of its flows. Nowadays, logistic companies must stand in a constant gait of evolution to remain competitive, in order to answer to waits and to client’s needs. Systems corresponding of such exigencies must

maintain an elevated flexibility level. So, the flexible logistic system of production imposesconstraints of reliability very severe and the least dysfunction of the system can affect the process ofmanufacture. The mastery and the resource management of the logistic system of production areessential to support aflexibleand effectiveprocess ofproduction.The multi -agents system offer a setting of modeling and simulation of the logistic system ofproduction while proposing to represent their elements, their behaviors and their interactions directlyunder the shape of computer entities having their own autonomy.In this article, we will describe, in a first time, a distributed logistic system. After a briefdescription of this system, we will approach its complexity as well as these limits and we will proposea solution based on the multi- agents approach through the management of the set of resources of thelogistic system considered.Thereafter, we are going to adopt a new resolution approach based on the holonic agents at whichwe will apply the fuzzy estimators in the goal to have a better optimization of the distributed logisticsystem.IIPROLEMATICThe management of the flows of a Distributed Logistic System (DLS) spreads on several zones oftreatment while leaving from the supplier of resources and the product to arrive to the customer. Therouting of the flows through the zones is a complex process submitted to several constraints.The difficulty of communication between the different zones, that is an essential element for thepipeline of the information and the management of the products circulating through this chain, presentthe constraints to which the distributed system must make face.Another shutter of the general problematic of our DLS, that is just as complicate that the difficultyof communication between the zones is the optimization of the flows.We chose like tool ofoptimization: the statistical estimators, they will have the rule to inform us on the quantities ofexpanded resources, the speeds of routing of the flows...In current time, the dynamic treatment of the information by the estimators is integrated in aprocess of help at the decision of the DLS. We achieve some models to make appear of the balancesand attractors between the elements, to control the dynamics or even the viability of a system, to helpat the decision and to predict the possible evolutions.2.1 DISTRIBUTED LOGISISTIC SYSTEM (DLS)The distributed logistic system can be considered according to two different ways. We can

maintain an elevated flexibility level. So, the flexible logistic system of production imposes constraints of reliability very severe and the least dysfunction of the system can affect the process of manufacture. The mastery and the resource management of the logistic system of production are essential to support a flexible and effective process of production. The multi -agents system offer a setting of modeling and simulation of the logistic system of production while proposing to represent their elements, their behaviors and their interactions directly under the shape of computer entities having their own autonomy. In this article, we will describe, in a first time, a distributed logistic system. After a brief description of this system, we will approach its complexity as well as these limits and we will propose a solution based on the multi- agents approach through the management of the set of resources of the logistic system considered. Thereafter, we are going to adopt a new resolution approach based on the holonic agents at which we will apply the fuzzy estimators in the goal to have a better optimization of the distributed logistic system. II PROLEMATIC The management of the flows of a Distributed Logistic System (DLS) spreads on several zones of treatment while leaving from the supplier of resources and the product to arrive to the customer. The routing of the flows through the zones is a complex process submitted to several constraints. The difficulty of communication between the different zones, that is an essential element for the pipeline of the information and the management of the products circulating through this chain, present the constraints to which the distributed system must make face. Another shutter of the general problematic of our DLS, that is just as complicate that the difficulty of communication between the zones is the optimization of the flows. We chose like tool of optimization: the statistical estimators, they will have the rule to inform us on the quantities of expanded resources, the speeds of routing of the flows. In current time, the dynamic treatment of the information by the estimators is integrated in a process of help at the decision of the DLS. We achieve some models to make appear of the balances and attractors between the elements, to control the dynamics or even the viability of a system, to help at the decision and to predict the possible evolutions. 2.1 DISTRIBUTED LOGISISTIC SYSTEM (DLS) The distributed logistic system can be considered according to two different ways. We can

maintain an anticipated action that leads us to treat a flows pushed of a supplier toward a customer orif we consider the problem in the opposite direction, from where the notion of drawn flows of thecustomertoward thesupplier.The system that we are going to study is represented by the figure 1.Figure1,Distributedlogisticsystem2.2DIFFICULTIESOFCOMMUNICATIONBETWEENTHEZONESAs we note it in the figure 1, this system presents several zones of treatment of flows andresources. The idea is to route the flows leaving from a regrouping zone via intermediate zones toreach the terminal zones (zones of distribution to the customers). In the terminal zones the flows areconsumed variable-speed.An optimal routing requires a communication between these differentzones.In the problem that interests us, cooperation and the relations of responsibility are essential. Theindependent treatment of the zones can generate redundancies of information or erroneous data sinceevery zone has the incomplete information and capacities limited to solve the problem. These limitswill be able to influence therefore on the global behavior of the system.For this reason, the coordination of the zones proves to be a key element for the reliability of thesystem. Thus, every actor of the chain is going to be able to play its own rule in the zone to which it isaffected on the one hand and associate to the other neighboring zone actors on the other hand.Lately the Multi - Agent modeling have been adopted for the resolution of the problems due to thecomplexity of the distributed logistic system.3MULTI-AGENTSYSTEM

maintain an anticipated action that leads us to treat a flows pushed of a supplier toward a customer or if we consider the problem in the opposite direction, from where the notion of drawn flows of the customer toward the supplier. The system that we are going to study is represented by the figure 1. Figure 1. Distributed logistic system 2.2 DIFFICULTIES OF COMMUNICATION BETWEEN THE ZONES As we note it in the figure 1, this system presents several zones of treatment of flows and resources. The idea is to route the flows leaving from a regrouping zone via intermediate zones to reach the terminal zones (zones of distribution to the customers). In the terminal zones the flows are consumed variable-speed. An optimal routing requires a communication between these different zones. In the problem that interests us, cooperation and the relations of responsibility are essential. The independent treatment of the zones can generate redundancies of information or erroneous data since every zone has the incomplete information and capacities limited to solve the problem. These limits will be able to influence therefore on the global behavior of the system. For this reason, the coordination of the zones proves to be a key element for the reliability of the system. Thus, every actor of the chain is going to be able to play its own rule in the zone to which it is affected on the one hand and associate to the other neighboring zone actors on the other hand. Lately the Multi - Agent modeling have been adopted for the resolution of the problems due to the complexity of the distributed logistic system. 3 MULTI-AGENT SYSTEM

Object for a long time of research in artificial intelligence, the Multi - Agents System form aninteresting type of modeling of societies, have very large application field, active until liberal arts.AMulti - Agent System (MAS) is a set of agents situated in a certain environment and interactingbetween them according to a certain organization [4]An agent is an entity characterized by the fact that it is, at least partially, autonomous. This maybe a process, a robot, a human being, etc.So the solution is gotten thanks to the individual behaviors and interactions. Then the Multi-Agents System represent a new approach for the analysis, the conception and the implantation of thecomputing complex systems [1]The MAS are characterized then by: [2]iA partial perception ofthe environment for every agent,ii The limited expertise that don't allow them to solve the problem individually,iiA decentralization of information,iv The treatments in asynchronous balanced mode3.1PRINCIPLE OF MODELING OFAMULTI-AGENTSA MAS is a network of agents (solvers) weakly coupled that cooperate to solve the problems thatpass the capacities or every agent's individual knowledge. These agents are autonomous and can be ofheterogeneous natures [2].The modeling is going to consist at the establishment of a certain number of distinctions toanalyze this complex reality.The first distinction consists of the separation of the structure of thesystem of agents actual of the one of the domain in which it operates. In our example, we consider asraising of the domain the notions of flows and zones of treatment.We will carry our attention on the modeling of a MAS. While following Ferber [3],[5], we choosethree essential components:i Models of agents (taking into account the individuality of the agents);ii Models of interactions (choose under shape of rules: a same agent capable to play severaldifferentrules);iii Organizational models (representing the global properties of the society of agents)3.2MULTI-AGENTARCHITECTUREPROPOSEDThe Multi - Agent System proposed is constituted of four types of agents: pilot Agent Agpregrouping resources agent AgR, intermediary zone agent Agl, and terminal zone agent AgT [9] The

Object for a long time of research in artificial intelligence, the Multi - Agents System form an interesting type of modeling of societies, have very large application field, active until liberal arts. A Multi - Agent System (MAS) is a set of agents situated in a certain environment and interacting between them according to a certain organization [4]. An agent is an entity characterized by the fact that it is, at least partially, autonomous. This may be a process, a robot, a human being, etc. So the solution is gotten thanks to the individual behaviors and interactions. Then the Multi – Agents System represent a new approach for the analysis, the conception and the implantation of the computing complex systems [1]. The MAS are characterized then by: [2] i A partial perception of the environment for every agent, ii The limited expertise that don't allow them to solve the problem individually, iii A decentralization of information, iv The treatments in asynchronous balanced mode. 3.1 PRINCIPLE OF MODELING OF A MULTI-AGENTS A MAS is a network of agents (solvers) weakly coupled that cooperate to solve the problems that pass the capacities or every agent's individual knowledge. These agents are autonomous and can be of heterogeneous natures [2]. The modeling is going to consist at the establishment of a certain number of distinctions to analyze this complex reality. The first distinction consists of the separation of the structure of the system of agents actual of the one of the domain in which it operates. In our example, we consider as raising of the domain the notions of flows and zones of treatment. We will carry our attention on the modeling of a MAS. While following Ferber [3],[5], we choose three essential components: i Models of agents (taking into account the individuality of the agents); ii Models of interactions (choose under shape of rules: a same agent capable to play several different rules); iii Organizational models (representing the global properties of the society of agents). 3.2 MULTI-AGENT ARCHITECTURE PROPOSED The Multi - Agent System proposed is constituted of four types of agents: pilot Agent Agp, regrouping resources agent AgR, intermediary zone agent Ag1, and terminal zone agent AgT [9] The

table1willincludethenature,theruleandeveryagent'sinteractionwithitsneighboursDeslghationruleInteractionspilot AgentTosupervise-AgkApthem variousstructures oftheAgnAgnDLS-AgrsAgmAgeregroupingStorage of the-Aspoftheresources andflows ready withresources-Agia --Agnthe routingAgentAgaAgent zoneToreceive-ABintemediaryresources andflow of the zone-Agriof regrouping ofAgrmthe resourcesand to distributeAgrthem towardsABa+variots finalAgnzonesfirul zoneAgnToreceive-A8Agertresources iandflowofthe-AgriintermediateAgrm!Zone Direetzone in contactwith Client(destinataire)AgtsTableI description ofthe agentsEvery agent is responsible for its zone, it can answer at a request coming either of the Pilotagent, either of an agent that is hierarchically superior to him.AgRAgiAgTsuppliersrecipientFigure.2Communication AgentsFigure 3 shows that agents of a same zone can cooperatebetween them to exchange theinformation, and also to cooperate with the agents of a neighbor zoneWe focus to optimize this communication on achieving organizations of agents from where theconceptofholonicagents

table 1 will include the nature, the rule and every agent's interaction with its neighbours. Table I description of the agents Every agent is responsible for its zone, it can answer at a request coming either of the Pilot agent, either of an agent that is hierarchically superior to him. Figure.2 Communication Agents Figure 3 shows that agents of a same zone can cooperate between them to exchange the information, and also to cooperate with the agents of a neighbor zone. We focus to optimize this communication on achieving organizations of agents from where the concept of holonic agents

AgpAglAgnAgRAginAgTmFigure3.Multi-AgentModelingof theDLS4HOLONICMULTIAGENTORGANIZATIONHolonic systems were described in 1967by Koestler[7]He started his analysis from thefollowing observation:《Thefirstuniversal characteristic of hierarchies istherelativity,an indeedambiguity of the terms part and 'whole' when applied to any of the sub-assemblies》. It means that inevery hierarchy, an element is viewed differently depending of who is looking at it. It is considered bya part of the system by parent agents, but its sub agent know it as the only parent that can exist, all theothers being hidden by it.So we can schematize a hierarchical system as an overlapping of holonic systems. Each holonicagent belongs to several systems: the one in which it is a sub agent and the one in which it is a parentagent.4.1HOLONICMULTI-AGENTORGANIZATIONOFADLSAn agent and its sub agents make a holonic system. The whole system can be considered as anoverlapping of holonic systems. In the case of a distributed logistic system compound of differentzones, each zone is a holonic agent which is an interface between its parents and its subelements. That means all the transactions between the parents and the sub agent will go through it. Forthe sub agent the only pay rent is the agent itself.The figure 4 presents the different holonic agents of the system

Figure3. Multi-Agent Modeling of the DLS. 4 HOLONIC MULTI AGENT ORGANIZATION Holonic systems were described in 1967 by Koestler[7]. He started his analysis from the following observation: 《The first universal characteristic of hierarchies is the relativity, an indeed ambiguity of the terms ‘part' and 'whole' when applied to any of the sub-assemblies》. It means that in every hierarchy, an element is viewed differently depending of who is looking at it. It is considered by a part of the system by parent agents, but its sub agent know it as the only parent that can exist, all the others being hidden by it. So we can schematize a hierarchical system as an overlapping of holonic systems. Each holonic agent belongs to several systems: the one in which it is a sub agent and the one in which it is a parent agent. 4.1 HOLONIC MULTI-AGENT ORGANIZATION OF A DLS An agent and its sub agents make a holonic system. The whole system can be considered as an overlapping of holonic systems. In the case of a distributed logistic system compound of different zones, each zone is a holonic agent which is an interface between its parents and its sub elements. That means all the transactions between the parents and the sub agent will go through it. For the sub agent the only pay rent is the agent itself. The figure 4 presents the different holonic agents of the system

WholeAemHolonicAgentSubholonicsystemSubholonic systemHolonic天Agent2天人天+天SubSubAgent3Agent4Figure4. Holonic Multi-Agent organization of a DLSHolonic Agent 1 only sees Holonic Agent 2 which represents all the Sub holonic system. The subagents 3 and 4 only know Holonic Agent 2: it is the whole part of their relative system.Especially in the terminal zone, we have a variable speed of consumption, that's why we have toestimate, in thebetter manner, the need of different flows (medicines,clothes, food...).4.2NEEDESTIMATINGAGENTThe Need Estimating Agent (NEA) is an interface for a whole holonic system which is supposedto indicate to a zone agent what it will need, using all the data that the zone agent can provide it4.2.1NEEDESTIMATINGAGENTINADLSEach zone agent has to know its own needs in order to ask for them to the head zone whichsupplies it. It uses two kinds of data to establish them:The zone agent may itself be a supplier for other zone agents in a sub holonic system. Its subagents ask it for what they need. The zone agent pools their requests to ask its own supplier the wholeat the same time. It is also able to satisfy the most urgent needs with a special stock their suppliers hadsent anticipating the consumption. All the requests received are precise and directly useful withoutprocessingthemA zone agent is a supplier for their sub agent, but it is also a consumer for its own needs. Thereare people to feed, engines to fill, etc. To estimate their needs, the system provides a tool that eachagent can use.Thistool isa complex holonic systemwewill call《NeedEstimating Agent》or《NEA》The most sub agents, the only ones which are part of one and only one holonic system, are only

Figure4. Holonic Multi-Agent organization of a DLS Holonic Agent 1 only sees Holonic Agent 2 which represents all the Sub holonic system. The sub agents 3 and 4 only know Holonic Agent 2: it is the whole part of their relative system. Especially in the terminal zone, we have a variable speed of consumption, that's why we have to estimate, in the better manner, the need of different flows (medicines, clothes, food.). 4.2 NEED ESTIMATING AGENT The Need Estimating Agent (NEA) is an interface for a whole holonic system which is supposed to indicate to a zone agent what it will need; using all the data that the zone agent can provide it. 4.2.1 NEED ESTIMATING AGENT IN A DLS Each zone agent has to know its own needs in order to ask for them to the head zone which supplies it. It uses two kinds of data to establish them: The zone agent may itself be a supplier for other zone agents in a sub holonic system. Its sub agents ask it for what they need. The zone agent pools their requests to ask its own supplier the whole at the same time. It is also able to satisfy the most urgent needs with a special stock their suppliers had sent anticipating the consumption. All the requests received are precise and directly useful without processing them. A zone agent is a supplier for their sub agent, but it is also a consumer for its own needs. There are people to feed, engines to fill, etc. To estimate their needs, the system provides a tool that each agent can use. This tool is a complex holonic system we will call《Need Estimating Agent》or《NEA》. The most sub agents, the only ones which are part of one and only one holonic system, are only

consumers. They just have to use the NEA to know what to order4.2.2NEAAPPROACHThe NEA mainly works using fuzzy logic calculation. The zone agent provides to the NEA theneeded data in order to complete the calculation. A human expert is in charge to estimate those data.He has to provide the real data acquired on the field (how many persons to feed, etc.) and someestimation inorderto createthemembershipfunctions andtherulematrixAnoptimizationprocesswillbeabletocorrectthoseestimationstomakethemorepreciseanswertheNEAcouldcalculate.Our system must react according to dun measures require the representation of the phenomenonmeasured under the shape of a dependent mathematical model of a certain number of parameters. Ingeneral the model doesn't give rigorously account of the reality.Besides, the measures are most of the time mixed with a noise and a too complex model wouldnot present a convenient interest anymore that a simplified model. To reach this goal, it is necessary todefinethe criteria first of all.The resolution of such criteria could be doneby recursive root mean square, or the method of themoments, by adjustment method..4.2.3USEOFFUZZYLOGICThe NEA algorithm is based in the fuzzy logic approach It uses the fuzzy data provided by thezone agent and optimized the different local variables giving by the others estimating agents describedin the figure 5.NEHolonic SystemNEAAlgorithmLocalLocalEstimatingEstimatingAgentiAgent3LocalEstimatingAgent2Figure5.Need estimating holonic systemThe NEA does not only do a fuzzy logic calculation. The input data for the calculation areoptimized to correct the expert's appraisal error using the NEA experience

consumers. They just have to use the NEA to know what to order. 4.2.2 NEA APPROACH The NEA mainly works using fuzzy logic calculation. The zone agent provides to the NEA the needed data in order to complete the calculation. A human expert is in charge to estimate those data. He has to provide the real data acquired on the field (how many persons to feed, etc.) and some estimation in order to create the membership functions and the rule matrix. An optimization process will be able to correct those estimations to make the more precise answer the NEA could calculate. Our system must react according to dun measures require the representation of the phenomenon measured under the shape of a dependent mathematical model of a certain number of parameters. In general the model doesn't give rigorously account of the reality. Besides, the measures are most of the time mixed with a noise and a too complex model would not present a convenient interest anymore that a simplified model. To reach this goal, it is necessary to define the criteria first of all. The resolution of such criteria could be done by recursive root mean square, or the method of the moments, by adjustment method. 4.2.3 USE OF FUZZY LOGIC The NEA algorithm is based in the fuzzy logic approach. It uses the fuzzy data provided by the zone agent and optimized the different local variables giving by the others estimating agents described in the figure 5. Figure5. Need estimating holonic system The NEA does not only do a fuzzy logic calculation. The input data for the calculation are optimized to correct the expert's appraisal error using the NEA experience

The NE holonic system contains several statistic estimating agents which are able to correct thosedata with their own experience, knowing older requests. A database agent will store all the previousresults and a mark to qualify each of them and to determine their relevance4.2.4 SIMULATION STEPSThe five following steps constitute the rules of optimization:(1) The holonic agent receives a request for an estimation made up of membership functions andrule matrices, as well as source values observed on the field. The functions and matrices are given byan expert,(2) Each of the functions and matrices will be optimized by the estimating agents. Each of themproduces an estimation according to the stats that it has memorized,(3) The NEA receives the results of the estimations. Using a genetic learning, it optimizes thereceived values to create a unique one, according to the marks it gave to each estimating agents, anddo the fuzzy logic calculation;(4) The NEA send the calculated results to the agent zone which asked for it;(5) Later, the zone agent sends a feedback to the NEA about the quality of the answer it gave. Thisfeedback will serveto improve thegenetic and the statistic optimization:i. The feedback is sent to the estimating agents to complete their statistic database and naturallyimprove the statistic estimations;ii. The feedback is used by the NEA too. It compares the real result with each optimization theestimating agents gave him during step 3. He gave each estimating agent a mark from this comparison.The average mark will be used to mix the estimating agents corrections during the next transactions5EVALUTIONOFTHERESULTSWe achieved some tests fortwo linear estimatorsi linear regression;ii point to point, it has the particularity to deactivate itself if the value to optimize overflow of theinterval of values that it knows.We will consider three parameters of optimization: the temperature, the humidity degree and thenumberofpresent people onthe site.Therefore we are going to vary the number of people and the Conditions weather report will bestable: 20 °, 90% of humidity.We also suppose that for the studied material, the middle debit is of 100 units per week for 100

The NE holonic system contains several statistic estimating agents which are able to correct those data with their own experience, knowing older requests. A database agent will store all the previous results and a mark to qualify each of them and to determine their relevance. 4.2.4 SIMULATION STEPS The five following steps constitute the rules of optimization: (1) The holonic agent receives a request for an estimation made up of membership functions and rule matrices, as well as source values observed on the field. The functions and matrices are given by an expert; (2) Each of the functions and matrices will be optimized by the estimating agents. Each of them produces an estimation according to the stats that it has memorized; (3) The NEA receives the results of the estimations. Using a genetic learning, it optimizes the received values to create a unique one, according to the marks it gave to each estimating agents, and do the fuzzy logic calculation; (4) The NEA send the calculated results to the agent zone which asked for it; (5) Later, the zone agent sends a feedback to the NEA about the quality of the answer it gave. This feedback will serve to improve the genetic and the statistic optimization: i. The feedback is sent to the estimating agents to complete their statistic database and naturally improve the statistic estimations; ii. The feedback is used by the NEA too. It compares the real result with each optimization the estimating agents gave him during step 3. He gave each estimating agent a mark from this comparison. The average mark will be used to mix the estimating agents corrections during the next transactions 5 EVALUTION OF THE RESULTS We achieved some tests for two linear estimators i linear regression; ii point to point, it has the particularity to deactivate itself if the value to optimize overflow of the interval of values that it knows. We will consider three parameters of optimization: the temperature, the humidity degree and the number of present people on the site. Therefore we are going to vary the number of people and the Conditions weather report will be stable: 20 °, 90% of humidity. We also suppose that for the studied material, the middle debit is of 100 units per week for 100

people.This debit varies according to the temperature on the site and the humidity (representativeinformation of the conditions weather report). This variation is calculated from a law based on thefuzzy logic. The original fuzzy law is written according to an expert's opinion and requires areasonablerefinementthereforeThe site has a life span of eight weeks. The first two weeks represent the establishment of the siteandthetwolastitsevacuation.The estimators need two statistical points to functionTherefore they will be considered from the third week5.1FIRSTTESTFor the Multi-Agent system design, we use the platform Jade which integrates the agent'sfunctionalitiesunderaCaionionBageneOcdng agctagent1agent 486.264486.264iransac186.26186.264450.015001ono33ransas58.71350.05001798.53ans1800.022000800.1on2AEEIrans699.4630002700.012249,2250.05002250.0A2249,rans92250.0525002250.0ons1171.111264.23Iransa70.181170.01300170.069174on6ransd675.0321S750265Table2FirsttestresultsTheresultsfoundinthetabletwopermitustodrawthefollowingfigure30025002000eapepetoo150010005000500100015002003000200003600nunberdpersonsFigure7.LinearEstimation5.2SECONDTEST

people. This debit varies according to the temperature on the site and the humidity (representative information of the conditions weather report). This variation is calculated from a law based on the fuzzy logic. The original fuzzy law is written according to an expert's opinion and requires a reasonable refinement therefore. The site has a life span of eight weeks. The first two weeks represent the establishment of the site, and the two last its evacuation. The estimators need two statistical points to function. Therefore they will be considered from the third week. 5.1 FIRST TEST For the Multi-Agent system design, we use the platform Jade which integrates the agent's functionalities. Table 2 First test results The results found in the table two permit us to draw the following figure Figure7. Linear Estimation 5.2 SECOND TEST