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A hybrid particle swarm optimisation algorithm andfuzzy logic for process planning and productionscheduling integration in holonic manufacturingsystemsFuqing Zhao a , Yi Hong a , Dongmei Yu a , Yahong Yang b & Qiuyu Zhang aa School of Computer and Communication, Lanzhou University of Technology , Lanzhou,730050, Gansu, P.R. Chinab College of Civil Engineering, Lanzhou University of Techchnology , Lanzhou, 730050,Gansu, P.R. ChinaPublished online: 11 Jan 2010.

To cite this article: Fuqing Zhao , Yi Hong , Dongmei Yu , Yahong Yang & Qiuyu Zhang (2010) A hybrid particle swarmoptimisation algorithm and fuzzy logic for process planning and production scheduling integration in holonic manufacturingsystems, International Journal of Computer Integrated Manufacturing, 23:1, 20-39, DOI: 10.1080/09511920903207472

To link to this article: http://dx.doi.org/10.1080/09511920903207472

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A hybrid particle swarm optimisation algorithm and fuzzy logic for process planning and production

scheduling integration in holonic manufacturing systems

Fuqing Zhaoa*, Yi Honga, Dongmei Yua, Yahong Yangb and Qiuyu Zhanga

aSchool of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu, P.R. China; bCollege ofCivil Engineering, Lanzhou University of Techchnology, Lanzhou 730050, Gansu, P.R. China

(Received 29 January 2009; final version received 25 July 2009)

Modern manufacturing systems have to cope with dynamic changes and uncertainties such as machine breakdown,hot orders and other kinds of disturbances. Holonic manufacturing systems (HMS) provide a flexible anddecentralised manufacturing environment to accommodate changes dynamically. HMS is based on the notion ofholon, an autonomous, co-operative and intelligent entity which is able to collaborate with other holons to completethe tasks. HMS requires a robust coordination and collaboration mechanism to allocate available resources toachieve the production goals.

In this paper, a basic integrated process planning and scheduling system, which is applicable to the holonicmanufacturing systems is presented. A basic architecture of holonic manufacturing system is proposed from theviewpoint of the process planning and the scheduling systems. Here, the process planning is defined as a process toselect suitable machining sequences of machining features and suitable operation sequences of machiningequipments, taking into consideration the short-term and long-term capacities of machining equipments. A fuzzyinference system (FIS), in choosing alternative machines for integrated process planning and scheduling of a jobshop in HMS, is presented. Instead of choosing alternative machines randomly, machines are being selected basedon the machine’s capacity. The mean time for failure (MTF) values are input in a fuzzy inference mechanism, whichoutputs the machine reliability. The machine is then being penalised based on the fuzzy output. The most reliablemachine will have the higher priority to be chosen. In order to overcome the problem of un-utilisation machines,sometimes faced by unreliable machine, the hybrid particle swarm optimisation (PSO) with differential evolution(DE) has been applied to balance the load for all the machines. Simulation studies show that the proposed systemcan be used as an effective way of choosing machines in integrated process planning and scheduling.

Keywords: holonic manufacturing systems (HMS); process planning, production scheduling; particle swarmoptimisation; differential evolution (DE)

1. Introduction

A holonic manufacturing system (HMS)(HMS Con-sortium) (Van Brussel et al. 1998) is a manufacturingsystem where key elements, such as machines, cells,factories, parts, products, operators, teams, etc., aremodelled as ‘holons’ having autonomous and co-operative properties.

The decentralised information structure, the dis-tributed decision-making authority, the integration ofphysical and informational aspects, and the coopera-tive relationship among holons, make HMS a newparadigm to meet today’s agile manufacturing chal-lenges (Valckanaers et al. 1997, Giret and Botti 2006).

Manufacturing scheduling is very important be-cause of its direct link to product delivery, inventorylevels, and machine utilisation. Effective scheduling,however, has been proven to be extremely difficultbecause of the combinatorial nature of integer

optimisation and the large size of practical problems(Cooke 2004). In practice, material planning systems,e.g. MRP or MRP II are often used for high-levelproduction planning and scheduling (Turgay andTaskin 2007). MRPII system is a hierarchically struc-tured information system which is based on the ideaof controlling all flows of materials and goods byintegrating the plans of sales, finance and operation, inapplying MRPII in practice, one of the main problemsis that there is little help with the necessary aggregationand disaggregation process, especially when uncertaindemand exists. Because these systems generally ignoreresource capacities, resulting plans or schedules areusually infeasible. Many heuristic methods have beendeveloped to dispatch parts at the local (resource ormachine) level based on due dates, criticality ofoperations, processing times, and machine utilisation(Malakooti 2004, Axsater 2007, Monch Lars et al. 2007,

*Corresponding author. Email: fzhao2000@hotmail.com

International Journal of Computer Integrated Manufacturing

Vol. 23, No. 1, January 2010, 20–39

ISSN 0951-192X print/ISSN 1362-3052 online

� 2010 Taylor & Francis

DOI: 10.1080/09511920903207472

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Pedersen et al. 2007). Artificial intelligence (AI)approaches have also been proposed based on theapplication of scheduling rules (Jawahar et al. 1998,Masood 2004, Yin Xiao-Feng and Wang Feng-Yu2004). Schedules obtained by heuristics, however, areoften of questionable quality, and there is no good waysystematically to improve the schedules generated.

The concept of holonic manufacturing has beenstudied by IMS-HMS consortium. Similar researchhas been performed under the banner of ‘agent-basedmanufacturing.’ When applied to manufacturing, anagent is a software object representing an element in amanufacturing system such as a product or a machine.Similar to a holon, an agent may have autonomousand cooperative properties, and is the building block ofthe system.

In practice, scheduling and planning problems areconsidered together as manifested in classic combina-torial problems (Wang et al. 2008, Chan et al. 2009,Shao Xinyu et al. 2009). The practical problems alwaysinvolve multiple objectives that need to be addressedsimultaneously. Hence, the actual optimisation objec-tive is to determine the process plan and scheduleconcurrently. Owing to the complexity of manufactur-ing systems, process planning and scheduling are oftencarried out sequentially with little communication.Process planning seldom considers job shop capacityand scheduling information, such as resource capacityand availability. Production scheduling, on the otherhand, is performed under fixed parameters withoutalternatives which provide alternative productionflows. Re-planning is frequently required by improvisa-tion with a long throughput time and other unexpectedproblems. During the last decade, several integrationapproaches have been proposed, but most integratedprocess planning and scheduling methods focused onthe time aspects of alternative machines when conduct-ing scheduling.

HMS is a holarchy which integrates all proceduresof manufacturing activities from order managementthrough design, production and marketing to fulfillthe agile manufacturing enterprise. An HMS istherefore a manufacturing system where key elements,such as raw materials, machines, products, parts, andAGVs, have autonomous and cooperative properties(Deen 2003.).

Currently, HMS consortium partners have devel-oped their own testbeds using their existing softwareand hardware environments under the same conceptsand similar system architectures. Most of the earlyresearch results on HMS were reported only internallyin the HMS consortium. However, some results havebeen published, (McFarlane and Bussman 2000) givea review of existing work in holonic manufactur-ing systems relevant to production planning and

control, and provide an analysis of the scope andapplicability for specific application domain. Heragu,et al. proposed a framework, which models the entities(e.g., parts) and resources (e.g., material handlingdevices, machines, cells, departments) as holonicstructures, and introduces real-time negotiation me-chanisms to solve task allocation and planningproblems (Heragu et al. 2002). Leitao, Paulo andRestivo, Francisco present a holonic approach tomanufacturing scheduling which combines centralisedand distributed strategies to improve responsiveness ofmanufacturing systems to emergence (Leitao andRestivo 2002, Leitao and Restivo 2008). A decentra-lised holonic approach in manufacturing planningand control is presented to allocate materialhandling operations to the available system resources(Babiceanu and Chen 2009). Shrestha et al., adoptgenetic algorithm (GA) and dispatching rule (DR) inan integrated process planning and scheduling systemwhich is applicable to HMS (Shrestha et al. 2008). Raiset al., applied the GA and the dynamic programming(DP) methods to select suitable machining sequencesand sequences of machining equipment in holonicmanufacturing control and planning systems (Raiset al. 2002). It has become a very active research areawith a large number of publications including severalrelated books (Deen 2003, Vladimır Marık 2007,Vicente and Adriana 2008).

Applications of HMS have been at the inter-enterprise level on holonic collaborative enterprises,and mostly at the enterprise and manufacturing sys-tem level, and at the manufacturing execution system(MES) level (Vladimır Marık et al. 2007, Vicente andAdriana 2008).

The objective of this paper is to present anintegrated process planning and scheduling systemwhich aims at realising a flexible production control inholonic manufacturing systems. This paper dealsmainly with the process planning of product machiningprocess, taking into consideration the future schedulesof machining equipments. The following issues arediscussed in the paper: (a) basic architecture of targetHMS and process planning systems; (b) formulation ofan objective function based on job time and machiningcost of products; and (c) procedure to select suitablemachining sequences and sequences of machiningequipment for integrating the process planning taskwith the scheduling task.

In this paper, a fuzzy logic (FL) is proposed todecide alternative machines for integrated processplanning and scheduling. The FL is introduced forthe purposes of choosing appropriate machinesbased on the machines’ reliability characteristics.This ensures the capability of the machine in fulfillingthe production demand. In addition, based on the

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capability information, the load for each machineis balanced by using the hybrid particle swarmoptimisation (PSO) with differential evolution (DE).The remainder of the paper is arranged as follows:Section 2 describes a holonic architecture for manu-facturing systems and common scheduling problemsand challenges. A proposed method to face thesechallenges is proposed in Section 3. Analysis resultsand discussions are provided in Section 4. Finally, theconclusions and future researches are given out inSection 5.

2. A holonic architecture for manufacturing systems

and common scheduling problems

Figure 1 illustrates a holonic architecture that we areproposing for manufacturing systems with the focus onthe system parts of process planning and productionplanning. The figure illustrates components of amanufacturing system holarchy. In Figure 1, resourceholons (e.g. machines, robots) and task holons(product orders) are grouped in scheduling holons.Scheduling holons are grouped with other holons (e.g.stock management holon, etc) and form productionplanning holons. One holon may be part of more thanone holarchy. For example, a resource holon may bethe member of a scheduling holon and of a processplanning holon at the same time. This kind ofarchitecture provides more flexibilities than static andtraditional computer integrated manufacturing (CIM)architectures do.

2.1. The initial planning holon

In the holonic manufacturing system, each holoncooperates with other holons and makes use ofexternal resource to accomplish the task delivered bythe system. So the chains from customer requirement,through internal production planning holon andcooperative production task holon to supplier deliv-ered task are established in the system, as shown inFigure 2.

After analysing the relationship and activity ofeach pair of entities, we find that we can model therelations between each pair of entities as the connec-tion of customers and suppliers. The role of the initialplanning holon is that of matching the task andresource capacity to accomplish the task that is fulfilledby the supplier. The decision processes are based on asupply and demand relationship and the outcomes aredecided by selling and buying activity in respect ofthe resource and by market behaviour. As shown inFigure 2, there are four basic elements in the marketbehaviour: supplier, customer, item required and rulesof transaction.

Suppliers are the holders of resource and theproviders of the requirement of the project. Thecustomer is the consumer of the requirement. Supplierand customer can be the rational entities of supplier,manufacturer, subseller, section in manufacturingenterprise and customer. The project requirement isthe stuff which has value for the customer, includingprocessed materials, semi-finished articles, final

Figure 1. The holonic architecture.

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product, services, and so on. Transaction rules arethe criteria of transfer of project ownership fromsupplier to customer. That is to say, the rules fortransaction and trade for resource capacity are indifferent time.

In the initial planning holon, all the relationsbetween suppliers and customers are dynamic.Customer orders first enter into the system, accord-ing to the item required by customers, and the initialorder details are generated by the order holon.Product holons generate the detailed information forthe concrete production according to the collabora-tion information delivered by the order holon, thenthe product holons need to select the suppliersaccording to the different component combinationto fulfil the customer order. In addition, productholons simultaneously need to collaborate withresource holons according to the capacity ofthe resource combination. All the processes in thecollaboration are guided by certain rules in theconcrete transaction.

In the application of the system, roles can change.For example, when one holon provides the resource toanother holon, its role is as supplier. It will, however,play the customer role when capacity cannot meet the

requirement and it turns for help to another holon. Inthe market mechanism all we need to do is to define theconnectivity and activity of the entities in the holonicmanufacturing system. So, when an enterprise holonlays out its production planning, it can use marketmechanism method based on market equilibriumtheory, and apply it to the modification feature thatmatches order/task to resource in the market, andconsequently lay out the appropriate strategy, rule, oroptimisation method to realise the optimum allocationof resource. The production planning and controlsystem can respond to the market quickly through theholonic manufacturing system. The responsiveness canbe seen at several points: 1) when the production taskand resource experience changes, the system canreconfigure to set a new production planning andcontrol system. 2) the system can collect, save, fetchand keep track of the information online. 3) it canrespond quickly when the resource encounters anyproblems.

2.2. The detailed planning holon

A scheduling holon includes two kind of holon:resource holons and task holons, as shown in Figure 3.

Figure 2. Initial planning holon.

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The resources are basic components of a manu-facturing system (robots, NC machine, conveyors) orthey can be cells made up of basic resources. Eachresource is presented by a holon. The number ofresources does not vary, except when resources areintroduced or removed from the manufacturingsystem. A resource holon represents one resourcewith status, such as delivered activities and activities tobe carried out. The activity of a resource is representedin an agenda. The agenda is the sequence of operationsto be carried out and it specifies the expected durationsfor these operations as well as the free time intervals ofthe resource (Cheng 2004). The activity of a resourcechanges according to the operation of the resourceand the dynamic situation of the manufacturing sys-tem (e.g. new orders, failures and delays in otherresources).

The function of a task holon is managing thetask system undertaken. It accepts the static pro-gramming and overall monitoring from the supplier;on the other hand, it will feedback the status of taskwhich is carried on to the supplier. In some cases, ifthe activities which are implemented by task holonsare the activities corresponding with input/outputinterface, task holons will communicate with thesuppliers by input message/output message. Inaddition, task holons will collaborate with othertask holons to propel the finish of the task under thesatisfactions of priority. Furthermore, task holonswill communicate with production holons andresource holons to instruct the task allocationaccording to the capacity constriction of the re-sources. Last but not least, task holons will monitorthe task progress online and adjust according to thetimely status collected in the system.

The ‘task manager’ interfaces with the userreceiving orders for new tasks for the manufacturingsystem. This holon is responsible for launching ‘taskholon’ whenever a new task is ordered. Besides, thetask manager is responsible for dealing with dynamicchanges of task conditions (e.g. when the userchanges the deadline of a task). Task holons

represent the possibilities to execute a plan for atask into a plan structure (Stahmer 2004, Babiceanuet al. 2005). The task manager has the knowledgeabout the resources that each task may need. Oncelaunched, they directly negotiate with appropriateresource holons. The task manager is responsible forlaunching task holons, however, it will not launchtask holons immediately after receiving requests fromusers. the task manager maintains a priority list ofwaiting tasks. The next task holon to be launched isthe one with more priority and that does not conflictwith other tasks that are still negotiating withresource holons. The possibility of conflict is detectedwhen a task needs a resource that has received taskannouncement messages but has not received thecorrespondent acknowledgements or ‘give up’ mes-sages. This means that this resource is still establish-ing a contract with other previously launched taskholons.

The task holon and initial planning holonexchange production operation information whichincludes the information and method on how toaccomplish certain processes in corresponding re-sources with constriction of time and cost, i.e. theprocess can be fulfilled by the certain resourcescombination with the required machining parametersand quality. The production knowledge, whichincludes information and methods on how to utilisecertain resources to produce a certain type produc-tion, is communicated between production holon andtask holon. In the process of communication withproduction holon and task holon, the productionprocesses certain resource, the data structure forexpressing production results and evaluation methodsfor production planning belong to production knowl-edge. The machining operation knowledge flowsbetween production holon and operation holon. Theprocedure in the collaboration is monitored by theon-line supervision holon, which can also makesuggestions for all the holons involved.

In an HMS, holons may form holarchies whosemembers collaborate through Cooperation Domains.Using the mechanism of virtual clustering, holons canbe dynamically involved in different clusters (holar-chies) and cooperate through a Cooperation Domain.The cluster exists for the duration of its cooperationtasks and disappears when the tasks are completed. Acooperation domain can be implemented and main-tained through the creation of a mediator holon (asshown in Figure 4).

The process of the operation is as follows.

(1) A new order/task is generated in the marketduring the system operation. The orderholon will send a bidding request to a

Figure 3. Task and resource holons for scheduling.

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resource holon. The information format can bedefined as

Bidding ¼ forder=taskID; title; Number;Time;Cost; Resource; order Descriptiong

order Description ¼ forder Deadline; orderConstriction; order Priority; order Statusg

order Status ¼ ffinished; performing;waiting; unschedulingg

The functions of order holon include thefollowing aspects.(a) Assess order: analyse the feasibility of the

order, obtain the validity of the order, andcompute the possibility of the candidateorder.

(b) Generate order, after the process of theassessment to the order, the detailed orderdocumentary, which has legality in thebusiness transaction, is generated. Mean-while, the uniform data format of thegenerated order which is convenient to beprocessed is needed.

(c) Reply to the collaboration request. In thisprocedure, order holon handles the colla-boration request during the process oforder assessment and communication withouter environment to facilitate the successof the order assessment.

(d) Reply to the request information fromcustomer, order holon handle the requestinformation when customers ask for a checkon the progress of the order and then

feedback the search information tocustomers.

(2) The resource holon will communicate with theproduct holon and make sure whether it cansatisfy the technical requirement for the pro-duction order such as machining methods,machining precision etc. Then it will decidewhether to bid for the order/task according tocapacity and benefit to the process. When theresource holon obtains the order/task it willcreate an order/task holon to group the virtualorder/task clustering and start up the planningholon.

(3) The planning holon will set up productionplanning for the order having the highestpriority. It communicates with the productionholon, breaks down the order/task accordingto the design, process and related informa-tion, and method, extracts the resourcerequirement model, acquires the scheme ofresource requirement, and confirms the objec-tive of the subtask/order to generate theinformation that constitutes the subtask/order.

(4) The planning holon invokes the mediator holonto deliver the subtask/order holon to themediator holon to apply the resource. Themediator holon sends the subtask/order infor-mation to subholon of local holon or candidateholon partner according to history and registerinformation. The planning holon also receivesbids from other holons.

Figure 4. The scheduling holon’s interaction with other holons.

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(5) The subresource holon and other resourceholons bid to undertake the task/order accord-ing to how they evaluate their interest in it. Themediator holon classifies the market and selectsthe resource holon according to task applicationresult, resource storage, priority etc. When thereis any collision in the system, it negotiates withother connected holons to adopt a differentnegotiation strategy. Finally, the mediatorholon informs the planning holon of thecandidate holon for carrying out the sub task/order.

(6) The planning holon invokes the schedulingholon. The scheduling holon allocates the taskto a candidate resource holon by applying aparticular optimisation algorithm. The schedul-ing holon creates a subtask holon whichconnects with the corresponding resource holonto analyse the task into its basic elements.

(7) If the task has not been broken down into itsirreducible elements, basic tasks which can notbe divided, and the resource has not been laidout into the basic resource holarchy constitutedby the manufacturing entities, then the aboveprocedure repeats and recursion operates. Thesubtasks for the realisation of the whole taskcan be isolated. The resource is also designatedfor each subtask. Different layer and taskoriented dynamic virtual clustering for thetask/order is built up.

The proposed holonic system and the interactionprocess are implemented on the JADE (Java AgentDevelopment Environment) platform. JADE is amulti-agent system platform which conforms strictlyto FIPA criteria. The JADE programmer can useJAVA to exploit systems when the agent is built(Administrator Guide, Programmer Guide). Mean-while, because JADE simplifies the communication

process between agents by delivering messages whichabide by FIPA criteria (FIPA), the message can alsobe inserted into the sequenced object to realise thestandardisation parameter delivery. Furthermore, theyellow function can be directly used because DFfunction is provided by JADE to guarantee the registerfor customer systems. With AMS and Sniffer toolsprovided by JADE, users can debug the implemen-tation platform and easily achieve the total function-ing of the system. The startup interface is shown inFigure 5.

2.3. Expanded job-shop scheduling problem (EJSSP)(Li and Pei-Huang 2004)

EJSSP is a deterministic and static scheduling problem.There are m distinct machines to process n jobs thathave their specific processing routines. Each job’soperation has its precedence and takes up a determi-nistic time period at a specific machine. At one time,there is only one operation at a machine and the jobdoes not leave this machine until the operation iscompleted. The operation starting time of each jobmust be within predefined regions, which are subject tothe available time and due dates of jobs. Enablingconditions of an operation are prescribed by techno-logical planning including job and resource require-ment such as machines and fix tools, as well as cuttingtools. It can be seen easily that EJSSP is significantlymore general than the standard job-shop schedulingproblem (JSSP).

2.4. Modelling and analysis of EJSSP

Expanded job-shop scheduling problem (EJSSP) is adeterministic and static scheduling problem. Each job’soperation has its precedence and takes up a determi-nistic time period at a specific machine (Yu Haibin2001, Petrovic Sanja and Petrovic 2008).

Figure 5. Startup interface of JADE platform.

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2.4.1. Notations for EJSSP

The symbols for modelling scheduling problems are asfollows:

n number of jobs;ni number of operations of job i;m type number of various resources;rs number of resources of type s, s 2 [1,2, . . . ,m];Ri set of pairs of operations {k,l} belonging to job

i, operation k precedes l;Qi set of pairs of operations {k,l} belonging to job i;Nq set of operations requiring resource q,

q 2 [1,2, . . . r];H large enough positive number;til processing time of operation l of job i,

l 2 [1, . . . , ni];xik starting time of operation k of job i,

k 2 [1, . . . , ni];xsi starting time of the first (or free) operation of

job i;xie completion time of the last (or free) operation

of job i;ai availability time of job i;di delivery due date of job i;[i,k] the kth operation of job i, also called

operation k in short if no confusion iscaused;

ykl ¼1 if operation k precedes operation l0 otherwise

�

where {k,l} 2 Qi, i ¼ 1,2, . . . ,n;

zij ¼1 if operation i precedes operation j0 otherwise

�

where {i,j} 2 Nq, q ¼ 1,2, . . . , rs, s ¼ 1,2, . . . , m.Note: i 2 [1, . . . , n]; s 2 [1, . . . , m]; free operationmeans operation without precedence restrictions fromtechnological planning.

2.4.2. Modelling and analysis of EJSSP

A feasible solution means that the scheduling satisfiesall constraint conditions. There are mainly four typesof major constraints for any operation as follows:

(1) Precedence constraint. Precedence constraintmeans that some jobs must be processed atdifferent machines in fixed precedence sequencedefined by technological planning. Concretely,the lth operation of job i must be before thekth operation of the same job, tik meansprocessing time of operation of k of job i, if{k,l} 2 Ri, i.e.

Xni¼1

Xnil¼1

xil �Xni¼1

Xnik¼1

xik

� max

�Xmj¼1

Xdit¼1ðtþ dijÞyijðtÞ;

Xmj¼1

Xdit¼1

tykjðtÞxil � tik

�ð1Þ

(2) Resource constraint. Resource constraint meansthat any resource can only provide service forone operation at a time; for example, resource qcan only be selected by one job waiting to beprocessed in the queue at any time.

Xni¼1

Xnij¼1

xij �Xnij¼1

Xmk¼1

xjk

þYni¼1

Xmi

j¼1

Xdt¼1

yijðtÞðxij � xjkÞ

þXnk¼1

Xnil¼1

Hð1� zklÞ � 0

iffk; lg 2 Nq

ð2Þ

(3) Job (hidden) constraint. Although there may beno precedence constraint among some opera-tions of a job, the constraint that the operationsl and k could not be processed at the same timestill exists because these two operations weredone by the same job, i.e.

Xni¼1

Xnij¼1

xij �Xni¼1

Xnil¼1

xil

þYnk¼1

Xni¼1

Xnit¼1ðzijðtÞðxij � xjkÞ

þHð1� yklÞÞ �Xni¼1

Xnik¼1

tik

iffk; lg 2 Qi

ð3Þ

(4) Starting and completion time constraint. Inpractice, the starting time and that the comple-tion time of a job are restricted by the availabletime and the due date of delivery. Mathemati-cally, it can be depicted by Equations (4)and (5).

Xnk¼1

Xdt¼1fxsiðyikðtÞ � zikðtÞÞ � aig � 0

i 2 ½1; � � � ; n�ð4Þ

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Xni¼1

Xdt¼1fxieðyikðtÞ� zikðtÞÞ�di� tieg� 0

i2 ½1; � � � ;n�ð5Þ

Minimising the total penalty for early andtardy jobs

Min Z ¼Xni¼1

Xdit¼1

Xnik¼1

½zikðtÞ �max ð0; di � xieÞ

þ yikðtÞ �max ð0; xie � diÞ�

ð6Þ

2.5. Problems of traditional process planning

While ‘manufacturing’ refers to producing parts thatmeet specifications, process planning refers to the setof instructions that is used to make parts that meetspecifications. In other words, process planningdetermines how a part will be manufactured and actsas a bridge between design and manufacturing. Inprocess planning, the objectives would be to minimisethe number of rejects, processing cost and manufactur-ing lead time. Therefore, process planning is a majordeterminant of the profitability of a product. Thereare several variables associated with raw materials:e.g. unit cost of raw material, amount of raw materialrequired and salvage value of scrap. In machiningprocesses, the variables are processing cost, processingtime, set-up time and standard deviation (whichdetermine the percentage of rejects).

The traditional and most widely used method ofprocess planning is based on human experience. Thedisadvantages of this approach are the time required toacquire the expertise and that the plans developed maynot be consistent due to the element of humanjudgment. The feasibility of a process plan is relyingon the quality of design, availability of machine toolsand other influences such as allocation of machinetools. Therefore, it is necessary to develop a processplan that has sufficient knowledge of both upstream(design) and downstream (scheduling) activities. Themethods described below have been developed toovercome these problems as much as possible.

2.6. Integration of process planning and scheduling

Sormaz et al. defined conventional scheduling as a taskthat uses input from rigid process plans (Sormaz et al.2004). These plans specify a unique choice of machinesfor each operation, and a unique sequence of opera-tions, whereas integrated process planning and sche-duling (or integrated scheduling) uses more flexible

process plans as input. The flexible plans allow a choiceof operation sequences and/or machines.

An increasing number of published papers havefocused on this subject. Various approaches to theintegrated scheduling problem have been introduced.Literature (Li and Mcmahon 2007, Shukla SanjayKumar et al. 2008) has shown that there exists a needfor integrating the process planning and schedulingfunctions in manufacturing in order to achieveproductivity improvements. Zhang et al. used heuristicprocedures as the integrated approach. Examples ofother approaches are integer programming (Zhanget al. 2003), rule-based approach (Li Jianxiang et al.2004), simulated annealing approach, tabu search(Reddy and Ponnambalam 2003) and GA approach(Chyu Chiuh-Cheng and Wei-Shung 2008, KimHaejoong and Park Woo 2008).

The concurrent integrated process planning andscheduling model mainly consists of an initial planningholon and a detailed planning holon. The initialplanning holon is the core at the initial planning. Itcooperates with other holons to finish the task at theinitial planning. The input data to initiate planningholon can be classified into two types. One is theproduct model from a design system which representsthe geometrical shape of the product, design toler-ances, surface requirement and the properties of thematerial; the other is the resource information from theproduction scheduling holon. The task of the initialplanning holon is to find all feasible operations asdetermined by part information and resource informa-tion. The initial planning holon does not carry out thecomplete process planning, but it can generate manyfeasible blocks made up of feasible processes based onindividual operations. A block is generally machinedon an individual machine unless it is mass production.The output of the initial planning holon is a series ofblocks; these blocks are assigned to each machinebased on feedback from production scheduling. Infact, the alternative process plans are made up of allthese alternative blocks. Another task of the initialplanning holon is to provide manufacturing evaluationfor the designer.

The designer can use the tool to check themanufacturing feasibility and cost of alternative de-signs. Thus, designers can modify their designs so thatthey are manufacturable and cost-effective accordingto the current shop floor environment. The manufac-turing evaluations produced by concurrent integratedprocess planning system should consider other ap-proaches, in that its evaluations are based not only onthe design (namely process capabilities that can bedescribed by the part shape, dimensions, tolerances,surface finish, geometric and technological constraints,and economics of a process), but also on information

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on the shop floor resources. Shop floor resourcesgreatly affect the manufacturability analysis. A designmay be manufacturable under one set of shop floorresources, but not under another.

The detailed planning holon is executed just beforethe beginning of manufacturing. It will generate thedetailed process planning, which includes selecting thecutting speed, feed rate, etc., and calculating machiningtime, programming the NC program for each operationof the processing route generated by the decisionmaking holon. The output of the detailed planningholon is an entire document of process planning to besent to the shop floor to guide the production.

In HMS, holons make autonomous decisions basedon guidelines or system-wide constraints provided byhigh-level holons. Each holon can participate in theconstruction of different virtual clusters. During theevolution of the holarchy, one holon can be included indifferent holonic society to form a dynamic virtualcluster, which is based on multiple dimension taskdriven, as shown in Figure 7.

In addition to having some common characteristicssuch as distribution, autonomy, interaction, andopenness, the architecture of the holonic systempossesses some other characteristics as follows:

(1) Reconfiguration. It supports easy reconfigura-tion to accommodate the introduction of newmanufacturing environments.

(2) Customisation. It supports customisable func-tionalities that enable users at all three planninglevels to interactively manipulate processplanning.

(3) Hybridisation. It has a hybrid architecture thatis composed of the peer-to-peer relationships(task holon with initial planning holon) and thehierarchical relationships between holons (suchas between planning holons).

3. A proposed approach

In HMS, any holon in the holon society may beinvolved in more than one cluster. With ongoingclustering and holons becoming involved in multiplecompositions, a multi-dimensional cluster negotiationprocess is illustrated in Figure 6. There are three kindsof holons in the system: each type represents certainfunctions such as scheduling holon, resource holon andsupervision holon. The interaction can be traced inJADE platform.

In a situation where an agent requires moreassistance or cooperation from outside its virtualcluster, it will create further clusters for its cooperationsubtasks. The subclustering process is then repeated,with subclusters and then subsubclusters etc. beingformed as needed, resulting in a dynamically inter-linked and overlapped cluster society. In this virtualcluster society, in principle, all tasks are distributedand solved cooperatively. Such an architecture isrecursive and scalable. The simulation result interfaceis shown in Figure 7.

An integrated process planning and schedulingsystem, which is applicable for scheduling holon of theHMS, is vital for high efficiency communication andexecution in the engineering application.

Figure 6. Multi-agent negotiation and interaction process based CNP (simulated result).

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3.1. PSO and its corresponding mapping mechanism

The proposed approach is exhibited in Figure 8, wherethe modules of PSO and FL (available in MatlabFuzzy Logic Toolbox) are the primary components.

PSO simulates a social behaviour such as birdflocking to a promising position for certain objectivesin a multidimensional space (Coello Coello et al. 2004,van den Bergh et al. 2004). Like evolutionaryalgorithms, PSO conducts search using a population(called swarm) of individuals (called particles) that areupdated from iteration to iteration. Each particlerepresents a candidate position (i.e. solution) to theproblem at hand, resembling the particle of GA. Aparticle is treated as a point in an M-dimension space,

and the status of a particle is characterised by itsposition and velocity (Izui Kazuhiro et al. 2008, Liet al. 2008). Initialised with a swarm of randomparticles, PSO is achieved through particles flyingalong the trajectory that will be adjusted based on thebest experience or position of the one particle (calledlocal best) and the best experience or position everfound by all particles (called global best). The M-dimension position for the ith particle in the tthiteration can be denoted as xi(t) ¼ {xi1(t), xi2(t), . . .xiM(t)}. Similarly, the velocity (i.e. distance change),also an M-dimension vector, for the ith particle inthe tth iteration can be described as. vi(t) ¼ {vi1(t),vi2(t), . . . ,viM(t)}. The particle-updating mechanismfor particle flying (search process) can be described as

vid ¼ wð$vid þ c1r1ðpid � xidÞ þ c2r2ðpgd � xidÞÞ ð7Þ

xid ¼ xid þ vid ð8Þ

where pi Pbest of agent i at iteration k, pg gbest of thewhole group w compress factor, r1,r2 random numbersin (0,1), c1, c2 weighting factor, $ inertia function, inthis paper, the inertia weight is set to the followingequation. PSO algorithm is problem-independent,which means little specific knowledge relevant to agiven problem is required. What we have to know isjust the fitness evaluation for each solution. Thisadvantage makes PSO more robust than many othersearch algorithms.Figure 7. Dynamic virtual cluster in holonic society.

Figure 8. The schematic diagram of the proposed approach.

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The algorithm keeps an updated version of twospecial variables throughout the course of its execu-tion. Generally, initial swarm and initial particlevelocities are generated randomly. In order to reducethe iterative time of PSO, a new method to generateinitial swarm is introduced in this paper. Notice thatmost feasible solutions in task allocation are arrangedaccording to the increasing order of the task and only afew tasks are reversed. Then, we arrange task order inour work according to the increasing order of task. Ifone task’s execution order is the same as the other, thetwo task’s orders are arranged randomly. For example,considering the tasks and operation on processor 1 inFigure 9, Figure 9 shows a mapping between onepossible assignment instance to particle positioncoordinates in the PSO domain. Using such particlerepresentation, the PSO population is represented as aP 6 M two-dimensional array consisting of N parti-cles, each represented as a vector of M tasks. Thus, aparticle flies in an M-dimensional search space. A taskis internally represented as an integer value indicatingthe processor number to which this task is assigned toduring the course of PSO. In our PSO algorithm, wemap an M-task assignment instance into correspond-ing M-coordinate particle position. The algorithmstarts by generating randomly as many potentialassignments for the problem as the size of the initialpopulation of the PSO. It then measures particles’fitness. We used Equation (10) as our fitness function.The algorithm keeps an updated version of two special

variables throughout the course of its execution:‘global-best’ position and ‘local-best’ position. It doesthat by conducting two ongoing comparisons: First, itcompares the fitness of each particle being in its‘current’ position with fitness of other particles in thepopulation in order to determine the global-bestposition for each generation. Then, it comparesdifferent visited positions of a particle with its currentposition, in order to determine a local-best position forevery particle. These two positions affect the newvelocity of every particle in the population accordingto Equation (7). Figure 10 shows two possibleexpressions of the first segment of an initial particlethat can be generated according to the new method. Iftasks on every processor are arranged in this way, theprobability that the initial particle may be a feasiblesolution, i.e. a feasible schedule, increases greatly.

In Equation (7), inertia weight (w) is an importantparameter to search ability of PSO algorithm. A largeinertia weight facilitates searching new area while asmall inertia weight facilitates fine-searching in thecurrent search area. Suitable selection of the inertiaweight provides a balance between global explorationand local exploitation, and results in less iterations onaverage to find a sufficiently good solution. Therefore,considering linearly decreasing the inertia weight froma relatively large value to a relatively small valuethrough the course of PSO run, PSO tends to havemore global search ability at the beginning of the runwhile having more local search ability near the end ofthe run. In this paper the inertia weight is set accordingto the following equation

$ ¼ $max �$max �$min

Imax� I

where $max ¼ initial value of weighting coefficient$min ¼ final value of weighting coefficientImax ¼ maximum number of iterations or

generationI ¼ current iteration or generation number

In numerical simulations, the inertia weight is set to1.4 to guarantee a wider search area and linearlydecreasing to 0.3 to assure a finer search area in nearoptimisation point.

The acceleration constants c1 and c2 in Equation(7) adjust the amount of ‘tension’ in PSO system. Low

Figure 9. Tasks allocation to PSO particle mapping.

Figure 10. Two possible expressions on processor 1.

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value allow particles to roam far from target regionsbefore being tugged back, while high values resultin abrupt movement toward, or past, target regions.According to experiences of other researchers, accel-eration constants c1 and c2 are set to 2.0 for allfollowing examples.

The parameter w is the compress factor (CF), andit is used as mechanisms for the control of the velocity’smagnitude. The basic system equation of PSO can beconsidered as a kind of difference equations. Therefore,the system dynamics, namely, search procedure, can beanalysed by the eigen value analysis. Namely, thevelocity of CF can be expressed as follows

w ¼ 2

2� j�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij2 � 4j

p��� ���where j ¼ c1 þ c2, f � 4.

For example, if j ¼ 4.0, then w ¼ 1.0. As jincreases above 4.0, w gets smaller. For example, if,j ¼ 5.0 then w ¼ 0.38, and the damping effect is evenmore pronounced. The convergence characteristicof the system can be controlled by j. Namely,Clerc (1999) found that the system behaviour can becontrolled so that the system behaviour has thefollowing features:

(a) The system does not diverge in a real valueregion and finally can converge.

(b) The system can search different regions effi-ciently by avoiding premature convergence.

Unlike other EC methods, CF of PSO ensures theconvergence of the search procedures based on themathematical theory. CF can generate higher-qualitysolutions than PSO with IWA (Eberhart 2000).

However, CF only considers dynamic behaviour ofone agent and the effect of the interaction amongagents. Namely, the equations were developed withfixed best positions (pi and pg) although pi and pg canbe changed during search procedure in the basic PSOequations. The effect of pi and pg in the systemdynamics is one for future works.

3.2. Hybrid PSO and differential evolutionalgorithm(HPSO)

PSO, which is a swarm evolution algorithm developedby the simulation of the food searching process in thenatural world, has the ability to remember the bestposition of particles and has available a communica-tion mechanism among the swarm, namely: throughthe cooperation and competition between individualsin the population to obtain the optimum of theproblem. PSO and artificial life, as well as evolution

algorithms have a close relationship, but comparedwith evolution algorithms, PSO keeps the globalsearching based strategy in the population. It adoptsa simple velocity-position model to avoid complexgenetic operations, and thanks to its special memoriesit can keep track on the current searching status andadjust the corresponding searching strategy.

PSO algorithm is problem-independent, whichmeans little specific knowledge relevant to a givenproblem is required. What we have to know is just thefitness evaluation for each solution. This advantagemakes PSO more robust than many other searchalgorithms. However, as a stochastic searchalgorithm, PSO is prone to lack global search abilityat the end of a run. PSO may fail to find the requiredoptima in case the problem to be solved is toocomplicated and complex. DE (Chang 2007, Qian Bin2008) has the merits of memorising the best solution andsharing the group information in the candidate. We cancontrol the search process and avoid individuals beingtrapped in local optimum more efficiently. Thus, ahybrid algorithm of PSO and DE, named HPSO, ispresented as follows.

BeginSTEP 1 Initialisation

Initialise swarm population, each particle’sposition and velocity;Evaluate each particle’s fitness;Initialise gbest position with the lowest fitnessparticle in swarm;Initialise pbest position with a copy of particleitself;Initialise $max, $min, c1, c2, maximum genera-tion, and generation ¼ 0.Determine T0,Tend, B.

STEP 2 OperationFor PSOdo {

generate next swarm by Equation (7) toEquation (8);find new gbest and pbest;update gbest of swarm and pbest of theparticle;generation þþ;}while (generation5maximum generation)

For DEFor gbest particle S of swarm{ BEGIN

Initialise: generate the DE population randomlyEvaluate the individualGet the best solution Xbest

While (the end qualification is not met)

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Exert mutation operation to each individual toacquire corresponding mutation individual

Viðtþ 1Þ ¼ XbestðtÞ þ FðXr1ðtÞ � Xr2ðtÞÞ

Exert mutation operation, then crossover opera-tion to get the experiment individual

ui; jðtþ1Þ¼vi;jðtþ1Þ; if ðrandðjÞ�CRÞ

or j¼ randnðiÞxi;jðtÞ otherwise:

8<: j¼1;2; � � � ;d

Evaluate the object value of experiment individualExert selection operation between individual

and individual to generate new individual

Xiðtþ 1Þ ¼ Uiðtþ 1Þ; if FðUiðtþ 1ÞÞ < FðXiðtÞÞXiðtÞ; otherwise

�

Update Xbest

End WhileOutput Xbest and objective valueENDWhere, r1, r2 2 {1,2, . . . N} are different to eachother;F 2 [0,2] is zoom scale factor which is used tocontrol the ratio of father generation differentialvector Xr1(t) – Xr2(t)Xbest(t) is the basic vector after exerting distur-bance. The generation will share the information ofbest solution;rand(j) is the random variable of jth separaterandom in [0,1]rand(i) is the random number in aggregation{1,2, . . . , d}CR 2 [0,1] is crossover parameter to control scatterdimension of population.

STEP 3 Output optimisation results.END

As a new evolutionary technique, differential evolu-tion (DE) was mainly proposed for continuous optimi-sation. DE is a population-based globally evolutionaryalgorithm, which uses a simple operator to create newcandidate solutions and one-to-one competition schemeto select new candidates greedily. DE has the merits ofmemorising the best solution and sharing the groupinformation in the candidate. DE adopts the differentialoperation to generate new candidates. The competemechanism DE used is the one to one greedy selection(Liu Bo andMaHannan 2008). The real number code isused in the algorithm, so the complicated gene opera-tion in GA algorithm is avoided.

In the first place, DE generates the initialisationpopulation random in the feasible solution in the

problem space. The current populations are exertedmutation and crossover operation to generate a newpopulation. Second, two populations are selected withone to one mechanism by greedy theory to gain theultimate new generation. The best solution in DE isobtained by the distance of individuals in population anddirection information. So each individual in populationchanges the search action by altering the direction ofdifferential item and step. In each generation, mutationand crossover operation is exerted to individuals togenerate a newpopulation. Finally, the next generation isgenerated by selection in the old generation.

From the chart, we can see that PSO providesinitial solution for DE during the hybrid searchprocess. Such hybrid algorithms can be converted totraditional DE by setting swarm size to one particle.HPSO implements easily and reserves the generality ofPSO and DE. Moreover, such HPSO can be applied tomany combinatorial optimisation problems by simplemodification.

Three objective values are used to measurethe effectiveness of the schedule. Those objectivesare:

(1) Minimise total completion time of all jobs orthe makespan;

(2) Minimise total number of rejects – the totalnumber of rejects can be calculated by addingall the number of scrap produced:

F1 ¼Xnl¼1

Ysl ¼

Xnl¼1

Yol

Xopj¼l

ksj

! ð9Þ

(3) Minimise total processing cost – the totalprocessing cost can be calculated by sum-ming all the processing costs for all theoperations;

F2¼Xnl¼1

Nil

Xopj¼1

kiljXilj�ksljX

sljþkiljf Yi

lj

� �h ið10Þ

For Equations (9) and (10): Ysl is the scrap unit, Yo

i

is the output unit, kij is the input technologicalcoefficient per unit output, ksj is the scrap technolo-gical coefficient per unit, Xi

j; Xsj are the unit average

cost of input and scrap respectively, f Yij

� �is the

processing cost per unit, n is the total number ofjobs, l is the job number, op is the total number ofoperations and Ni is the number of input units.Equations (9) and (10) are detailed in Singh (1996).

3.3. Fuzzy interference system for machine balance

Each machine will be assigned an imaginary MTFvalue randomly. The values will be in a range between

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0 to 50 units. These values are represented by thetriangular membership function as shown in Figure 11.Where, (cþa,cþb), (c–a,c–b) and (cia,cib), (i ¼ 0,1, . . . ,4)is the border value for corresponding membershipfunction.

A set of fuzzy sets is set up when the input isfuzzified. It is denoted by {NB,NM,NS,Z,PS,PM,PB},where, NB-Negative big, NM-negative middle, NS-negative small, Z-zero, PS-positive small, PM-positivemiddle and PB-positive big.

The fuzzy membership function f for each fuzzy setis represented as below.

fNB ¼1 if x < c�a

c�b�xc�b�c�a if c�a � x � c�b

0 if x > c�b

8<:

fi;D ¼

0 if x < cia2 x�ciacib�cia if cia � x � ciaþcib

2

2 cib�xcib�cia if cibþcia

2 < x � cib0 if x > cib

8>><>>:

fPB ¼0 if x < cþa

x�cþbcþb�cþa if cþa � x � cþb

1 if x > cþb

8<:

The input for the inference process is a singlenumber set given by the antecedent and the output by afuzzy set. The fuzzy reasoning methods that we usedare built-in methods supported by Matlab Fuzzy Logic

Toolbox (The Mathworks 1998), which truncates theoutput of fuzzy sets.

The fuzzy rules are in the format as follows.

if 5antecedent, related to the MTF4 then5consequent, the machine reliability4

Rules used in the FL are:

If (MTF is very low) then (machine reliability isvery low)If (MTF is low) then (machine reliability is low)If (MTF is medium) then (machine reliability ifstandard)If (MTF is high) then (machine reliability is high)If (MTF if very high) then (machine reliability isvery high)

A decision is based on the testing of all the rulesin an FL. A combination of the rules is necessary fordecision making. Aggregation is the process by whichthe fuzzy sets that represent the outputs of each outputare combined into a single fuzzy set. The input of theaggregation process is the list of truncated outputfunctions returned by the implication process for eachrule. The output of the aggregation process is onefuzzy set for each output variable.

The last step is to defuzzify the aggregate outputfuzzy set. The result from this step is a single number.In this work the result is the reliability index. Figure 12shows the example of the output of FL. The firstcolumn shows how the input variable is used in therules. The input variable is shown at the top, i.e.MTF ¼ 21.2. The second column shows how theoutput variable, i.e. machine reliability (mac_reliabil-ity), is used in the rules. Each row of plots representsone rule. The five plots (i.e. the triangle plots) in theinput column show the membership functions refer-enced by the antecedent, or if part of each rule. Thesecond column of plots shows the membership func-tions referenced by the consequent, or the then part ofeach rule. The shaded input plots represent the MTFvalue, 21.2 belongs to the membership function A2 andA3. The truncated output plots show the implication

Figure 11. Membership functions.

Figure 12. Example of the input-output of the fuzzy inference system.

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process. It has been truncated to exactly the samedegree as the antecedent. The lower plot of the outputcolumn is the resultant aggregate plot. A defuzzifiedoutput value is shown by the line passing through theaggregate fuzzy set. In this example, if the MTF is 21.2,the machine reliability index is 3.6. The index is thedefuzzification result of the FL. It is in the range of 0to 10.

In a case where numeric input is not available,FL can be modified to accept linguistic or fuzzyinput (such as ‘low’). This is one of the advantagesof using FL in integrating machine capability toscheduling.

4. Results and discussion

In our experiment, utilising test datum used by Morad(Morad and Zalzala 1997), the acceptable value for thetotal completion time is 1287 units of time, the totalnumber of rejects is 12 units and total processing costis 678 units of dollar. Figure 13 represents the finalschedule in a Gantt chart form.

In the above experiment, it can be seen thatmachine 23 is left empty without doing any process-ing. In this case the unreliable machine is not given ajob. In a real manufacturing environment, this case isunfavourable. Even though machine 23 is unreliable, inthis case, it should not be left without doing any jobs.At least some operations can be assigned to thismachine, in order to avoid any wasting resources.

To overcome this problem, another approachis proposed in this work. The HPSO will be usedto balance the load for each machine. The load will bedistributed based on the machine capability, whichis measured by the reliability index. For the mostreliable machine, the load given to the machine willbe more compared to the unreliable one. The load oneach machine is measured by the machine utilisation,i.e. the percent of time the machine is being utilised.

For this purpose, the ranking values from the FL arebeing grouped into three levels for penalty purposes:

(1) Unreliable when the machine reliability index isless or equal to 2;

(2) Standard when the machine reliability index isequal to 3;

(3) Reliable when the machine reliability index ismore than 3;

A list of if-then rules has been developed to penalisemachines based on its utilisation. For unreliablemachines, the machine utilisation should be less oraround 20, for the standard machine the machineutilisation should be less or around 40, and for thereliable machine, the machine utilisation should bearound total utilisation. The utilisation is measured inpercentage. It can be summarised as:

If machine reliablity �2If machine utilisation 4 20% or machineutilisation ¼ 0

Penalty(x) ¼ 10Else if machine reliability ¼ 3If machine utilisation 4 40% or machineutilisation ¼ 0

Penalty(x) ¼ 70ElseIf machine utilisation 4 total utilisation ormachine utilisation ¼ 0

Penalty ¼ 100End

If these machines exceed the utilisation limits,it will be penalised. This criteria will be checked foreach particle in each generation. The HPSO will tryto minimise the total penalty value until the bestparticles which present the most balanced load isachieved.

Figure 13. Gantt chart of the schedule.

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Another simulation, using the same data set, hasbeen conducted for the proposed approach. Instead ofassigning the MTF values randomly, in this simulationeach machine is being assigned an imaginary value ofMTF. The values are 30, 10 and 50 for machine 21,machine 22 and machine 23, respectively. Based on theFL, the ranking for the machines are 3, 1 and 5 formachine 21, machine 22 and machine 23, respectively.After 50 generations, the optimised schedule is shownin Figure 14.

From the Gantt chart shown in Figure 14, themachine utilisation can be calculated as:

Machine 21 utilisation ¼ 970/2910 ¼ 33.3%Machine 22 utilisation ¼ 415/2910 ¼ 14.3%Machine 23 utilisation ¼ 1525/2910 ¼ 52.4%

From the calculation, the unreliable machine (i.e.machine 22) has the least load compared with othermachines. This machine is being utilised up to 14.2%of the time. The standard machine, that is machine 21,uses 33.3% of its time processing the jobs. Lastly, themost reliable machine, that is machine 23, has the mostloads compared to other machines. From the calcula-tion, the utilisation is 52.4%. From the results, itshows that each machine received loads within a rangerespective to its capability.

In this experiment, the total penalty value becomesthe objective function of the HPSO. The HPSO isminimising the objective individually. The details ofthe schedule are shown in Table 1. It shows the orderof the jobs, the machines involved in processingoperations, operation sequence, start time of theoperation and finish time of the operation.

Compared with the solution obtained by the simplePSO and Simulated annealing (SA) (Table 2), it can beseen that the solution is an optimal one and that ituses less time than the simple PSO and SA. Thegeneration process is shown in Figure 15. From thisfigure, it can be found that the evolution process of theHPSO tends to be stable when the generation reachesmore than 50.

Figure 14. Gantt chart for improved method.

Table 1. The detailed information of the schedule.

Job Machine Operation Start time Finish time

4 3 1 1 4061 2 1 4 1093 1 1 2 1572 3 1 406 7024 1 2 406 8111 3 2 702 8593 2 2 157 3622 1 2 811 9864 1 3 859 10211 3 3 986 11123 2 3 362 4672 3 3 1021 1180

Table 2. The comparison of different algorithms.

Best rate (100%) HPSO result PSO result SA result

Best 1180 1295 1378Mean 1221 1396 1482Maximum 1262 1497 1586CPU time 48.00’’ 79.00’’ 1029.0’’

Figure 15. The generation process of the differentalgorithm.

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When considering the larger size problem, thePSO and SA usually find it hard to obtain the optimalsolution in the desired time, so the HPSO isintroduced. To test the performance of the HPSO,we randomly produced some problems with differentsizes. The result together with the comparison of thePSO without the embedded rule and genetic algorithms(GA) are shown in Table 3.

We compare our results with the GA for 10 fullyconnected homogeneous processors. Two types ofcomparisons are carried out based on the resultsobtained by running each algorithm on this suite of150 graphs. First, we compare the computational costfor all the random graphs generated by the techniqueand the average running times of these algorithms. Thecost generated by GA technique and HPSO techniquefor randomly generated process graphs is shown inFigure 15. Each point in the figure is the average of25 test cases. PSO solution quality is on average16.63% better than GA. On average, the GAalgorithm is 1.511 times slower than PSO technique.These results indicate that the proposed HPSOalgorithm is a viable alternative for solving the processplanning and scheduling problem.

5. Conclusion and future work

This paper has presented a holonic architecture fordynamic scheduling of manufacturing systems. Anintegrated process planning and scheduling systemof machine product, aimed at realising a flexibleproduction control in holonic manufacturing systemsis presented. Instead of choosing alternative machinesrandomly, this paper proposed the usage of FL tochoose the most reliable machine. This is an alternativeway to integrate the production capability duringscheduling. This paper shows some promising resultsin integrating production capability and load balancing

during scheduling activity. There are a few objectivesthat could be optimised individually or simultaneously.This will give a choice to the scheduler in determiningwhich objective is the most important.

The great benefit of a holonic architecture fordynamic scheduling of manufacturing systems is thegraphical and concise representation of activities,resources and constraints of a operation of schedulingholon in a single coherent formulation, which is veryhelpful for designers to better understand and for-mulate scheduling problems. Moreover, it is under-stood from this research that the FL and HPSOapproach has a great potential for solving a variety ofcomplicated scheduling problems in scheduling holon.In this regard, further research is also being under-taken to accommodate complicated situations such asvariable task size, variable cycle time, scheduling ofmixed batch/continuous plants and implementation ofintegrated supervisory control and scheduler using themodel and algorithm.

Acknowledgements

This research is supported by 863 High Technology PlanFoundation of China (grant NO 2002AA415270), NationalNatural Science Foundation of China (Contract No.2001BA201A32) and Natural Science foundation of GANSUprovince (grant NO3ZS062-B25-033).

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