generation of optimum sequence of operations using ant colony algorithm by sudeep singh

7/30/2019 Generation of Optimum Sequence of Operations Using Ant Colony Algorithm by Sudeep Singh

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Int. J. Advanced Operations Management, Vol. 4, No. 4, 2012 253

Copyright 2012 Inderscience Enterprises Ltd.

Generation of optimum sequence of operations usingant colony algorithm

D. Sreeramulu* and Sudeep Kumar Singh

Department of Mechanical Engineering,

Gandhi Institute of Engineering and Technology,

Gunupur 765022, Orissa, India

E-mail: [email protected]


*Corresponding author

C.S.P. Rao

Department of Mechanical Engineering,

National Institute of Technology,

Warangal 506004, Andra Pradesh, India


Abstract: Computer-aided process planning (CAPP) forms an importantinterface between computer-aided design (CAD) and computer-aidedmanufacturing (CAM). It is concerned with determining the sequence ofindividual manufacturing operations required to produce a product as pertechnical specifications given in the part drawing. In this paper the processplanning is modelled as a combinatorial optimisation problem with constraints,

and an ant colony optimisation (ACO) approach has been used to solve it. Thisis a newly developed metaheuristic algorithm used as a global search techniquefor the quick identification of the optimal operations sequence by consideringvarious feasibility constraints.

Keywords: process plan; ant colony optimisation; ACO; optimisation.

Reference to this paper should be made as follows: Sreeramulu, D.,Singh, S.K. and Rao, C.S.P. (2012) Generation of optimum sequence ofoperations using ant colony algorithm, Int. J. Advanced OperationsManagement, Vol. 4, No. 4, pp.253271.

Biographical notes: D. Sreeramulu is working as an Associate Professorat G.I.E.T., Gunupur. He obtained his PhD in 2010. He has published eightpapers in international journals and presented in more than 15 internationalconferences. His research interests include process plan, feature recognitionand scheduling.

Sudeep Kumar Singh is working as an Assistant Professor in G.I.E.T.,Gunupur. He graduated in 2008. He has presented in more than fiveconferences. His research interests include tool selection, process plan, geneticalgorithm and feature recognition.

C.S.P. Rao is working as a Professor in the Mechanical EngineeringDepartment at the National Institute of Technology, Warangal, AP, India. Hecompleted his PhD from NIT, Warangal and he guided 12 PhDs and guiding


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254 D. Sreeramulu et al.

10 PhDs. He has published 50 international journals and more than 100

conference papers. He was awarded the Young Scientist of the Year andEngineer of the Year in 2008. His research interests include process planning,scheduling and petrinets.

1 Introduction

Process planning is the systematic determination of the detailed methods by which work

pieces or parts can be manufactured economically and competitively from initial stages

(raw material form) to finished stages (desired form) or process planning translates

design information into the process steps and instructions to efficiently and effectively

manufacture products. Process planning activities basically include the interpretation of

product design data, selection of machining processes, selection of cutting tools, selection

of machine tools, determination of setup requirements, sequencing of operations,

determination of the production tolerances, determination of the cutting conditions,

design of jigs and fixtures, calculation of process times, tool path planning and NC

program generation, generation of process route sheets etc. As the design process is

supported by many computer-aided tools, computer-aided process planning (CAPP) has

evolved to simplify and improve process planning and achieve more effective use of

manufacturing resources. Process planning encompasses the activities and functions to

prepare a detailed set of plans and instructions to produce a part. The planning begins

with engineering drawings, specifications, parts or material lists and a forecast of

demand. CAPP systems support this activity, providing the process planner with different

tools to improve her/his performance. In computer-integrated manufacturing (CIM),CAPP is the link between computer-aided design (CAD) and computer-aided

manufacturing (CAM).

Optimisation of process planning is one of the foremost targets of manufacturing

systems, since it is believed that only those industries capable of making effective

productions would withstand international competition in this millennium. Numbers of

research works are performed for generating optimum process plan. The optimum

process plan may be on the basis of time or cost or on the basis of some weighted

combination of these two. Tool selection, machine selection, process selection

and tool path selection, process parameter selection are the most important areas for

optimisation in process planning. This paper presents a novel population-based

approach recently proposed for several discrete optimisation problems have been

discussed. In this, how the almost blind animals like ants, could manage to establishthe shortest routes between their nest and food source is investigated. The paper reveals

that the pheromone trail is the most important medium of communication among

individual ants in a swarm. A moving ant lays varying quantities of the chemical

pheromone on the ground as it moves, thus marking its journey by a trail of

pheromone. The more the number of ants traces a given path, the more attractive this

path (trail) becomes and is followed by other ants by depositing their own

pheromone. This auto catalytic and collective behaviour results in the establishment of

the shortest route. This data is utilised for generating the optimum sequence of operations

in a machining process.


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Generation of optimum sequence of operations using ant colony algorithm 255

2 Related work

There is a lot of research going on from late 60s on CAPP. This section describes some

literature on process planning. In 1996, Usher and Bowden proposed an application of a

genetic algorithm (GA) for finding near-optimal operation sequences for use within the

context of CAPP. In their application, an improved coding strategy for operation

sequence was presented, that reduces the size of the solution space by taking into account

a set of feasibility constraints in the coding process and it enhances the performance of

the GA permitting the application of the system to more complex parts and supporting the

notion of dynamic planning. Zhang et al. in 1997 proposed a CAPP system for prismatic

parts machined in a conventional job shop. In their approach, the process planning

problem for a part is modelled in a network and five aspects of machining costs were

introduced for plan evaluation, i.e.,

1 machines

2 tools

3 machine changes

4 setup changes

5 tool changes.

In 1998 Marri et al. made an attempt to review the existing literature with the objectives

of gaining insights into the design and implementation of CAPP systems. Dereli and Filiz

(1999) developed optimisation modules of a process planning system for prismatic parts;

called OPPS-PRI (Optimised Process Planning System for Prismatic Parts).

Zhang et al. (1999) presented a novel CAPP model for machined parts in a job shopenvironment that contains customer-specified machine tools and cutters. The approach

models process planning problems in a concurrent manner to generate the entire solution

space by considering the multiple planning tasks, i.e., operations (machine, tool, and tool

approach direction (TAD)) selection and operations sequencing simultaneously. Tiwari et

al. in 1999 used GA to obtain a set of process plans for a given set of parts and

production volume. Ahmad et al. proposed in 2001 a comprehensive overview of the

current trend in research works on CAPP, classifying those works into several categories

according to their focus. In 2002 Li et al. used a hybrid GA and simulated annealing (SA)

to consider concurrently the processes of selecting machining resources, determining

set-up plans and sequencing operations for a prismatic part in an optimisation procedure.

Shen et al. (2006) described the complexity of manufacturing process-planning and

scheduling problems, and reviewed the research literature in manufacturing process

planning, manufacturing scheduling, and the integration of process planning and

scheduling, particularly focusing on agent-based approaches in these areas.

Gopala Krishna and Mallikarjuna Rao (2006) presented an application of a newly

developed metaheuristic called the ant colony algorithm as a global search technique for

the quick identification of the optimal operations sequence by considering various

feasibility constrains in their work. A couple of case studies were taken from the

literature to comparing the results obtained by the proposed method. Jain and Gupta

(2006) explained ant colony optimisation (ACO) technique which has been used to solve

the operation sequencing problem. The approach proposed by them analyses the PR


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among features to generate a precedence relationship matrix (PRM). The operation-

sequencing problem in process planning is considered to produce a part with theobjective of minimising the sum of machine, setup and tool change costs. In general, the

problem has combinatorial characteristics and complex PR, which makes the problem

difficult to solve. It highlights a methodology that takes into account the various

technological constraints while sequencing and minimise the total change over cost.

3 Ant colony optimisation

In the early 1990s, ACO was introduced by Dorigo et al. (1996),Dorigo and Gambardella

(1997, 1996) andGambardella et al. (1997) as a novel nature-inspired metaheuristic for

the solution of hard combinatorial optimisation (CO) problems. ACO belongs to the class

of metaheuristics, which are approximate algorithms used to obtain good enough

solutions to hard CO problems in a reasonable amount of computation time. Other

examples of metaheuristics are tabu search, SA, and evolutionary computation. The

inspiring source of ACO is the foraging behaviour of real ants. When searching for

food, ants initially explore the area surrounding their nest in a random manner.

As soon as an ant finds a food source, it evaluates the quantity and the quality of the

food and carries some of it back to the nest. During the return trip, the ant deposits a

chemical pheromone trail on the ground. The quantity of pheromone deposited, which

may depend on the quantity and quality of the food, will guide other ants to the food

source. The more the number of ants traces a given path, the more attractive this path

(trail) becomes and is followed by other ants by depositing their own pheromone. As it

has been shown as, indirect communication between the ants via pheromone trails

enables them to find shortest paths between their nest and food sources. Thischaracteristic of real ant colonies is exploited in artificial ant colonies in order to solve

CO problems.

Consider for example the experimental setting shown in Figure 1. There is a path

along which ants are walking (for example from food source A to the nest E, and vice

versa, Figure 1a). Suddenly an obstacle appears and the path is cut off. So at position B

the ants walking from A to E (or at position D those walking in the opposite direction)

have to decide whether to turn right or left Figure 1b). The choice is influenced by the

intensity of the pheromone trails left by preceding ants. A higher level of pheromone on

the right path gives an ant a stronger stimulus and thus a higher probability to turn right.

The first ant reaching point B (or D) has the same probability to turn right or left (as there

was no previous pheromone on the two alternative paths). Because path BCD is shorter

than BHD, the first ant following it will reach D before the first ant following path BHDFigure 1c). The result is that an ant returning from E to D will find a stronger trail on path

DCB, caused by the half of all the ants that by chance decided to approach the obstacle

via DCBA and by the already arrived ones coming via BCD: they will therefore prefer (in

probability) path DCB to path DHB. As a consequence, the number of ants following

path BCD per unit of time will be higher than the number of ants following BHD. This

causes the quantity of pheromone on the shorter path to grow faster than on the longer

one, and therefore the probability with which any single ant chooses the path to follow is

quickly biased towards the shorter one. The final result is that very quickly all ants will

choose the shorter path.


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Figure 1 An example with real ants

Figure 2 shows an example of experimental set up of artificial ants. Figure 2a) shows the

initial position of the obstacles on the path, Figure 2b) indicates at time t = 0 there is no

trail on the graph edges; therefore, ants choose whether to turn right or left with equal

probability and Figure 2c) indicates at time t = 1 trail is stronger on shorter edges, which

are therefore, in the average, preferred by ants.

Figure 2 An example with artificial ants

Some major differences with a real (natural) one:

artificial ants will have some memory

they will not be completely blind

they will live in an environment where time is discrete.

The idea is that if at a given point an ant has to choose among different paths, those

which were heavily chosen by preceding ants (that is, those with a high trail level) are

chosen with higher probability. Furthermore, high trail levels are synonymous with short

paths. It is this real-life intelligent cooperative search behaviour of almost blind ants was

the key motivation factor inspiring and leading to the formulation of artificial ant

algorithms to solve several large-scale combinatorial and function optimisation problems.

In all these algorithms, a set of ant-like agents or software ants solves the problem under


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consideration through a cooperative effort. This effort is mediated by exchanging

information on the problem structure the agents concurrently collect while stochasticallywe building solutions. This paper presents the usefulness of ant algorithm with the

specific example of manufacturing process planning problems.

3.1 Some of the properties of ant colony (Marco Dorigo and Luca Maria)

An ant searches for minimum cost feasible solutions min ( , )J J L t

= .

An ant khas a memoryMk that it can use to store information on the path it followed

so far. Memory can be used to build feasible solutions, to evaluate the solution

found, and to retrace the path backward.

An ant k in state Sr= S

r-1, i can move to any nodej in itsfeasible neighbourhood,

kiN , defined as { }( ) ( ,ki i rN j j N S j S= .

An ant k can be assigned astart state ksS and one or more termination conditions ek.

Usually, the start state is expressed as a unit length sequence, that is, a single

component.

Ants start from the start state and move to feasible neighbour states, building the

solution in an incremental way. The construction procedure stops when for at least

one ant kat least one of the termination conditions ek is satisfied.

An ant klocated on node i can move to a nodej chosen in kiN . The move is selected

applying a probabilistic decision rule.

The ants probabilistic decision rule is a function of

(i) the values stored in a node local data structureAi = [aij] called ant-routing

table, obtained by a functional composition of node locally available

pheromone trails and heuristic values

(ii) the ants private memory storing its past history

(iii) the problem constraints.

When moving from node i to neighbour nodej the ant can update the pheromone

trail ij on the arc (i,j). This is called online step-by-step pheromone update.

Once built a solution, the ant can retrace the same path backward and update the

pheromone trails on the traversed arcs. This is called online delayed pheromoneupdate.

Once it has built a solution, and, if the case, after it has retraced the path back to the

source node, the ant dies, freeing all the allocated resources.

3.2 ACO algorithm

At the beginning of the algorithm, pheromone matrix is initialised. The level of initial

pheromone values, as well as which values are initialised depends on the problem being


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considered. Furthermore, an ACO algorithm includes two more mechanisms: Pheromone

trail evaporation and, optionally, daemon actions. Pheromone trail evaporation and

daemon actions. Pheromone evaporation is the process by means of which the pheromone

trail intensity on the connections automatically decreases over time. From a practical

point of view, pheromone evaporation is needed to avoid a too rapid convergence of the

algorithm towards a sub-optimal region. It implements a useful form of forgetting,

favouring the exploration of new areas of the search space.

The generalised flowchart of ant colony algorithm is shown in Figure 3. Daemon

actions, that are an optional component of the ACO meta-heuristic, can be used to

implement centralised actions which cannot be performed by single ants. Examples are

the activation of a local optimisation procedure, or the collection of global information

that can be used to decide whether it is useful or not to deposit additional pheromone to

bias the search process from a non-local perspective. As a practical example, the daemon

can observe the path found by each ant in the colony and choose to deposit extrapheromone on the arcs used by the ant that made the shortest path. Pheromone

updates performed by the daemon are called offline pheromone updates (Krishnaiyer and

Cheraghi, 2002).

4 Optimisation of process plan using ACO

CAPP forms an important interface between CAD and CAM. It is concerned with

determining the sequence of individual manufacturing operations required to produce a

product as per technical specifications given in the part drawing. Any sequence of

manufacturing operations that is generated in a process plan cannot be the best possible

sequence every time in a changing production environment. It means operation

sequencing is combinatorial in nature and is said to be NP-complete problem. As the

complexity of the product increases, the number of feasible sequences increases

exponentially and there is a need to choose the best among them. To solve this problem a

newly developed metaheuristic called the ant colony algorithm as a global search

technique is used for the quick identification of the optimal operations sequence by

considering various feasibility constrains, Optimisation criteria is described later with

reference to minimum cost.

In the ACO metaheuristic a colony of artificial ants, cooperates in finding good

solutions to difficult discrete optimisation problems. Cooperation is a key design

component of ACO algorithms and good solutions are an emergent property of the ants

cooperative interaction. The technique involves observing the part feature details form

available drawings, and operations required for each feature, and also PR amongoperations. Generate A number of artificial ants, where A is assumed to be equal to

the number of operations n. Set initial value of pheromone (ij ) equal to a constant

value (e = 0.1) for every pair of operations (i.e., ij = e). ij is the pheromone

present on the link joining operations i and j. Assign n operations to A ants in

sequence starting with first operation. Now move all ants to positions, which ants

position didnt follow precedence give move probability 0. By following this for all

operations, few ants can only complete their sequence. The objective function (FFk) for

each completed sequence is calculated. Now update the pheromone differentially. As


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shortest path is the emergent property of ACO, the completed sequences should be

strengthened and the incomplete sequences should be weakened. This step helps in theeliminating the incomplete sequences form the future iterations. Separate the ants

completing operation sequences from the ants unable to complete their operation

sequences. For each of these complete operation sequences add pheromone on their

edges, to improve their chances of selection in next iteration also. The amount of

pheromone to be added on the edges of a sequence completed by kth

ant (say) is given by

the following expression.

Figure 3 Generalised flowchart for ant algorithm


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kij

k

Q

FF = (1)

Where, Q is a pheromone deposition constant. In the present study, a value of 10 was

taken from literature. FFk is the value of the objective function for the sequence under

consideration (i.e., sequence generated by kth

ant). Reduce pheromone on the edges of

incomplete sequences to weaken it chances for selection in the next iteration. The

following expression is used to reduce the pheromone on the edges of an incomplete

sequence.

(1 ).ij ij = (2)

where, [0, 1] is the persistence of the pheromone trail, and (1 ) represents the

evaporation of pheromone from edge (i,j). Moreover, parameter also avoids unlimited

accumulation of the pheromone trails on the edges and thus allows the algorithm to forget

previously done bad choices. Researches in the past have used a range of values for

varying from 0 to 0.5, but in our algorithm a value of 0.1 for has taken. After each

iteration the pheromone updation and evaporation takes place after certain number of

iterations or position values of each operations are not improving then pick the highest

pheromone position for each operation according to precedence constraints, this is the

best sequence.

4.1 PR between operations

The PRs between operations come from geometrical and technological consideration to

produce every feature with the best possible accuracy. They must be satisfied by the final

operations sequence. Some of the feasibility constraints are (Zhang et al., 1997):

Types of constraints, i.e., fixture requirement, datum requirement, good manufacturing

practice, and geometric tolerance are considered to determine the PR between

features.

Fixture requirement: PR between two features exists when machining one feature

first may cause another to be unfixturable. An example is given in Figure 4 where F1

(through hole) must be drilled before F2 (slot) is machined. Otherwise, deformation

of the slot shoulder would occur.

Datum requirement: when two features have a dimensional or geometrical tolerance

relationship, the feature containing the datum should be machined first. For example,

F2 should be machined before F4 (blind-hole) since the bottom face of F2 is the

datum of F4 (see Figure 4).

Good manufacturing practice: good manufacturing practice or rules-of-thumb may

also result in PR between features. In Figure 4, F4 sits on F3 (slant face). F4 should

be drilled before F3 to avoid tool damage.

Geometric tolerance: The last constraint pertains to the geometric tolerances define

for the part. The types of tolerances that affect sequencing include: profile of a line

and surface, perpendicularity, angularity, parallelism, total and circular runout,


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position, symmetry, and concentricity. The result of this analysis is the identification

of those features which must be cut in the same setup.

In Figure 4 the through hole (F1) can in theory be reached by the TADs +y and -y;

however, a drill cannot access F1 along +y, so this option is discarded. Features: F1

(through hole), F2 (slot), F3 (taper), F4 (blind hole), and F5 (slot) are technological

attributes: xxx (positional tolerance between F4 and F2).

Figure 4 An example part for the operations selection

4.2 Criteria for optimising the precedence sequence (Zhang et al., 1997)

The precedence sequence optimisation is based on the weighted cost, which consists of,

Machine cost,

1

n

i

i

C MCI

=

= (3)

where n is the total number of OpMs and MCI is the machine cost index for using

machine-i.

Tool cost,

1

n

i

i

TC TCI

=

= (4)

where TCIiis the tool cost index for using tool-i.

Machine change cost (MCC): a machine change is needed when two adjacent

operations are performed on different machines,

1

1

1

* (1 ( ))

n

i i

i

MCC MCCI M M

+

=

= (5)

where MCCI is the machine change cost index, and Mi is the machine ID used for

operation i.

{11 0( )i iM M+ = 1, if i jM M and 0, if i jM= (6)


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Setup change cost (SCC): A setup change is needed when two adjacent OpMs

performed on the same machine have different TADs.

1

1 1

1

* ((1 ( )) * ( ))

n

i i i i

i

SCC SCCI M M TAD TAD

+ +

=

= (7)

where SCCIis the setup change cost index.

Table 1 Set-up change

Conditions for machining two consequent operations Set-up change

Same TAD and same M/C No

Same TAD and different M/Cs Yes

Different TAD and same M/C Yes

Different TAD and different M/Cs Yes

Tool change cost (TCC): A tool change is needed when two adjacent OpMs

performed on the same machine use different tools.

1

1 1

1

* ((1 ( )) * ( ))

n

i i i i

i

TCC TCCI M M T T

+ +

=

= (8)

where TCCIis the tool change cost index.

Table 2 Tool change

Conditions for machining two consequent operations Tool change

Same Tool and same M/C No

Same Tool and different M/Cs No

Different Tools and same M/C Yes

Different Tools and different M/Cs No

Total manufacturing cost,

FGC MC TC MCC TCC SCC= + + + + (9)

These cost factors can be used either individually or collectively as a cost compound

based on the requirement and the data availability of the job shop.

4.3 Constraint adjustment algorithm

For initially generated process plan (random sequence) after the crossover and mutation

the precedence constraints might not be satisfied. A constraint adjustment algorithm,

which can be applied to a complicated and multiple constraint condition, is proposed to

rearrange the process plan according to the constraints while random properties in it can

kept. For a process plan with n bits (operations), the constrained adjustment algorithm

described as follows:


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Select the bits that do not have constraint relationships with other bits in process plan

and keep their positions unchanged in process plan. Assume the number of bitsselected in this step isx.

The remaining (n-x) bits, which are constrained to be prior to other bits in process

plan, are used to form a double linked list (DLL) according to the relative position in

the process plan. The adaptation of a DLL is to make deletion and insert

manipulations convenient and efficient. In DLL, each bit has prior and next

references pointing to its prior and next bit respectively.

Traverse DLL from the tail. Set the traversed node as the current bit if it is not

assigned as the handled, otherwise the current bit is moved to its prior bit. If there is

one or more bits, which are prior to the current bit in the DLL. That should be

posterior to the current bit according to the preliminary precedence constraints: these

bits are deleted from the DLL and used to form another DLL1, which is initially setas void, according to their relative positions in DLL. DLL1 is inserted to DLL just

after the current bit. Move the reference to the tail, set the just handled current bit as

handled. Repeat this step.

After all bits assigned as handled in step-3m the order in DLL reflects the proper

relative PR of the constraint bits.

Fill the bits in the DLL one-by-one back to the (n-x) positions of process plan

according to their order in DLL. The updated process plan satisfies the PR while

some randomness can be kept.

After applying the constraint adjustment algorithm to the random sequences among the

features it will generates the set of possible sequences that satisfy the PR. These possible

sequences are taken as the initial feasible sequences for ACO algorithm. Explanation of

constraint adjustment algorithm is described as follows with an example.

For example, for a 14-bit chromosome (n = 14), the bits sequence and precedence

constraints are listed in Table 3. Six bits (Oper[1], Oper[4], Oper[6], Oper[11], Oper[13],

Oper[14]) have no constraint relationships with other operations (x = 6). Hence, their

positions are kept and a LL is formed for the other eight bits (n-x= 8). The first current

bit is Oper[8], and Oper[3], Oper[9] and Oper[5] should be posterior to it according to the

constraints. The updating process of LL is shown in Figure 5 After Oper[8] has been

handled, the reference to the current bit is moved to the tail and the same procedure is

continued until all bits are assigned as handled. The finally updated process plan satisfies

all the constraints.

Table 3 Example of a process and operations constraints

Original process plan Oper7- Oper14- Oper2- Oper10- Oper4- Oper11- Oper9-

Oper12- Oper3- Oper13- Oper6- Oper5- Oper8- Oper1

Constraint 1 Oper5 and Oper9 should be before Oper2 and Oper7

Constraint 2 Oper12 and Oper8 should be before Oper3, Oper5 and Oper9

Constraint 3 Oper3 should be before Oper5

Constraint 4 Oper10 should be before Oper7


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Figure 5 Example process of the constraint adjustment algorithm

Oper7- Oper14- Oper2- Oper10- Oper4- Oper11- Oper9- Oper12- Oper3- Oper13- Oper6- Oper5-Oper8- Oper1

Oper Oper Oper Oper

Oper Oper

Oper

Oper Oper

Oper Oper OperOper

Oper Oper Oper

Oper

OperOper

Oper Oper

Oper

Oper

Oper

Oper10- Oper14- Oper2- Oper8- Oper4- Oper11- Oper9- Oper3- Oper5- Oper13- Oper6- Oper7-

Oper2- Oper1

Head

The current

The u dated DLL after DLL1Head

Tail

Tail

Head

PP Uncha

Uncha

Uncha

The initially formed DLL

Uncha Uncha Uncha Uncha

The formatted DLL1 and updated DLL for the current bit-Oper [8]

L

LL1

Uncha Uncha Uncha UnchaUncha

move to

The currentThe current

so on

PP

Handl Tail


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Figure 6 Flow chart for the ant colony algorithm for process planning

Rearrange the random sequences according to precedenceconstraints

Cost calculation

Update pheromone trail values

Generate a sequence according to highest pheromone value

If

iteration = given

iteration

End

Generate initial random sequences

Start

Mutation

Yes

Initialization of pheromone

Send 90 % of G Global ants for crossover

Send 10 % of G lobal ants for trail diffusion

Constraint adjustment algorithm

Cost calculation

Evaporation of pheromone trailvalue

No

Constraint checking and cost calculation

Print the operation sequence details with cost


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Notations

1 The constant variables used are

n = Number of operations

A = Total number of Ants = n

G = Number of global ants

L = Number of local ants

CP = Crossover probability = 0.90

MP = Mutation probability = 0.10

Q = Pheromone position constant =10

RHO = Evaporation rate of pheromone trial = 0.10

ITER_Max = Maximum number of iteration = 100

2 Other variables are

tau = pheromone matrix of size [100] [100].

Child = Child matrix.

Mfgc = Manufacturing cost

FF = cost matrix

The program algorithm of the Ant colony that we have used for the manufacturing

process planning is as follows. We have done this program in C++ with Microsoft Visual

C++ software. The program can be used for any problem with input file. The various

notations that we have used are also stated below.

5 Implementation of ACO with example

A prismatic part having 19 features is shown in Figure 7. The operations, alternate

machines, tools and TAD can be shown in Table 4. Table 5 shows the PR between theoperations.

Based on the formula given in Section 4.2, the total manufacturing cost is calculated

for each sequence and it is optimised using ant colony algorithm discussed in Section 4.4.

The results for the above example with the given input i.e., the details of operation,

machine, tool, TAD and precedence constraints among operations are discussed.


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Figure 7 Example part

Source: Zhang et al. (1997)

Table 4 Feature details of example part

Feature Operation No. M/C No. Tool No. TAD

F1 1 1 1 6

F2 2 1 1 6

F3 3 2 7 5

F4 4 2 5 3

F5 5 2 5 3

F6 6 2 5 3

7 1 2 5

8 1 3 5

F7

9 3 4 5

F8 10 1 1 6

11 1 2 5

12 1 3 5

F9

13 3 4 5

F10 14 2 5 1

F11 15 1 1 6

F12 16 1 1 6

F13 17 2 5 4

F14 18 2 5 4

F15 19 1 1 5

F16 20 1 1 5

F17 21 2 5 4

F18 22 1 1 4

F19 23 1 1 4


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Table 5 Precedence constraints between features and operations

Feature Operation No. Precedence constraint description

F1 1 F1 (Op 1) is after F17 (Op 21)

F2 2 F2 (Op 2) is after F1 (Op 1) and F17 (Op 21)

F3 3 F3 (Op 3) is after F1 (Op 1), F2 (Op 2), F4 (Op 4), F10 (Op14) and F17 (Op 21)

F4 4 F4 (Op 4) is after F5 (Op 5), F6 (Op 6), F10 (Op 14)

F5 5 -----

F6 6 F6 (Op6) is after F5 (Op 5)

7

8

F7

9

F7 (Op 7) is before (Op 9 and 10) and after F17 (Op 21), (Op9) is before (Op 10) for the fixed order of machining

operations

F8 10 F8 (Op 10) is after F7 (Op 7,8 and 9) and F9 (Op 11,12 and13)

11

12

F9

13

F9 (Op 11) is before (Op 12 and 13) and after F7 (Op 7,8 and9) and F17 (Op 21). (Op 12) is before (Op 13) for the fixed

order of machining operations

F10 14 ---

F11 15 F11 (Op 15) is after F5 (Op 5) and F6 (Op 6)

F12 16 F12 (Op 16) is after F5 (Op 5), F6 (Op 6) and F11 (Op 15)

F13 17 F13 (Op 17) is after F5 (Op 5), F6 (Op 6), F10 (Op 14), F14(Op 18) and F17 (Op 21)

F14 18 F14 (Op 18) is after F5 (Op 5), F6 (Op 6), F10 (Op 14) andF17 (Op 21)

F15 19 F15 (Op 19) is after F5 (Op 5), F6 (Op 6), F10 (Op 14), F14(Op 18) and F17 (Op 21)



F18 22 F18 (Op 22) is after F5 (Op 5), F6 (Op 6), F10 (Op 14) andF17 (Op 21)

F19 23 F19 (Op 23) is after F5 (Op 5), F6 (Op 6), F10 (Op 14), F17(Op 21) F18 (Op 22)

5.1 Results

A generalised C-program has been written to implement ACO Algorithm. After the no. of

iterations the two best possible sequences are given below. Table 6 shows the first best

sequence having the Total M/C usage Cost = Rs. 249/-, Total Tool usage Cost = Rs.

43.5/-, M/C Change Cost = Rs. 1650/-(No. of machine changes = 11), Tool Change

Cost = Rs. 80/- (No. of tool changes = 4), Set-up Change Cost = Rs. 450/-(No. of setup

changes = 5) and the total cost is about Rs.2472.5/-.


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Table 6 First best sequence

Processplan 1

14 5 6 15 16 20 21 22 23 1 2 7 8 9 11 12 13 18 19 17 10 4 3

MachineNo.

2 2 2 1 1 1 2 1 1 1 1 1 1 3 1 1 3 2 1 2 1 2 2

TAD 1 3 3 6 6 5 4 4 4 6 6 5 5 5 5 5 5 4 5 4 6 3 5

Tool No. 5 5 5 1 1 1 5 1 1 1 1 2 3 4 2 3 4 5 1 5 1 5 7

Table-7 shows the second best sequence having the total M/C usage cost = Rs.

249/-, total tool usage cost = Rs. 43.5/-, M/C change cost = Rs. 1800/-(No. of machine

changes = 12), tool change cost = Rs. 40/- (No. of tool changes = 2), set-up change cost =

Rs. 360/-(No. of setup changes = 4) and the total cost is about Rs. 2492.5/-.

Table 7 Second best sequence

Processplan 2

14 5 6 15 16 20 4 21 22 23 1 2 3 7 8 9 11 12 13 18 19 17 10

MachineNo.

2 2 2 1 1 1 2 2 1 1 1 1 2 1 1 3 1 1 3 2 1 2 1

TAD 1 3 3 6 6 5 3 4 4 4 6 6 5 5 5 5 5 5 5 4 5 4 6

Tool No. 5 5 5 1 1 1 5 5 1 1 1 1 7 2 3 4 2 3 4 5 1 5 1

6 Conclusions

The generation of various feasible plans and to find the best among them constitutes an

NP-complete combinatorial problem. Hence an efficient heuristic search is required tosolve such problem. We applied the ant colony algorithm to solve the problem of

generating optimal process plan for a given part. The approach models process planning

considering the machine, tool, and tool approach directions for each operation. PR among

all the operations required for a given part are used as the constraints for the solution

space. The various costs considered for finding the optimal plan are machine change cost,

tool change cost, setup change cost, machine usage cost and tool usage cost. The optimal

process plan is found based on the minimum total cost criteria. The proposed ant colony

algorithm is coded in Micro Soft Visual C++ and executed on P3 personal computer with

1GHz processor. The system is developed based on a customisable job shop environment

so that users can modify the manufacturing database to suit their needs. This makes the

system more realistic compared to the approaches in which a fixed machining

environment is assumed. This is found to be advantageous over the previous approaches.This work can be further extended by integrating the process planning with scheduling

with an objective of minimising the make span.


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generation of optimum sequence of operations using ant colony algorithm by sudeep singh

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