HYBRID LEARNING METHOD FOR DISCRETE

MANUFACTURING CONTROL

USING KNOWLEDGE BASED MODEL

Ewa Dudek

Institute of Automatics, AGH University of Science and Technology

Mickiewicza 30, 30-059 Krakow, Poland

Tadeusz Dyduch

Institute of Computer Science, AGH University of Science and Technology

Mickiewicza 30, 30-059 Krakow, Poland

Keywords:

Control, knowledge acquisition, knowledge representation, learning system, discrete manufacturing process.

Abstract:

The aim of the paper is to present a conception of a hybrid learning method for discrete manufacturing

processes control.The method is based on a special form of a knowledge based model of discrete manufactur-

ing process, named here hybrid knowledge based model (HKBM). The model consists of two parts, each of a

different type of model: algebraic-logical model in a state spacethat is created on a basis of process technology

description and set of expert rules referring to control. A general scheme of HKBM of a vast class of discrete

manufacturing processes (DMP) is given in the paper. Then the method of synthesis of intelligent, learning

algorithms that use information on the process gained in previous iterations as well as an expert knowledge is

described. To illustrate the presented ideas, the scheduling algorithm for a special NP-hard problem is given.

1 INTRODUCTION

The paper deals with a learning based method applied

to control of discrete manufacturing process. A lot of

different learning methods have been developed (Ci-

chosz, 2000). They are suitable for application aims

and character of available pieces of information. The

conception of a learning method, however, depends

most essentially on knowledge representation (KR)

method utilised for a learning process. This paper

presents conception of a learning method based on

a hybrid knowledge representation model. Recently,

a lot of investigations referring to knowledge based

control method are carried out because models and

knowledge about controlled processes are the vital

parts of the controlling systems. In the knowledge-

based intelligent process planning systems a signiﬁ-

cant role plays knowledge acquisition. In order to dis-

cover association rules under uncertainty, fuzzy deci-

sion techniques and entropy-based analysis methods

as well as fuzzy clustering integrated with variable

precision rough set are used (Zhonghao et al., 2005).

On the other hand e.g. for autonomous unmanned

vehicle the system is required being able to dynam-

ically construct a knowledge structure representing a

process under control, meeting the constraints associ-

ated with a particular process. The system should be

able to manage and monitor changes in the structure

and derive knowledge about it. Usually process con-

straints are speciﬁed with temporal logic formulas and

monitored using appropriate execution monitor (Do-

herty, 2005).

At the same time KR methods for computer aided

manufacturing have been developed (McGuinness

and Patel-Schneider, 1998), (Liebowitz, 1998). They

are vital for information system for manufacturing

management such as MRPII or/and ERPII. Each of

the system contains components so called shop ﬂoor

control, especially referring to control of discrete

manufacturing processes and scheduling. However,

there are no proper optimal control algorithms imple-

mented in the components. The implemented algo-

rithms use only simple control rules. On the other

hand a variety of discrete processes have been de-

scribed and their optimisation algorithms have been

presented in the scientiﬁc literature. The question

arises: why there are no these optimisation algo-

rithms implemented in information management sys-

tems, produced even by the best computer ﬁrms such

as SAP, Oracle or IFS? According to the authors one

of the reasons is lack of common knowledge represen-

tation method for manufacturing processes control.

The paper deals with knowledge based modelling

of discrete manufacturing/production processes and

its applications for manufacturing process planning

algorithms. It presents developing of ideas given in

160

Dudek E. and Dyduch T. (2006).

HYBRID LEARNING METHOD FOR DISCRETE MANUFACTURING CONTROL USING KNOWLEDGE BASED MODEL.

In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics, pages 160-166

DOI: 10.5220/0001219201600166

Copyright

c

SciTePress

(Dudek-Dyduch, 2000). Its aim is 3-fold:

– to present a scheme for general, hybrid knowl-

edge based model of a class of discrete manufac-

turing/production processes (DMP),

– to present a learning method based on the hybrid

knowledge based model

– to present learning algorithm for scheduling an ex-

emplary NP-hard problem.

The control of DMP (scheduling DMP) lies in de-

termining a manner of performing some set of jobs

under restrictions referring to machines/devices, re-

sources, energy, time, transportation possibilities, or-

der of operation performing and others. Most of

control algorithms are approximate (heuristic) due to

NP-hardness of the optimisation problems. Within

the frame of artiﬁcial intelligence, one attempts both

formal elucidation of heuristic algorithm ideas and

giving some rules for creating them (metaheuristics)

(Dudek-Dyduch and Fuchs-Seliger, 1993), (Dudek-

Dyduch and Dyduch, 1988), (Pearl, 1988), (Rajedran,

1994). The paper is connected with this direction of

the research. It uses formal model based on a special

kind of the multistage decision process enlarged with

an expert knowledge.

2 HYBRID KNOWLEDGE BASED

MODEL OF DMP

In (Dudek-Dyduch, 1990), (Dudek-Dyduch and Dy-

duch, 1992), (Dudek-Dyduch and Dyduch, 1993) the

general scheme of algebraic-logical model of DMP,

that is a special form of knowledge based model,

has been presented. It represents a discrete decision

process jointed with simulation process.Simulation

aimed at scheduling of any DMP consists in deter-

mining a sequence of process states and the related

time instances. The new state and its time instant de-

pend on the previous state and the decision that has

been realised (taken) then. Decision determines the

job to be performed, resources, transport unit etc. The

algebraic-logical model of DDP will be extended to

HKBM. Let’s recall it brieﬂy.

Deﬁnition 2.1 A discrete manufacturing/production

process DMP is a process that is deﬁned by the sextu-

ple DMP=

U, S, s

0

, f, S

N

, S

G

where

U is a set of control decisions or control signals,

S = X × T is a set named a set of generalized states,

X is a set of proper states,

T ⊂ R

+

∪ {0} is a subset of non negative real num-

bers representing the time instants,

f : U ×S → S is a partial function called a transition

function, (it has not to be determined for all elements

of the set U × S),

s

0

=

x

0

, t

0

, S

N

⊂ S, S

G

⊂ S are respectively: an

initial generalized state, a set of not admissible gener-

alized states, and a set of goal generalized states, i.e.

the states in which we want the process to take place

at the end.

The transition function is deﬁned by means of two

functions, f = (f

x

, f

t

) where

f

x

: U × X × T → X determines the next state,

f

t

: U × X × T → T determines the next time

instant.

It is assumed that the difference ∆t = f

t

(u, x, t)−t

has a value that is both ﬁnite and positive.

Thus, as a result of the decision u that is taken or

realised at the proper state x and the moment t, the

state of the process changes for x

0

= f

x

(u, x, t) that

is observed at the moment t

0

= f

t

(u, x, t) = t + ∆t.

Because not all decisions deﬁned formally make

sense in certain situations, the transition function f

is deﬁned as a partial one. Thanks to it, all limita-

tions concerning the control decisions in a given state

s can be deﬁned in a convenient way by means of so-

called sets of possible decisions U

p

(s), and deﬁned

as: U

p

(s) = {u ∈ U : (u, s) ∈ Dom f }.

At the same time a DMP is represented by a set of

its trajectories that starts from the initial state s

0

. It

is assumed that no state of a trajectory, apart from the

last one, may belong to the set S

N

or has an empty

set of possible decisions. Only a trajectory that ends

in the set of goal states is admissible. The control

sequence determining an admissible trajectory is an

admissible control sequence (decision sequence). The

task of optimisation lies in the fact of ﬁnding such an

admissible decision sequence ˜u that would minimize

a certain criterion Q.

In the most general case, sets U and X may be pre-

sented as a cartesian product U = U

1

×U

2

×. . . U

m

,

X = X

1

× X

2

× . . . X

n

i.e. u = (u

1

, u

2

, . . . u

m

),

x = (x

1

, x

2

, . . . , x

n

). There are no limitations im-

posed on the sets, in particular they have not to be nu-

merical ones. Thus values of particular co-ordinates

of a state may be names of elements (symbols) as

well as some objects (e.g. ﬁnite set, sequence etc.).

Particular u

i

represent separate decisions that must

or may be taken at the same time. The sets S

N

,

S

F

, and U

p

are formally deﬁned with use of logi-

cal formulae. Therefore, the complete model consti-

tutes a specialised form of a knowledge based model

(logic-algebraic model). According to it’s structure

the knowledge on DMP is represented by coded in-

formation on U, S, s

0

, f , S

N

, S

G

. Function f may

be deﬁned by mean of procedure or by means of rules

of type IF..THEN.

The presented paradigm of knowledge based model

consists of the following main procedures realising

rules IF..THEN, utilizes by control algorithms: proce-

dure that generates and examines subsets of possible

HYBRID LEARNING METHOD FOR DISCRETE MANUFACTURING CONTROL USING KNOWLEDGE BASED

MODEL

161

decisions U

p

(s), procedures that realize the function

f (in the most cases it is a vector function), i.e. deter-

mine the next state (x

0

, t

0

) = f(u, x, t), procedures

that examine if the state belongs to the set S

N

or S

G

.

The basic structure of a ﬁxed DMP (Def.2.1) is usu-

ally created on a basis of process technology descrip-

tion. Basing on additional expert knowledge and/or

analysis of DMP subsets of states can be differenti-

ated, for which best decisions or some decision choice

rules R (control rules) are known. Similarly, some

subsets of advantageous or disadvantageous states for

the controlled process can be determined. Formally,

the knowledge allow us restrict sets of possible deci-

sions U

p

.

Knowledge represented by the basic knowledge

structure DMP (Def.2.1) enriched by expert knowl-

edge create the hybrid knowledge based model

(HKBM) of DMP. The knowledge can be enriched

further additionately as a result of simulation exper-

iments.

Basing on the model of DMP different classes

of algorithms can be formally deﬁned and analysed.

For example in (Dudek-Dyduch and Dyduch, 1992),

(Tadeusiewicz and Dudek-Dyduch, 1998), classes of

branch & bound algorithms for DMP control opti-

misation have been differentiated as well as some

rules of automatic creation of lower bounds have been

given. In the next section application of HKBM of

DMP for intelligent, learning algoritm is presented.

3 SEARCH METHOD WITH

GATHERING INFORMATION

The most popular search algorithms consist in gener-

ating consecutive, possibly better and better, trajecto-

ries. They use a specially created function or local

optimisation task for the choice of the best decision

at each state of the generated trajectory. The crite-

rion for local optimisation is called a preference func-

tion or simply heuristics. In this section we present a

conception of algorithms that gain information on the

process and also use expert knowledge.

In the author’s earlier paper (Dudek-Dyduch and

Fuchs-Seliger, 1993), (Dudek-Dyduch and Dyduch,

1993), a certain general 3-stage method for designing

local optimisation task is proposed. Let us recall it

brieﬂy.

At the ﬁrst stage, one formulates some conditions

for the optimal (suboptimal) solution. They refer di-

rectly to subsets of decisions, or/and determine the

state sets that are advantageous (or disadvantageous)

from the criterion point of view or for a possibility

of generation of an admissible trajectory. The condi-

tions can result from theoretical analysis of the model

or can be formulated by experts.

At the second stage, one determines a local optimi-

sation task. In order to do it, the information about the

distinguished, at the ﬁrst stage, advantageous or dis-

advantageous states as well as information on S

G

, S

N

and sets of possible decisions is used. As we need the

generated trajectory to run only through the advanta-

geous states and to avoid the disadvantageous ones, it

seems most natural to introduce any measure of dis-

tance in the state space, and to assume some local

criterions.. It was explained in (Dudek-Dyduch and

Dyduch, 1993) that different semimetrics can be used

as an approximate measures of distance. Basing on

the local change of the global criterion Q and maxi-

mization (minimization) of the mentioned distances,

we obtain the substitute local problem, usually a mul-

ticriteria one.

At the third stage, one should determine the manner

of solving the local multicriteria optimisation task.

The basic ideas of multicriteria decision approach

(Dudek-Dyduch, 1990), (Dudek-Dyduch and Fuchs-

Seliger, 1993), (Vincke, 1992), can be applied here.

For learning algorithms, however, the most useful are

these solving manners that assume priority or weight

coefﬁcients for the particular criterions because these

priorities may be modiﬁed during consecutive simu-

lation experiments.

A learning algorithm acquires and gathers a knowl-

edge about the process in the following way. Each

new generated trajectory is analysed. If it is not ad-

missible, the reasons of the failure are examined. For

example, it is examined through which subsets of not

advantageous states the trajectory has passed. A role

of the criterions connected with this subsets should be

strengthened for the next trajectory i.e. the weights

(priorities) of these criterions should increase. When

the generated trajectory is admissible, the role of the

criterions responsible for the trajectory quality can

be strengthened, i.e. their weights can be increased.

Basing on the gained information, the local optimisa-

tion task is being improved during simulation exper-

iments. This process is treated as learning or intel-

ligent searching algorithm. The gathered knowledge

is represented by means of coefﬁcients at particular

components of the criterium. This conception has

been examined and is presented in (Dudek-Dyduch,

2000).

If one posses additional expert knowledge then a

better algorithm can be proposed. If some state sub-

sets S

di

, i = 1, 2, . . . are distinguished and for these

states some rules for decision choice R

i

, i = 1, 2, . . .

are given by an expert then algorithm should verify

additionally to which subset the new generated state

belongs and should realise the suitable rule R

i

. If

rules given by expert excludes some decisions then

the suitable sets of possible decision U

p

(s) are de-

creased.

Another idea of learning algorithm for some

ICINCO 2006 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

162

scheduling problem is given in (Kolish and Drexel,

1995), (Sprecher et al., 1995).

4 SCHEDULING PROBLEM

WITH RETOOLING

DEPENDING ON PROCESS

STATE

To illustrate the application of the presented method,

let us consider the following scheduling problem that

takes place when scheduling preparatory works in

mines.

The set of headings in the mine must be driven

in order to render the exploitation ﬁeld accessible.

The headings form a net, formally represented by a

nonoriented multigraph G = (I, J, P ) where the set

of branches J and the set of nodes I represent the

set of headings and the set of heading crossings re-

spectively, and relation P ⊂ (I × J × I) determines

connections between the headings (a partial order be-

tween the headings). There are two kinds of driving

machines, that differ in efﬁciency, cost of driving and

necessity of transport. The ﬁrst kind machines (set

M1) are more effective but a cost of driving by means

of them is much higher than for the second kind (set

M2). Additionally, the ﬁrst kind machines must be

transported when driving starts from another head-

ing crossing than the one in which the machine is,

while the second type machines need no transport.

Driving a heading cannot be interrupted before its

completion and can be done only by one machine a

time. There are given due dates for some of the head-

ings. They result from the formerly prepared plan of

ﬁelds exploitation. One must determine the order of

heading driving and the machine by means of which

each heading should be driven so that the total cost of

driving be minimal and each of headings be complete

before its due date.

There are given: lengths of the headings, efﬁciency

of both kinds of machines (driving length per time

unit), cost of a length unit driven for both kinds of

machines, cost of the time unit waiting for both kinds

of machines, speed of machine transport and transport

cost per a length unit.

The problem is NP-hard (Dudek-Dyduch, 2000).

NP-hardness of the problem justiﬁes the application

of approximate (heuristic) algorithms. A role of a

machine transport corresponds to retooling during a

manufacturing process. The time needed for a trans-

port of a machine depends on headings that have been

driven earlier, thus it depends on a process state.

The process state at any instant t is deﬁned as a

vector

x = (x

1

, x

2

, . . . , x

n

), n = |J|.

A coordinate x

j

describes the state of the j-th head-

ing (branch),

x

j

= (m, ∆, i, s) where

m denotes the number of the machine that is as-

signed to the j-th heading,

∆ denotes the time after which the machine will be

accessible,

s is a parameter that deﬁnes whether the machine is

driving the heading (s = 1), whether it is transported

in the heading (s = 2) whether it is waiting in one

of the heading ends (the nearest heading crossings)

(s = 3),

i denotes the number of the heading crossing

(node) to which the machine is moving or in which

it is waiting. If there is no machine assigned to the

heading then m = 0 and s = 0.

If the driving of a heading has been not started

yet, then ∆ = ∞ and when it is complete, then

∆ = 0. The initial state x

0

= (0, ∞, 0, 0). For any

state (x, t) one can determine a set of headings that

are being driven (J

1

), the driving of which is com-

plete (J

2

), and not started yet (J

3

). A state (x, t)

belongs to the set of not admissible states if there is

a heading whose driving is not complete yet and its

due date is earlier than t. Formally, S

N

= {(x, t) :

there exists j /∈ J

2

such that d(j) < t} where d(j)

denotes the due date for the j-th heading. A state

(x, t) is a goal if all the headings have been driven,

i.e. S

G

= {(x, t) : ∀j ∈ J, j ∈ J

2

}.

A decision determines the headings that should

be started at the moment t, machines which drive,

machines that should be transported, headings along

which machines are to be transported and ma-

chines that should wait. Thus, the decision u =

(u

1

, u

2

, . . . , u

n

) where the co-ordinate u

j

refers to

the j-th heading and is of the form: u

j

= (m, q). The

symbol m denotes the number of a machine that is as-

signed to the heading. The parameter q ∈ {0, 1, 2, 3}

and denotes respectively: waiting, driving, transport

and withdrawing of the machine. When a machine

m ∈ M1 is in the node i and should drive the k-th

heading that is not adjacent to the i-th node, then the

machine is transported in the nearest way accessible

in the considered state. This way is computed by the

Ford’s algorithm (a polynomial one).

Obviously, not all the pairs (m, q) constitute pos-

sible decisions in the state (x, t). For example, a de-

cision u

j

= (m

k

, 1) is possible only when the j-th

heading is neither being driven nor complete and the

machine m

k

is in the one of the heading crossing ad-

jacent to the j-th heading. The complete deﬁnition

of the set of the possible decision U

p

(x, t) will be

omitted here because it is not necessary to explain the

idea of the algorithm. The detailed description of the

formal model for the considered problem is given in

(Dudek-Dyduch, 2000).

HYBRID LEARNING METHOD FOR DISCRETE MANUFACTURING CONTROL USING KNOWLEDGE BASED

MODEL

163

∆

∆

∆

Figure 1: Block-schema of the algorithm.

ICINCO 2006 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

164

5 LEARNING ALGORITHM

The algorithm for the solution of the problem consists

in generating consecutive trajectories. Each of them is

generated with the use of the specially designed local

optimisation task and then is analysed. The informa-

tion gained as a result of the analysis is used in order

to modify the local optimisation task for the next tra-

jectory, i.e. for the next simulation experiment. This

approach is treated as a learning without a teacher.

The construction of the local optimisation criterion

q for the presented example is based on two criterions.

The ﬁrst one, denoted as q

1

refers to the minimal in-

crement of the global criterion value, computed from

the current to the last state of a generated trajectory.

The second one denoted as q

2

takes into account

that the trajectory should pass possibly far from the

not admissible states, or from the states from which

there is a little chance to accomplish a goal state. Thus

the local criterion q = q

1

+bq

2

, where b is a parameter

that is being changed during simulation experiments.

q

1

= ∆Q(u, x, t) + Q

0

(x

0

, t

0

) (1)

where ∆Q denotes the increment of the global crite-

rion Q during a simulation step, i.e. when the current

state (x, t) is changed, as a result of the decision u,

to the state (x

0

, t

0

) = f(u, x, t). Q

0

(x

0

, t

0

) is a lower

estimation of the global criterion value for the latter

part of the trajectory, i.e. for the part that starts from

the state (x

0

, t

0

). This estimation is equal to the low-

est cost of the driving of the remaining headings when

the limitations referring to the due dates are neglected.

The lowest cost is computed under assumption that

only machines of the second type (set M2) are ap-

plied.

Criterion q

2

takes into account consequences of the

decision u from the due date limitations point of view.

L(x

0

, t

0

) estimates a minimal distance between the

new state (x

0

, t

0

) and the set of not admissible states

S

N

.

q

2

=

1

L(x

0

, t

0

)

(2)

L(x

0

, t

0

) is computed as follows. For the state x

0

, the

set of accessible headings’ crossings is determined,

i.e. the crossings from which driving can be started.

There is also determined the set of headings whose

driving has been not started yet and which have the

due dates. For each of the headings, the shortest time

needed for performing it is computed. It is denoted

as st(j) where j is the number of the heading. The

time is needed for driving all the headings that con-

stitute the shortest way from an accessible heading

crossing and for performing of the considered head-

ing. It is assumed that the driving is performed by

means of the ﬁrst kind machines (i.e. the more effec-

tive ones) and their transport to the accessible cross-

ing is neglected. Then, for the each of the headings

the difference d(j) − st(j) − t

0

is computed. If any

of the differences has negative value, the generated

trajectory cannot be admissible and is rejected. If all

the differences are nonnegative, L(x

0

, t

0

) is given by

formula:

L(x

0

, t

0

) = min

d(j) − st(j) − t

0

d(j) − t

0

=

= min

1 −

st(j)

d(j) − t

0

(3)

The formula is not applied for the headings that

had been determined earlier on a basis of the expert

knowledge or bottom up analysis. Finally the local

criterion q consists of 3 components:

q = ∆Q(u, x, t) + Q

0

(x

0

, t

0

) + b

1

L(x

0

, t

0

)

(4)

The value of the criterion q is computed for each

u ∈ U

p

(x, t). This decision u

∗

for which the crite-

rion value is minimal is chosen. Then the next state

(x

0

, t

0

) = f(u

∗

, x, t) is generated and the new best

decision u ∈ U

p

(x

0

, t

0

) is chosen. If a newly gener-

ated trajectory is admissible and for most of its states

the distance to the set of not admissible states is rela-

tively big, the parameter b can be decreased. In such a

situation the role of the optimisation compound is en-

larged. On the contrary, when the generated trajectory

is not admissible, the parameter b should be increased

because then the greater emphasis should be put to the

due date limitations.

The presented conception is an essential extension

of the one given in (Dudek-Dyduch, 2000). Com-

puter experiments that have been carried out for the

simpler algorithm are presented in (Dudek-Dyduch,

2000). They conﬁrmed that learning-based approach

is very efﬁcient. Basing on those results one may be

sure that the presented algorithm that use additionally

an expert knowledge will be very efﬁcient too.

6 CONCLUSIONS

The paper presents a conception of intelligent search

method (learning-based algorithms) for scheduling.

A large number of difﬁcult scheduling problems in

manufacturing can be efﬁciently solved by means of

these method. A basis for the algorithms is a special

kind of hybrid knowledge based model(HKBM) of

discrete manufacturing processes (DMP), that is given

in the paper. The model for a ﬁxed DMP consists

of two parts. The ﬁrst part corresponds to algebraic-

ligical model in the state space and is created mainly

on a basis of DMP technology description. The sec-

ond part constitutes a set of expert’s rules.

It should be pointed out that the presented hybrid

KR structure is also useful for creating simulation

HYBRID LEARNING METHOD FOR DISCRETE MANUFACTURING CONTROL USING KNOWLEDGE BASED

MODEL

165

packages for a large class of discrete processes be-

cause the special form of the model enables one to

create the simulation package of a modular form.

Such simulation package of a mixed structure,

combining KR and multiagent system can be used for

testing and developing strategies, prepared for crisis

management. To illustrate the conception, the learn-

ing based algorithm for preparatory work in a mine is

presented.

ACKNOWLEDGEMENTS

The research was supported in part by grant No 3

T11C 025 27 from Polish Committee of Scientiﬁc Re-

search.

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