A neuro-based expert system for facility layout construction

Journal of Intelligent Manufacturing (1999) 10, 359±385

A neuro-based expert system for facility layout

construction

Y U N - K U N G C H U N G

Department of Industrial Engineering, Yuan-Ze University, Nei-Li 32026, Taiwan

Received June 1997 and accepted December 1997

Motivated by the success of implementing expert systems (ESs) based on arti®cial neural networks

(ANNs) to improved classical rule-based expert systems (RBESs), this paper reports on the

development of a neuro-based expert system (NBES) for facility layout construction in a

manufacturing system. In an arti®cial intelligence (AI) technique such as the NBES, the semantic

structure of If-Then rules is preserved, while incorporating the learning capability of ANNs into the

inference mechanism. Unlike implementing a popular back propagation network (BPN) as an ES, the

proposed BAMFLO (Bidirectional Associative Memories for Facility LayOut) system is an

intelligent layout consultant system consisting of pipeline BAM neural networks with simple, fast

incremental learning and multiple bidirectional generalization characteristics. This incrementability

makes BAMFLO effective at acquiring, adding or adapting learned layout knowledge; thus it is

possible to memorize newly extended If-Then layout rules without retraining old ones. The multi-

bidirectionality gives BAMFLO the ability to quickly and reliably generalize a layout solution, and

to further infer unknown facts from known facts through a complex knowledge base (memorization)

without losing information. The solution process of BAMFLO contains three essential steps: training

example generation, incremental learning and solution generalization. The examples (layout

knowledge) can be generated from practical experience and/or classical layout software solutions for

incrementally training BAMFLO; the process then derives multiply bidirectionally generalized

construction layout solutions. The experimental results show that the BAMFLO scheme outperforms

®ve classical layout methods used to generate training examples.

Keywords: Facility layout, ¯exible manufacturing systems, BAM neural networks, expert systems,

arti®cial intelligence

1. Introduction

Facility layout design plays a crucial role in

determining the throughout time of a manufacturing

process. It is important to identify an ef®cient facility

layout or machine placement while considering

constraints such as speci®ed location, functional

relationship and material ¯ow optimization.

Generally, solution methods used to solve identi®ca-

tion and placement problems are either of the

construction or the improvement type (Fig. 1).

Construction procedures are used when a layout is

developed for the ®rst time and improvement

procedures are used when an existing layout, or the

one developed by a construction procedure, should be

rearranged to reduce its material moving cost.

Although the improvement method may appear to

be preferable to the construction method, the

objectives of both layout approaches are essentially

different. The maximization of facility functionality,

the goal of a construction layout, may be unsatis®ed

under the goal of minimizing material movement cost.

As a result, the trade-offs between these two

approaches should be carefully considered to deter-

mine how to inexpensively build a ¯exible layout.

Furthermore, complex routing factors lead both

layout methods to be loosely structured problems in

which a number of qualitative constraints and

0956-5515 # 1999 Kluwer Academic Publishers

practical layout experiences are arduously modeled by

analytical algorithms. In this paper, the ill-structured

construction layout problems that have previously

been solved by classical rule-based expert systems

(RBESs) are considered by a neuro-based expert

system (NBES), a rapidly developing ES technique

distinguished from RBESs.

RBES has become an acceptable AI methodology

and has been successfully used to solve unstructured,

loosely de®ned, or dif®cult-to-communicate pro-

blems. Nevertheless, it still has a number of

weaknesses, such as tediousness of knowledge

acquisition, dif®culty of knowledge base modi®ca-

tion, inconsistency of rule implementation,

incompleteness of knowledge contents, incorrectness

of inferred solutions, and inability to incorporate

learning changes or to handle data imprecision.

Accordingly, an innovative RBES with both the

ability to adapt its knowledge base is proposed to

overcome those RBES weaknesses by recon®guring

ANN structures to be NBESs.

In practice, an NBES offers an alternative and

advances RBES technology to analyze highly

complex nonlinear relationships or ill-structured

problems by means of its capability to learn from

past experiences, experimental data or typical

examples, tolerating imprecise data, and then gen-

eralize an approximate solution. Problems of facility

layout design are always ill-structured. Much of the

layout information used for the facility layout design

is noisy, incomplete and full of uncertainties. The

results of this paper indicate that the NBES can handle

imperfect or incomplete data in many layout cases,

providing a measure of knowledge fault tolerance, and

the ability to handle data uncertainty and incorporate

layout routing ¯exibility.

Due to the inherent advantages of NBES as well as

its successful implementation experience, this paper

investigates the feasibilty of using the proposed NBES

system named BAMFLO to construct a ¯exible

facility layout with a given set of typical layout

examples in terms of neural rules. In particular, the

motivation of BAMFLO implementation seeks to

determine:

(1) How different characteristics of uncertain

layout data, such as facility closeness level or location

size, affect the system's accuracy in generalizing a

solution;

(2) How the solution generalization accuracy of

this system compares to those solutions of analytical

layout models;

(3) The effectiveness of the proposed pipeline

BAM structure with the modi®ed BAM learning.

Based on the above three issues, this paper will

evaluate BAMFLO performance using simulated data

in order to control the extent of uncertain layout

characteristics such as closeness degree, relative

Fig. 1. Two types of facility layout method.

360 Yun-Kung Chung

position, block area and speci®ed facilities site. The

accuracy of BAMFLO solutions will be compared to

those from classical layout techniques using several

sets of test examples taken from published research.

Moreover, because an ANN's structure has a

signi®cant effect on the length and success of its

training, the suitability of an ANN as a practical tool

could be enhanced by modifying its structure as

required by the problem domain during the training

process. This paper will provide an extensible BAM

structure composed of a series of BAMs that can be

effective in solution generalization.

Investigation of the above issues can lead to

¯exibly laid-out manufacturing facilities to direct

material ¯ow and execution in manufacturing ®rms.

BAMFLO is an intelligent, simple and fast construc-

tion layout approach that incorporates high rerouting

¯exibility achieved by both its learning-from-

example capability and its knowledge base adapt-

ability, therefore, it can be used to resolve the ill-

structured layout problems. As a result, the contribu-

tions of this paper, corresponding to the above three

issues, include:

(1) The development of the novel neural design for

an intelligent facility layout system consisting of

multiple BAM-based ESs (BAMESs) capable of

providing effective solutions to problems encountered

in an ill-structured facility layout, emulating an

individual planner's layout expertise;

(2) The demonstration of BAMES learning which

can deal with the mixed-product production routings

and ¯exibly revise facility layouts;

(3) A start towards implementing a large-scale

BAMES that may have a more ¯exible architecture

than the widespread BPN-based ES (BPNES),

exempli®ed by Pao and Sobajic (1991), Lacher et al.(1992), Sanou et al. (1996) and Wang (1997).

The contents of this paper are organized as follows.

Layout approaches are brie¯y surveyed in Section 2.

Section 3 compares the RBES and NBES character-

istics. The reasons for employing BAMs as the

mechanism to build an NBES are explained in

Section 4. The incremental learning theory of

BAMFLO is introduced in Section 5. The main

presentations of this paper, BAMFLO's structure

and its implementation are addressed in Sections 6

and 7, respectively. Section 8 presents an example

whose solutions are compared to those from previous

research in order to assess the quality of BAMFLO

solutions. The ®nal section summarizes the ®ndings of

this research project.

2. Literature survey

Most of the computer-aided facility layout tools use

one or some combination of the following methods:

AI search techniques like simulated annealing

(Kouvelis, Chiang and Fitzimmons, 1992; Meller

and Bozer, 1996), genetic algorithms (Gupta et al.,1996; Peters and Rajasekharan, 1996), tabu search

(Chiang and Kouvelis, 1996), operations research

(Silva, 1992; Bancrjee et al., 1997; Lacksonen,

1997), graph theory (Welgama et al., 1994;

Cimikowski and Mooney, 1997), simulation (Chan

et al., 1995), $$$ (Barakat et al., 1995; DeLaney etal., 1995), fuzzy sets (Badiru and Arif, 1996; Dweiri

and Meiri, 1996), rule-based expert systems (Kumara

et al., 1988b; Kusiak and Heragu, 1988; Arinze et al.,1989; Abdou and Dutta, 1990; Babu and Yao, 1996),

pattern recognition (ElMaraghy and Gu, 1988;

Kumara et al., 1988a; Banerjee et al., 1992), and

hybrid methods (Heragu and Kusiak, 1990;

Sirinaovakul and Thajchayapong, 1994; Song and

Hitomi, 1996; Welgama and Gibson, 1996). In

addition, Kouvelis et al. (1992) Bancrjee and Nof

(1994), Hassan (1995), and Meller and Gau (1996)

have also provided good state-of-the-art papers

regarding facility layout methodologies.

The above diversi®ed layout strategies have

certain common characteristics: they employ proce-

dure models, production rules and/or pattern

recognition, collectively known as ``classical''

approaches. A procedure model is a set of iterated

processes for solution-®nding, dealing with quantita-

tive (numeric) data. Production rules are an ordered

sequence or program of `Ìf-Then'' rules, executed in

the given order, transferring out of sequence only

when commanded explicity by the program. These

rules work with qualitative (semantic) data. Both

approaches favour the traditional layout system, in

which a ``complete'' or an `ìntact'' requirement for

a well-de®ned layout task is absolutely necessary;

however, they suffer from their combinatorial nature.

Pattern recognition strategy is conceptually similar to

the rule-based procedure. There, both heuristic

search and grammar search are used to recognize

syntactic patterns in terms of n-tuple sentences

describing constraints and facts. The heuristic

A neuro-based expert system for facility layout construction 361

search sets up all relative attribute tuples; the

grammar search uses the sequential syntactic rules

to ®nd the n-tuple attributes that best match the input

requirement. The syntactic pattern recognition can

slightly tolerate `ìmperfect'' data, but its grammar

search also has the combinatorial nature.

The three kinds of classical layout approaches

basically all have the same pragmatic application

problems, differing from ANN approaches. The ANN

approach is also a pattern recognition technique, but is

totally different from syntactic pattern recognition

and other classical approaches. When an ANN is used

to recognize real layout problems, it can start with an

`ìncomplete'' or `ìncorrect'' speci®cation for an ill-

de®ned layout problem, then train the ANN by using a

variety of layout examples ( patterns) collected from

real situations. After the training is complete, the

ANN can provide fast generalized solutions (Kapura,

1996).

Figure 2 (Barakat et al., 1995) expresses the

relative degree of layout ¯exibility using various

computer-aided methods. The ANN layout

approaches can be seen to have highly detailed

problem representation and low computational

effort. The combinatorial nature of classical methods

results in high computational effort and rough

problem representation. However, the above paper

did not address the solution of layout problems by

ANNs, although it did mention it as a prospective

research area.

3. NBES versus RBES

Both an RBES and an NBES attempt to simulate

human judgement in reaching a conclusion. Their

areas of usefulness, while not identical, do overlap.

If one has expert staff but few test cases, RBESs are

perhaps more effective to use, owing to the fact that

they construct the conscious problem-solving pro-

cess of experts, deducing approximate solutions by

the RBESs. In contrast, if one has many test cases

but limited expert staff, NBESs can be a useful

technology by taking advantage of the way they

model the problem solver's thought process,

providing an approximate solution. Both RBES

and NBES are capable of providing semantic

descriptions and appending with an explanation

mechanism.

The major differences between an RBES and an

NBES lie in the acquisition (Lauria, 1988) and the

representation (Hanson and Burr, 1990) of domain

knowledge. In an RBES, domain knowledge is

acquired from experts and is explicitly saved in the

Fig. 2. Flexibility of various facility layout techniques (Barakat et al., 1995).

362 Yun-Kung Chung

form of well-de®ned rules and facts that can be easily

analyzed, modi®ed, documented and explained, but

the process knows nothing about the underlying

problem. Moreover, since the rules and facts are

often only approximate descriptions of a domain

problem, the imprecision and context dependence

among them can produce inconsistency during

deductive inference and may cause errors in the

®nal solution.

On the other hand, the domain knowledge stored in

an NBES memory is directly abstracted from a set of

training examples through its self-learning and self-

organization capabilities. These training examples

were acquired from experiments, experiences, theore-

tical results or from historical databases, and were

implicitly incorporated into the ANN parameters.

This abstraction allows relatively imprecise represen-

tation of complex relationships between the input and

the output variables de®ned in the domain knowledge.

Thus, self-learning captures the meanings of the

underlying problem, while self-organization adapts

the context of the learned knowledge. Because this

adaptive knowledge base is distributed over numerous

neural connections, an NBES can work with data that

is incomplete or even wrong, thus accommodating

input variations. Although this fault-tolerant cap-

ability can induce a solution to indeterminate

situations from experience or learned examples,

spurious solutions can be generalized due to weak or

improper learning parameters. Table 1 exhibits the

conceptual differences between the two types of ESs.

4. Why BAM-based expert systems?

As discussed above, the motivation for developing a

neural layout system, in addition to the advantages of

ANN, comes from the fact that the construction of an

appropriate and ¯exible facility layout for a given set

of requirements can re-lay out facilities or reroute

¯ow paths for the production of different types of

products. As a consequence, the problem of how to

determine an appropriate ANN model to design the

¯exible facility layout system is raised.

The primary reason for taking Kosko's (1988a, b)

BAM as an NBES framework is that it has a very

simple architecture for easy and effective implemen-

tation. Section 5 will describe the implementation.

The second reason is that BAM needs fewer

training patterns than required by BPN. It is well

known that in order for BPN to attain greater

recognition or generalization accuracy, the number

of (statistical) training patterns must be suf®ciently

large. Usually, in the case of practical facility layouts,

because the available number of layout patterns to

train BPN may not be suf®cient, then BAM could be a

better ANN model to implement an NBES.

Table 1. Comparison of NBES with RBES characteristics

Characteristics NBES RBES

Rules Implicit weight connectivity Explicit If-Then predicates

Facts Abstract neurons Linguistic variables

Knowledge base Weights Rules and facts

Reasoning type Inductive (best matching) Deductive (exact matching)

Incomplete reasoning Yes No

Knowledge generation Yes No

Knowledge representation Data vectors Rules and facts

Knowledge acquisition Learn from examples Interview with experts

Knowledge maintenance Easy Dif®cult

Combinatorial expansion of knowledge Low High

Natural parallellism Yes No

Learnability Yes No

Contradictory conclusion Yes Yes

Fault tolerance Yes No

Problem size expansion Possible Dif®cult

Explanation facility No Yes

Real-time control High Low


The third and most important reason is that in

describing a layout application area, a planner may

not know all the cases or typical situations, so that the

initial layout speci®cation is only partial.

Consequently, the primary layout information is

put through a stage of interpretive testing and

incremental reformulation by identifying imprecise

or incorrect pieces of layout information. This

incremental reformulation process is dif®cult to

implement using classical layout methods, including

BPNESs. The development of BAMES approaches,

however, can provide the procedure for the incre-

mental reformulation.

The proposed BAMFLO system is constructed by

a pipeline structure with multiple BAM incremental

learning, thus it is a very effective method to set up

a large-scale NBES for facility layout problems.

The ability of a BAM for incremental learning to

update its knowledge by incorporating new layout

examples without retraining all old examples as

well as the pipeline structure (Haque and Cheung,

1994; Kang, 1994) gives BAMFLO a high bidirec-

tional generalization accuracy. The incremental

nature and the bidirectionality of BAM distinguish

it from the more broadly used BPNES. BPN does

not have incrementability since its learning is done

based on a predetermined number of example pairs

(input vs. output) in a given training set, thus it will

forget learned knowledge if this learned knowledge

is not incorporated along with new knowledge to re-

form an updated training set. To retrain learned

knowledge requires excessive computational time.

In principle, BPN will not favour NBES implemen-

tation for domain circumstances where the

knowledge may be dynamically updated, changed

or increased.

5. BAM rationale

The discussion in the above sections illuminates

several properties of BAM which distinguishes it from

BPNs in regard to memory. Because the associations

in BAM are allowed to interact with each other, an

implicit representation of structural relationships and

contextual information can develop, and as a

consequence, a very rich level of interactions can be

captured. Even there are few associated rules, BAM

still has extensive indexing and cross-referencing in

its memory. BAM self-organizes a distributed

representation which is context-dependent. Recent

comparison with several associative memories indi-

cates that BAM provides superior performance

(Michel and Farrell, 1990; Lee and Wang, 1996).

Furthermore, it has successfully demonstrated its

capability to recognize part shapes distorted by

various means such as scaling and noise (Lu et al.,1989). Recently, BAM has also been enhanced and

applied for pattern recognition (Wang et al., 1994;

Shi, 1997) as well as image processing (Jiang and

Yuan, 1994).

5.1. BAM structure

The schematic representation of a BAM neural

network is shown in Fig. 3. The network consists of

a layer of p neurons, X, and a layer of q neurons, Y.

The neurons of both layers are fully interconnected.

Fig. 3. BAM architecture.

364 Yun-Kung Chung

Each neuron in X is connected to each neuron of Ythrough a set of weights, M, which is a p6q synaptic

matrix (memory). Similarly, each neuron in Y is

connected to neurons in X via weights, MT , the

transpose matrix of M. BidirectionalityÐforward and

reverse information ¯owÐis introduced in BAM to

permit two-way associative (i.e., hetero-associative)

search for a stored stimulus-response (If-Then)

association �A�i�;B�i�� for 0 � i � n, where i denotes

an index of intermediate association recollecting in

the generalization search. The hetero-associative

generalization search accepts either one or two input

patterns on one or two layers of neurons and produces

the related but different output patterns on both layers

of neurons; namely, given pattern vector A and/or B(or some noisy portion of them), generalize both Aand B. The inputs to BAM layers are the bipolar (or

binary) value represented for the existence or the lack

of an attribute of the inputs. The input attribute is 1 if

it is active or existing, or ÿ 1 if it is inactive or

missing.

5.2. BAM incremental learning and generalization

BAM adopts an unsupervised method of incremental

learning and functions in two phases:

(1) Memory construction (i.e., learning) phase. The

memory matrix is created by learning the stimulus-

response associations, or If-Then rule patterns, one by

one. The domain knowledge consisting of the If-Then

associations is distributively encoded into the con-

structed memories (weights) on the interconnections

between BAM neurons. Once a new association is

found in the domain, it can be directly individually

added into the existing memories by means of a very

simple matrix product computation without retraining

the former learned associations;

(2) Solution recall (i.e., generalization) phase.

When an unsure or a known If-pattern is used to

recollect its associated Then-pattern (or its close

approximation), the solution of the pattern will be

generalized from the constructed memories by means

of very fast inverse matrix computation.

Memory construction is accomplished by asso-

ciating m pairs of vectors into BAM. This can be

written as

M �Xm

i�1

ATi Bi �1�

which describes a p6q real matrix M, interpreted as a

matrix of memory between the two layers of neurons.

During the solution recalling, information can be

generalized in either direction; i.e., AM generalizes Band BMT generalizes A. Both generalizations are

accomplished via a threshold function f to each

element x in the either generalization matrix product.

Here, f is a step function de®ned in terms of a

threshold value S, by:

f �x� � ÿ1 if x5S

f �x� � 1 if x4S

f �x� � x if xÿ S

8><>: �2�

Selecting S � 0 assures a bipolar output pattern, and it

is easily shown that, given A � A�1�, this threshold

procedure generates B�1� in a single iteration. If one or

two attributes of the original A�1� are ¯ipped (to

simulate unknown or erroncous input data), several

iterations are required to reach a stable solution. These

iterations are such that B�1� is fed back through MT

and thresholded to produce A�2�, which produces B�2�

when multiplied by M and thresholded through S. The

whole iterated procedure constitutes the sequence of

the BAM generalization: A�1�?M?B�1�?MT

?A�2�?M?B�2�? � � �?MT?A�n�?M?B�n�. This

back-and-forth ¯ow of distributed information will

continue until equilibrium is reached on a ®xed vector

pair �A�n�;B�n��. Likewise, if an associative memory

matrix M reaches its equilibrium for every input

vector pair (A, B), then M is said to be bidirectionally

stable. It has been shown that BAM will always

converge rapidly (Kosko, 1988a, b). The following

iterative algorithm summarizes the above solution

generalization:

(1) Read pattern A�t�; i � 0;

(2) Compute pattern B by the matrix product

B�i� ÿ A�i�M;B � f �B�i��;(3) Compute vector A by the matrix product

A�i�1� � B�i�MT ;A � f �A�i�1��.(4) Repeat steps 2 and 3 until a stable (A, B)

solution is reached.

Finally, the energy function E for BAM is written as

follows:

E � ÿBTMA �3�


5.3. A numerical BAM example

Here, an example of the BAM processing is

introduced in some detail. Suppose there are two

pairs of training associations:

A1 � �1;ÿ 1;ÿ 1; 1;ÿ 1; 1; 1;ÿ 1;ÿ 1; 1�;B1 � �1;ÿ 1;ÿ 1;ÿ 1;ÿ 1; 1�A2 � �1; 1; 1;ÿ 1;ÿ 1;ÿ 1; 1; 1;ÿ 1;ÿ 1�;B2 � �1; 1; 1; 1;ÿ 1;ÿ 1�

According to Equation 1, the memory matrix M is

constructed as follows:

M �

2 0 0 0 ÿ 2 0 2 0 ÿ 2 0

0 2 2 ÿ 2 0 ÿ 2 0 2 0 ÿ 2

0 2 2 ÿ 2 0 ÿ 2 0 2 0 ÿ 2

0 2 2 ÿ 2 0 ÿ 2 0 2 0 ÿ 2

ÿ 2 0 0 0 2 0 ÿ 2 0 2 0

0 ÿ 2 ÿ 2 2 0 2 0 ÿ 2 0 2

266666666664

377777777775�4�

and its transpose matrix is readily constructed. Using

Equation 3, the energy of the BAM with the two

associations is ÿ 64.

To observe BAM generalization progression,

assume that an initial A�1� pattern differs from the

®rst training pattern A1 by only one attribute value.

The initial B�1� vector will be equal to the second

training pattern B2, i.e.,

A�0� � �ÿ 1;ÿ 1;ÿ 1; 1;ÿ 1; 1; 1;ÿ 1;ÿ 1; 1�

B�0� � �1; 1; 1; 1;ÿ 1;ÿ1�

The energy of BAM in this initial state is ÿ 40. Based

on Equation 2 and running the four steps of the

solution generalization, the partial intermediate

associations are:

B�1� � �1;ÿ 1;ÿ 1;ÿ 1;ÿ 1; 1�;E � ÿ 56;

A�1� � �1;ÿ 1;ÿ 1; 1;ÿ 1; 1; 1;ÿ 1;ÿ 1; 1�;E � ÿ 56;

B�2� � �1;ÿ 1;ÿ 1;ÿ 1;ÿ 1; 1�;E � ÿ 64;

A�2� � �1;ÿ 1;ÿ 1; 1;ÿ 1; 1; 1;ÿ 1;ÿ 1; 1�;E � ÿ 64;

final B�3� � �1;ÿ 1;ÿ 1;ÿ 1;ÿ 1; 1�;E � ÿ 64;

final A�3� � �1;ÿ 1;ÿ 1; 1;ÿ 1; 1; 1;ÿ 1;ÿ 1; 1�;E � ÿ 64

Notice that the ®nal energy value is never changed

and the ®rst training pattern A1 has been stably

generalized.

6. Structure of BAMFLO

This section presents the contents and functions of

various modules of BAMFLO as well as their inter-

relationships. There are two essential design features

of BAMFLO. First, in terms of the conceptual

framework suggested in the literature for intelligent

systems (Kusiak, 1987; Jacob et al., 1991; Sim et al.,1994) BAMFLO closely approximates some of the ES-

oriented approaches, in that it has a separate BAMES

attached to various phases of a layout problem solving

(see Fig. 4). This multi-BAMES structure is structured

such that there is high degree of cohesion within each

BAMES but a very low degree of coupling between

them. This feature provides a convenient platform for

further developing each individual BAMES and

facilitates debugging. It also speeds up memory

construction and solution generalization because

each BAMES deals with only one kind of layout

problem containing a ®xed number of facilities.

The second feature is that appropriate classical

layout programs can be attached in tandem to

BAMFLO. This can help improve the construction

layout solutions generalized from BAMFLO; how-

ever, it also can reduce the functionality relationships

366 Yun-Kung Chung

among facilities to a signi®cant degree as the material

¯ow is improved within the layout. This con¯ict and

the tandem structure will not be considered in the

current BAMFLO development. Figure 4 exhibits the

modules considered:

(1) Dialogue management module coordinates the

information ¯ow and provides a backward commu-

nication loop between modules;

(2) Database module contains the structures of a

variety of representative layout data or examples

acquired from the user or the solution base. The data

conform to a format that facilitates exact formulation

of a layout problem via an interactive dialogue;

(3) Example generation module transforms input

layout data received from both the solution base and

the database or the classical software modules to

ef®cient neural layout patterns (rules). Both new

layout experience and the latest layout solution can be

inserted readily and incrementally into an appropriate

BAMES to adapt neural layout knowledge;

(4) Model base module is composed of BAMES

models in parallel, based on different layout problems.

As can be seen, BAMFLO has a decentralized structure

Fig. 4. Structure of BAMFLO system.


for its inference engine and knowledge base to be

distributed in each BAMES. The inference process

used in each BAMES is an invisible type of multiple

bidirectional generalization, and the BAMES knowl-

edge base is composed of implicit weight memories;

(5) Solution base module retains ef®cient layout

solution alternatives in the form of neural patterns

generalized from BAMESs in the model base. This

module can be further attached in tandem to the

improvement layout module. The solution base

module also screens inef®cient alternatives by means

of a dialogue management module. After developing

as many feasible and ef®cient alternatives as allowed

by user speci®cations, the set of all such alternatives

can be passed on to the example generation module for

incremental learning of BAMFLO.

The modularity makes BAMFLO easier to add or

revise its layout knowledge base, and more con-

venient for integration in tandem with other

improvement layout software without complete

development. BAMFLO is one subsystem of this

paper's intelligent integrated facility layout system,

and can be further cooperatively used with other

classical layout subsystems used to create qualitative

layout examples for training or to compute quantita-

tive analytical data.

7. Implementation of BAMFLO

As shown in Fig. 5, there are three major steps used to

implement BAMFLO for a construction layout

problem; (1) training example generation; (2) incre-

mental learning; (3) solution generalization. Training

examples used to build layout knowledge can be

generated from a classical construction or an

improvement layout software. Without loss of

generality, the training layout examples of this paper

will be borrowed from published literature to evaluate

the performance of BAMFLO by comparing its

solutions with the original solutions.

After incorporation of training examples, the

dedicated C�� language programs transform the

speci®cations of the acquired training examples to

neural layout patterns input to BAMFLO for incre-

mental training. Then, the trained BAMFLO will use

the acquired knowledge to multibidirectionally gen-

eralize a solution. If there are useful layout rules

discovered in the generalized layout solution, they can

also form one of the sources of incremental training

examples. The unique incrementability of BAMFLO

can be salient with training new layout experience,

new layout rules or additional solutions output from

classical layout software (e.g. CORELAP or

COMLAD (Sule, 1992)).

Before explaining the major steps for BAMFLO

implementation, a detailed example of embedding If-

Then layout rules into BAMES is put forth to illustrate

the idea of an NBES implementation based on BAMs.

7.1. Embedding of layout rules into a BAM-basedES

Early precursors of the NBES methodology research

that inspired this present work were:

(1) The idea of memory-based reasoning (Koch

and Fchsenfeld, 1995; Sanou et al., 1996) that

involves drawing inferences directly from a large

database of undigested facts and experiences as well

as discovering new rules or facts from the database;

(2) The work of Denker et al. (1987), Gallant

(1988) and Kasabov (1996), for the methodology in

which an RBES can be cast into an NBES by viewing

the conditions and the consequences of If-Then rules

as either data or facts; namely, neural patterns can be

thought of as being divided into If and Then ®elds by

the rule's semantic interpretation;

(3) The proposal of Ajjanagadde and Shastri

(1991) for addressing that a basic component of an

ANN mechanism is the ability to adaptively learn

variables or rules standing for the data and the facts in

the domain. The variables are embedded into the

ANN's neurons and the rules are mapped onto the

ANN's interconnections. Both of such neurons and

such interconnections are the knowledge used to

generalize a solution.

The idea of casting or embedding If-Then rules into

a BAM process is illustrated in Fig. 6 by a three-layer

BAMES consisted of two BAMs. Consider the three

If-Then layout rules de®ned by Malakooti and

Tsurushima (1989):

Rule 1:

IF the Department is not assigned yet

And Other_Department is assigned to Other_Site

And the Site is adjacent to Other_Site

And the Site is available to be occupied

And assigning the Department to the Site is not

368 Yun-Kung Chung

Fig. 5. Structure of the intelligent BAMFLO system.


prohibited

THEN assign the Department to the Site

Rule 2:


And the Department requires electric power


And the Site has electric power


prohibited


Rule 3:


And the Department requires compressed air


And the Site has compressed air


prohibited


Let the corresponding neural layout patterns be

broken down into several ®elds (layers) as

Department, Dept-Site and Site, respectively,

according to semantic interpretations of the three If-

Then rules:

Each ®eld attribute (neuron) can be the values � 1,

ÿ 1 and 0 depending on whether the assertion is true,

false or unknown. The neuron representatives for the

®elds are also shown in Fig. 6. As a result, the above

layout rules can thus be represented respectively by

neural pattern vectors as follows:

Rule 1: x1 � �1 ÿ 1 ÿ 1 1�; y1 � �1 1 1�;z1 � �1 ÿ 1 ÿ 1 1 1�

Rule 2: x2 � �1 1 ÿ 1 ÿ 1�; y2 � �1 ÿ 1 1�;z2 � �1 1 ÿ 1 ÿ 1 ÿ 1�

Rule 3: x3 � �1 ÿ 1 1 ÿ 1�; y3 � �1 ÿ 1 1�;z3 � �1 ÿ 1 1 ÿ 1 ÿ 1�

Therefore, two pairs of knowledge bases set up by the

BAMES incremental learning derived in Section 5.2

are:

Mxy �

3 ÿ 1 3

ÿ 1 ÿ 1 ÿ 1

ÿ 1 ÿ 1 ÿ 1

ÿ 1 3 ÿ 1

26666664

37777775 MTxy �

3 ÿ 1 ÿ 1 ÿ 1

ÿ 1 ÿ 1 ÿ 1 3

3 ÿ 1 ÿ 1 ÿ 1

26643775

Myz �3 ÿ 1 ÿ 1 ÿ 1 ÿ 1

ÿ 1 ÿ 1 ÿ 1 3 3

3 ÿ 1 ÿ 1 ÿ 1 ÿ 1

26643775 MT

yz �

3 ÿ 1 3

ÿ 1 ÿ 1 ÿ 1

ÿ 1 ÿ 1 ÿ 1

ÿ 1 3 ÿ 1

ÿ 1 3 ÿ 1

26666666664

37777777775

Fig. 6. Embedding of layout rules into a three-layer BAMES.

Layer X (Department Layer) Layer Y (Dept_Site Layer) Layer Z (Site Layer)

x1: `ìs_not_assigned'' y1: `ìs_not_prohibited'' z1: `ìs_available''

x2: ``required_electric_power'' y2: `àssign_to_other'' z2: ``has_electric_power''

x3: ``requires_compressed_air'' y3: `àssign_to'' z3: ``has_compressed_air''

x4: `òther_dept'' z4: `ìs_adjacent_to''

z5: `òther_site''

370 Yun-Kung Chung

The following are examples that are multi-bidirec-

tionally generalized through the knowledge bases

(generalizers), where the question mark (?) denotes an

output attribute:

�1� x � �� 1 ? ÿ 1 ?� )Mxy �� 1 � 1 � 1� )

Mxy �1 ÿ 1 ÿ 1 1 1�

�2� y � �? ÿ 1 ?� )Mxy �� 1 0 � 1 0 0� )

MTxy �� 1 � 1 0 0�

The second example clearly represents a reasonable

response to contradictory information being not

explicitly considered in the knowledge base. Also,

from the embedding methodology, it can be seen that

the neural layout rules represent expert knowledge

that simultaneously describes relationships between

``layout requirements (inputs)'' and ``layout exam-

ples (con®gurations)''. That is, the neural rules have

functions that abstract and characterize requirements

of the layout rule set. At the same time, the neural

rules also function as the representation of a layout

con®guration (or example) of the rule set.

Moreover, in the generalization phase, BAMES can

rapidly process its input layout requirements to

produce associated facts and consequences. The

trained BAMES is useful for fast identi®cation of

implicit and hidden layout rules by automatically

analyzing cases of historical layout data and experi-

enced layout con®gurations from the learning phase.

The trained system analyzes the layout clues to

identify patterns and relationships that may subse-

quently lead to rules for laying out facilities. The

identi®ed layout rules then can be extracted to form

the generalized layout con®guration.

To sum up, a BAMES realization of classical

RBESs has the following characteristics:

(1) Complete or preferred inputs or outputs are not

required and each memory matrix M is bidirectionally

stable in the sense that, starting with any layer,

BAMES will converge to a stable state within de®nite

iterations;

(2) The incremental learning and the embedding

methodology are readily implemented and are capable

of learning knowledge from past experience,

abstracting features from correlated or associated

data without relearning the learned knowledge;

(3) BAMES will develop an adaptive knowledge

base containing structured or unstructured assertions

that can be interpreted by a multiple bidirectional

generalization inference mechanism or an induction

reasoning process in order to quickly derive a solution

from unforeseen inputs;

(4) Domain layout knowledge is adaptable and does

not need to have a complete and consistent knowledge

of the problem. It can be utilized to aid in perfecting

and re®ning BAMES by allowing experimentation and

incremental growth of practical layout experience.

7.2. Training example generation

The collection of layout examples for training

BAMFLO is inexpensive. Figure 7 shows that the

training examples can be generated from empirical

simulations, historical data or layout software pro-

grams. The training examples they generate should be

accurate, re¯ect the experienced descriptions covering

the broad range of potential layout designs, and

contain only relevant factors. In this way, the layouts

generalized will then be able to ®nd useful semantic

descriptions for new layout con®gurations. If the

evaluation results of the interpretations are within the

constraints enforced by layout requirements, then

information to decide which rules of a layout

con®guration are desirable for BAMFLO learning

can be derived from proper semantic interpretations.

The evaluation criteria can be the maximized facility

functionality or the minimized material ¯ow, or an

experienced layout planner's judgement.

The problem of selecting rational layout examples

is especially critical when using an incremental

learning mechanism with consistent input rules or

examples (Schlimmer and Granger, 1986). The term

``consistent'' indicates that if certain rules must be

modi®ed or selected in order to maintain consistency,

then no two rules can be simultaneously matched for

the same input conditions, and no rules contain

opposite output values in the same rule set. If a new

rule is given conditions, then old rules which match

with the new rule but give different outputs are

deleted or modi®ed such that the matching cannot

take place. Neural rules can also be increased when

the different information is presented by fewer rules

or variables.

The procedure for screening inconsistent or

inef®cient alternatives is a preprocessing for selecting

rational examples saved in the database and for

speeding up the generalization. For example, to delete

unimportant variables in advance allows only critical


variables to remain in training rules, thus increasing

the speed of critical variable generalization

(Ajjanagadde and Shastri, 1991). The ``Neural

Layout Rule Development'' oval block in Fig. 7 is

such a preprocessing procedure for the design of

neural layout rules discussed below. The procedure

transforms the selected examples (consistent rules)

with critical layout factors (variables) into complete,

detailed neural patterns ready to be embedded into

BAMFLO. Extensive efforts in the embedding process

and on its analysis are conducted to limit layout

complexity, to make the ®nal selection of rules, and to

draw up a layout con®guration. The layout con®gura-

tion is conducted on four types of training layout

patterns: relationship, relative position, area block

and site-ordained patterns. The four factors are

frequently taken into account in classical layout

models as well.

Fig. 7. Layout example generator.

372 Yun-Kung Chung

Figure 8 illustrates the codi®cation of the repre-

sentation for the four neural patterns of a layout

training example taken from Malakooti and

Tsurushima (1989). To acquire enough consistent

semantic descriptions for this example, the generation

of the training patterns are structurally and system-

atically reconsidered based on the embedding concept

proposed in Section 7.1, and on the principles for

designing one-to-one associations in a decision table

(Seagle and Duchessi, 1995). This reconsideration is

able to eliminate inconsistent rules. Both Fig. 8(a), the

four-machine optimal solution, and Fig. 8(b), the

layout's closeness relationship, are obtained from the

RBES of Malakooti and Tsurushima (1989). Parts (c),

(d), (e) and (f ) of the ®gure are the four cogitated

neural patterns.

7.2.1. Neural closeness relationship representation

The layout of facilities should re¯ect their functional

relationships. Muther's facility function relationship

classi®cation AEIOUX (Sule, 1992) is generally used

to state whether the closeness degree between any two

facilities is extremely important (A) down to

unimportant (U), or whether facility non-closeness is

extremely important (X). For example, if the paint

facility is located next to the welding facility, an

explosion is possible. The closeness degree is

determined by layout designers' experience and

functional layout restrictions.

In order to represent the neural closeness relation-

ship, the number of l's is used to express the extent of

the relationship: the more l's the higher the closeness

degree. Six l's represent degree A, ®ve for E, four for

I, . . ., one for X. For example, Figure 8(b) shows the

degree of closeness relationship between the milling

machine and the grinding machine is E, thus the row

indicated by the symbol G-M in Fig. 8(c) contains ®ve

l's, and each of other spaces of the row contains a ÿ l.

7.2.2. Neural relative position representation

The difference between the closeness relationship and

the relative position is that the former focuses on the

degree of closeness between facilities, but the latter

considers the four reference positions (above, below,

left and right) which are the placement sites of a

facility relative to other facilities. When one facility

should be positioned to the right side of another

facility does not indicate that the facilities have to be

near one another. This layout requirement is one form

of the non-adjacency assignment introduced by

Kumara et al. (1988a, b), who encoded the relative

facility positions into their syntactic pattern recogni-

tion rules. The consideration of the relative facility

positions is related to the manufacturing process path,

facility support, and AGV delivery path.

In order to generate a neural position pattern, the

principle for codifying the four relative positions of a

facility is: four l's are for the ``right'' position of one

facility relative to another, three for ``left'', two for

``below'' and one for `àbove''. In Fig. 8(a), the

drilling machine is positioned to the `right' of the

milling machine, thus in Fig. 8(d) the row D-M

corresponding to the ``right'' position in the neural

position pattern is codi®ed with four l's. If the abstract

representation of the relative position D-M were to be

two l's, the meaning will be that the drilling machine

is ``below'' the milling machine. Each remaining

space of the row contains a ÿ l.

7.2.3. Neural area block representation

The key idea of the area assignment process in facility

layout is to maximize the space utilization for material

receiving and shipping, to keep components and

products as close to each facility as practical, and also

to provide for employee safety and job satisfaction.

Practical discrete block representation of areas is

considered by BAMFLO. The shape of a machine is

always represented by a rectangle. The area block

requirement of a particular facility can be the

dimension of the facility, and the available shop¯oor

space for all layout facilities is rectangular with its

maximum dimensions known.

In order to neurally represent a facility's work area,

each of the `àrea neurons'' in the neural layout

system is de®ned as one unit of area. For example, one

area neuron (unit) could be 5 m2. Suppose the turning

machine requires ®ve area units and the row T

corresponding to it in the neural area pattern has ®ve

l's, as shown in Fig. 8(c). A general principle of the

codi®cation is: a l stands for a unit of area, two l's for

two units, and so forth. The maximum number of area

units available for a facility is limited to six, and this

can be increased to any number by modifying the

dimension of the area block pattern. If the area of a

facility is less than six units, the remaining units (dies)

are marked with ÿ l's.

7.2.4. Neural site constraint representation

In addition, allocating a facility to an ordained site

also frequently occurs in actual practice, as the result


Fig. 8. An example used to train the BAM-based layout system ((a) and (b) are from Malakooti and Tsurushima, 1989).

374 Yun-Kung Chung

of the facility closeness relationships described above.

The efforts to review the ordained site allocation

include layout topology, water ¯ow, roadways,

material ¯ow, load/unload spots, AGV path, facility

operation constraints and physical utility locations.

Malakooti and Tsurushima (1989) took these types of

site constraints into their RBES.

An example of the neural pattern for representing a

site allocation is shown in Fig. 8(f ), in which row T is

®lled with three 1's. This implies that the turning

machine in Fig. 8(a) must be allocated to Site 3. In

principle, the number of 1's correspond to the acting

code for a speci®ed site. Subsequently, ÿ l's ®ll out

the other spaces of the site constraint row (rule).

7.3. BAMES incremental learning

BAMES can be used to closely mimic nonlinear

layout relationships based on the above four neural

layout representatives. These four high-dimensional

layout associations can be represented by a pipeline

BAM, which is a novel extended BAM structure

proposed here. The information obtained from If-

Then rules of a layout example is used to establish

neural layout patterns to be learned by BAMES.

These patterns increase as a result of layout

experience and become the basis for maintenance

practices of the layout knowledge base consistency.

As training experience accumulates, the increase in

learning patterns is presented to BAMES and then the

capability of the layout knowledge is adapted without

reviewing old (learned) layout patterns. Thus, the

BAMES learning algorithm incrementally embeds

new arrival layout patterns into its knowledge base. In

other words, it learns the rules of example 2 based on

the previously learned rules of example 1, then learns

rules of example 3 based on both rules of examples 1

and 2, and so on. In general, the consistent rules of any

old or new example to be learned at a certain time

point are based on all rules learned before that time

point. Figure 9 shows the multiple incremental

learning strategy of BAMES.

Figure 10 unfolds a four-layer BAMES consisting

of three BAMs. As explained in Section 7.1, each type

of the four major neural representatives for construc-

tion layout is individually embedded into one layer.

The layout rules' semantic interpretations and the

layout variables are hidden in weight connections and

in connected neurons, respectively, Each neuron in

one layer represents both the If-®eld and the Then-

®eld, given by layout rules as conditions and

consequences. This means that each neuron in a

Fig. 9. BAMES multiple incremental learning strategy.


layer stands for one abstract concept (assertion) of a

layout rule. With the aid of the simple and direct

embedding methodology explained in Section 7.1,

three BAM memories de®ne each stored layout

example, for which the ®rst memory MAB stores the

associations between the closeness relationship and

the relative position, MBC de®nes the associations

between the relative position and the area block, while

MCD contains the associations between the area block

and the site constraint.

Let �Ai;Bi;Ci;Di� for i � 1; 2; . . . ;m, be the

bipolar vectors of layout associative factors to be

learned. Mathematically, the equation for building the

BAMES layout knowledge base can be extended from

Equation 1 and becomes:

MAB �Xm

i�1

ATi Bi

MBC �Xm

i�1

BTi Ci �5�

MCD �Xm

i�1

CTi Di

where the ®rst and second subscripts of the matrices

denote the source and the destination layers, respec-

tively. Obviously, the value assigned to a connection

weight comes directly from the multiplication value

of attributes of all training layout rules. Thus, the

semantic interpretation of these connection weights

Fig. 10. A BAMES composed of three BAMs.

376 Yun-Kung Chung

can be derived from the attributes' information

contained in layout rules. Moreover, when the

information in one of these rules is updated, the

connection weights can be also easily via the

matrices' product operations.

With the associations encoded, as in Equation 5, in

directions A?B, B?C, C?D, and reverse direction

associations obtained through the respective weight

matrix transposes, the algorithm for BAMES incre-

mental learning proceeds as follows:

Step 1. Initialize all memories Mij and layout

associative rules A�i� B�i� C�i� and D�i� for all i and j.Step 2. Transform the experienced layout rules and/

or the best solutions generated by a classical layout

software program to the bipolar neural layout patterns.

Step 3. Read the bipolar neural layout patterns into

A�i�, B�i�, C�i� and D�i� for the layout rule associations

to be learned.

Step 4. Learn the desired associations by com-

puting Equation 5.

Step 5. Repeat steps 2 and 3 until there are no

further layout rule associations to learn.

Step 6. Save the layout con®gurations into the

database.

Step 7. Keep memories constructed in step 5.

Step 8. If new training layout patterns occur, go to

step 2.

The numerical calculation processes of the incre-

mental learning and the multiple bidirectional

generalization described next are similar to those in

Sections 5.3 and 7.1.

7.4. Bidirectional solution generalization

Generalization is the ability for an ANN, when

presented with an input not encountered during

learning, to still produce an output with good

probability to be correct. BAMES incremental

learning has been proposed as means for automating

the acquisition of knowledge (Cox et al., 1995) for

domain layout problems. Its interlayer connection

weights are con®gured with the required knowledge to

store the ideal patterns of the rules that form the layout

con®gurations for matching input requirement in the

generalization process. For the input layout require-

ments, which may be uncertain, each entry represents

a ®ring attribute of a neuron during the solution

generalization process.

In Fig. 10, three BAMs that constitute a BAMES

are used to create generalizers MAB, MBC and MCD

and their transposes based on Equation 5. Their

generalizations proceed as follows. Each neuron

independently and synchronously updates its output

based on its input sum from other layers:

A� j� � f �B� j�MTAB�

B� j� � f �MABA� j�� f �C�j�MTBC� �6�

C� j� � f �MBCB� j�� f �D�j�MTCD�

D� j� � f �MCDC� j��where the threshold function f and superscript j are the

same as those described in Section 5.2. The neurons'

states change synchronously according to Equation 6

until three bidirectional stable states are reached.

To generalize a recommended layout for a certain

input condition, BAMES recollects the connections of

the well-trained layout con®guration. This is accom-

plished by manipulation of the association memories

and each transpose. The generalization of BAMFLO

can start at any one or more layers. The generalization

of the four layers yields a layout con®guration by

referring to the database. Schematically, the general-

ization algorithm of BAMES proceeds as follows:

Step 1. Input new layout associative requirements

A� j�, B� j�, C� j� and/or D� j� to be generalized by

BAMES.

Step 2. Generalize any layout association, e.g., A� j�

and C� j�, to other associations, e.g., B� j� and D� j�, by

computing Equations 6 and 2.

Step 3. Repeat the generalization step until there

are no changes in all generalized associations.

Step 4. Search the historical layout database to ®nd

the best matched layout con®guration.

Step 5. If such a con®guration is found, save it into

the solution base and give it to the layout planner;

otherwise, terminate BAMFLO, or manually analyze

and extract new layout rules implicit in the general-

ized layout, if necessary.

Step 6. Read the extracted layout rules into the

database for incremental learning; i.e., go to step 8 of

the BAMES multiple incremental learning algorithm.

8. Operation and performance of BAMFLO

In developing BAMFLO implementation, the goal has

been to enhance application potential, user-


Fig. 11. Cases for learning BAMFLO system.

378 Yun-Kung Chung

friendliness, ef®ciency and availability of BAMES

incremental learnability for the multiple bidirectional

generalization of the best layout solution. In this

section, ®ve pilot runs are conducted to test the

performance of the current BAMFLO; of which, four

test cases from previously published research are

shown in Fig. 11. Case 5 is shown in Appendix A,

where a four-machine layout problem from Malakooti

and Tsurushima (1989) is used as an example to

demonstrate how BAMFLO works for a layout

problem. It should be mentioned that the original

layout con®gurations in Cases 1 and 3 had irregular

block shapes, which poses a serious problem for

laying out real facilities whose shapes are rectangular,

thus, these examples are appropriately and slightly

revised to suit the BAMFLO learning process.

The arrow indicators listed in Appendix B are

requests for data input. The sequence of steps by

which BAMFLO arrives at its solution for a layout

problem includes: (1) problem data acquisition; (2)

elimination of infeasible and inconsistent problem

data; (3) user interaction for the transformation of

layout rules; (4) generating ef®cient layout alter-

natives; (5) generalizing the best solution. Owing to

space limitation, not all screen displays are listed.

This BAMFLO system was programmed in Borland

C�� on a personal computer.

In Case 5, the optimal layout solution was general-

ized even though some of the trained input layout

requirements were missing. This manifests that

BAMFLO can handle new imprecise data considered

as routing changes or uncertain requirements, which

the classical RBES by Malakooti and Tsurushima

(1989) could not deal with. Similar results are also

shown in Cases 1 to 4. The time required for the

training pattern generation for BAMFLO incremental

learning depends on the size of the learning layout

problem; nevertheless, the solution generalization of

BAMFLO requires much less time than the classical

iterated solution procedures.

Table 2 presents the data of BAMFLO's perfor-

mance, as described below:

(1) In all four cases, an optimal solution can be

generalized if the input data is completely precise; the

solutions are the same as those solutions obtained from

the layout approaches presented in the source papers.

(2) The number of optimal solutions to a large-scale

problem (Cases 1 and 4) is greater than that for a small-

scale problem. The reason for this may be that the

number of codi®ed neural rules for training is larger,

Table 2. Solution performance of BAMFLO system

Testing cases Percentage ofimprecise data input

Generalizedsolution

Case 1 0% Optimal

10% Optimal

20% Optimal

30% Feasible 2

40% Novel

50% Feasible 1

60% Novel

Case 2 0% Optimal

10% Feasible 3

20% Optimal

30% Novel

40% Feasible 2

50% Feasible 1

60% Novel

Case 3 0% Optimal

10% Optimal

20% Novel

30% Feasible 1

40% Feasible 1

50% Novel

60% Novel

Case 4 0% Optimal

10% Optimal

20% Feasible 2

30% Feasible 1

40% Feasible 1

50% Novel

60% Novel

Fig. 12. A prospective recurrent BAMES architecture.


thus they cause BAMFLO to have a high ``density'' of

distributed knowledge, or a strong connection strength.

As the connection strength is increased, BAMES may

be not affected by ``degradation''.

(3) The solution is sensitive to the attribute value

of an input layout requirement. For example, a

solution can be generalized even if the percentage of

imprecise input data is high. In contrast, more precise

input data may not generalize the predictable solution

but instead produce a ``novel'' generalized solution

for all testing cases. The meaning of ``novel'' is that

the generalized solution does not belong to one of the

trained layout examples in the database and implies

that it contains the additional implicit layout knowl-

edge unknown to an experienced expert. The

unknown knowledge or novelty could be manually

extracted by the expert to form new layout rules to be

incrementally learned by an appropriate. BAMES or

to physically re-lay out facilities on the shop ¯oor.

That Case 3 did not generalize the feasible solution 2

is another example for layout attribute sensitivity.

(4) Although BAMFLO technique represents a

unique opportunity for the codi®cation of adaptive

layout knowledge, the complete codi®cation proce-

dure still requires greater rule re®nement, coupled

with better learnability and generality, so that

generalized layout solutions will be of high quality.

For instance, Wang et al. (1991) provided such a BAM

with high learning performance in theory.

These ®ndings have implications for the implementa-

tion and the applications of BAMES in the future.

To improve the solution quality of BAMFLO, it is

also possible for the currently proposed BAMES to

cover the domain of more BAMs whose learning

schemes are recurrent (see Fig. 12). The recurrence

indicates some of the interesting research directions

such as high learning schemes. This architecture may

evolve, leading in a natural progression toward the

power of a prospective BAMES model. In this case,

stored associations are multiple and should be stable,

if the connection matrices are chosen appropriately so

that the associations remain unchanged along all

closed learning loops. However, it seems to be

dif®cult to analyze such complicated systems further.

9. Conclusion

To enhance re-layout ¯exibility in a manufacturing

system, a facility layout framework was proposed in

this paper that adapts a knowledge base and handles

data uncertainties. The simplicity and robustness of

BAM invites uncomplicated NBES implementation,

such as the proposed BAMFLO system. The system is

an off-line ES utility that will help layout planners to

more effectively work with the construction of facility

layout. The system exploits a BAM-based neural

network to classify layout requirements, including

closeness relationship, relative position, area size, and

site constraints into their corresponding layout

con®guration by means of the capability to learn

either past experienced layouts or theoretical layouts

output from computer software.

Borrowing layout examples from published litera-

ture, the ability of BAMFLO's multiple bidirectional

associative generalization was utilized to determine

the layout best ful®lling the input requirements. Five

cases from previous literature were used to test the

performance of BAMFLO solutions by taking advan-

tage of expertizing BAMFLO with the optimal and

feasible solutions obtained from the classical methods

described in the cited papers. The compared

performance results indicated that the level of quality

of a BAMFLO solution might be proportional to the

number of neurons that represent layout pattern

vectors. This indicates that the suf®cient training

patterns are necessary.

This paper describes several interesting character-

istics and capabilities of the BAMFLO system that

make it a promising alternative to supplement and

enhance current facility layout tools. Those character-

istics and capabilities include the following. The

BAMFLO system:

(1) Has a parallel and distributed structure that is

knowledge fault-tolerant and provides fast learning

and generalization processes, as compared to

BPNESs;

(2) Learns neural patterns transformed from the

training set; hence, there is no need for derivation and

computation of complex layout equations;

(3) Learns from layout examples obtained with

limited knowledge acquisition problems;

(4) Learns complex layout relationships without

requiring a knowledge engineer to undergo the time-

consuming task of rule formulation;

(5) Adequately generalizes layout solutions from a

set of limited training examples;

(6) Responds to noisy, incomplete, or unforeseen

inputs in an associative and adaptive manner;

380 Yun-Kung Chung

(7) Can be quickly and easily modi®ed to

implement other applications;

(8) Is able to perform dynamic and real time

functions, which is one of the most dif®cult task in

automation today;

(9) Has great potential for integration with other

algorithmic and knowledge-based expert system

tools, providing more ef®cient design, decision-

making and management systems.

Ultimately, the prevalence of NBESs in practice can

be judged by Wang (1997), Shin and Vishnupad

(1996), Burke et al. (1996) and Lin and Chang. As

NBES development is prevalent in various manufac-

turing processes, the overwhelming scope of NBES

applications becomes apparent. By taking the ®ndings

of the multiple BAM learning and generalization, this

paper has set a novel application of BAMs to design

¯exible and intelligent layout systems with adaptive

knowledge.

Acknowledgments

This work was supported by the National Science

Council in Taiwan under grant No. NSC84-2213-

E155-025. The author would also like to thank Mr.

Yun-Long Pen, a research assistant, for his extensive

help in computer programming for the system

described in the paper.

Appendix A. Training database module (testingcase 5)

Four possible training layout examples acquired from

Malakooti and Tsurushima (1989).

Appendix B. Running process of the BAM-basedlayout system

The operation of BAMFLO using the set of training

layout patterns is demonstrated as follows.

BAMFLO System for Facility Layout

Construction

AI/WWW Implementation Room

Industrial Engineering Department

Yuan-Ze Institute of Technology,

TAIWAN

Main Menu

(1) Create Neural Layout Patterns

File

(2) Create BAM Architecture of the

Layout

(3) Train the system

(4) Generalize a Layout Con®guration

(5) Quit the System

Input the Option Number ) 1

Numberoftraininglayoutexamples)4

Number of Facilities for a training

example ) 4

Name of Facility 1 ) Milling

Name of Facility 2 ) Drilling

Name of Facility 3 ) Turning

Name of Facility 4 ) Grinding

File name storing these training data

) BAMES4

Training layout example 1:

Create Relationship Pattern

[AEIOUX]:

Drilling - Grinding ) o

Drilling - Milling ) a

Drilling - Turning) u

Grinding - Milling ) e

Grinding - Turning) e

Milling - Turning ) u

want to see the relationship pattern

created

[(Y)es, (N)o] ) y

Drilling - Grilling: 111ÿ 1ÿ 1ÿ 1

Milling: 1 1 1 1 1 1

Turning: 11ÿ 1ÿ 1ÿ 1ÿ 1

Grilling - Milling: 11111ÿ 1

Turning: 11111ÿ 1

Milling - Turning: 11ÿ 1ÿ 1ÿ 1ÿ 1

Site1 Milling Site2 Drilling Site1 Turning Site2 Drilling

Site1 Turning Site4 Grinding Site3 Grinding Site3 Milling

(a) Optional solution (b) Feasable solution 1

Site1 Drilling Site2 Miling Site1 Milling Site2 Turning

Site3 Grinding Site4 Turning Site3 Grinding Site4 Drilling

(c) Feasable solution 2 (d) Feasable solution3


Create Relative Position Pattern

[(A)bove, (B)elow, (L)eft, (R)ight:

Grinding to Drilling) 1

Milling to Drilling ) b

Turning to Drilling ) b

Milling to Grinding ) b

Turning to Grinding ) b

Turning to Milling ) r

want to see the relative position

pattern created

[(Y)es, (N)o] ) n

Create Area Pattern:

Maximal limination of the area units

for a facility ) 6

Area units of Milling) 6

Area units of Drilling ) 4

Area units of Turning) 5

Area units of Grinding ) 6

want to see the area pattern created

[(Y)es, (N)o] ) n

Create Site Pattern

Code of available site of allocating

Milling ) 1


Drilling ) 2


Turning) 3


Grinding ) 4

want to see the orientation pattern

created

[(Y)es, (N)o ) y

Milling: 1ÿ 1ÿ 1ÿ 1

Drilling: 11ÿ 1ÿ 1

Turning: 111ÿ 1

Grinding: 1 1 1 1

Correction for all four patterns of

thetrainingexample 1[(Y)es,(N)o])n

Training layout example 2::::

Correction for four neural patterns

of the training example 4 [(Y)es, (N)o]

) n

Main Menu

(1) Create Neural Layout Patterns

File

(2) Create BAM Arohitecture of the

Layout

(3) Train the System

(4) Generalize a Layout Con®guration

(5) Quit the System

Input the Option Number ) 4

Input the number of facilities: 4

Requirement for facility closeness

[AEIOUX]

in terms of (facility, facility, clo-

seness).

Enter (0, 0, 0) to stop ��) (Drilling,

Grinding, o)

(Grinding, Milling, i)

(Milling, Turning, o)

(0, 0, 0)

Requirement for facility relative

position

[(A)bove, (B)elow, (L)eft, (R)ight]

in terms of (facility, facility,

relative).

Enter (0, 0, 0) to stop ��) (Turning,

Drilling, b)

(Turning, Milling, r)

(0, 0, 0)

Requirement for facility area units

�maximum � 6�in terms of (facility, area).

Enter (0, 0) to stop ��) (Grinding, 6)

(0, 0)

Requirement for facility site allo-

cation

interms of (facility, site).

Enter (0, 0) to stop ��) (Drilling, 2)

(Turning, 3)

(0, 0, 0

The generalized layout con®guration

is: Example 1

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A neuro-based expert system for facility layout construction