An Artificial Immune System for Solving Production

7/30/2019 An Artificial Immune System for Solving Production

1/12

Artif Intell Rev

DOI 10.1007/s10462-011-9259-1

An artificial immune system for solving production

scheduling problems: a review

Ahmad Shahrizal Muhamad Safaai Deris

Springer Science+Business Media B.V. 2011

Abstract This article reviews the production scheduling problems focusing on those

related to flexible job-shop scheduling. Job-shop and flexible job-shop scheduling prob-

lems are one of the most frequently encountered and hardest to optimize. This article begins

with a review of the job-shop and flexible job-shop scheduling problem, and follow by the

literature on artificial immune systems (AIS) and suggests ways them in solving job-shop

and flexible job-shop scheduling problems. For the purposes of this study, AIS is defined as

a computational system based on metaphors borrowed from the biological immune system.This article also, summarizes the direction of current research and suggests areas that might

most profitably be given further scholarly attention.

Keywords Production scheduling Job-shop scheduling Flexible job-shop scheduling

Artificial intelligence Artificial immune system Evolutionary computation

1 Introduction

Scheduling can be defined as a process to allocate limited resources in order to complete

activities or tasks in a given period of time with the all constraints given (Baker 1974).

Scheduling also can be considered as the optimizing of a problem, with the goal of finding

the best sequencing of functions. Production scheduling are among the most common and

significant problems faced by the manufacturing industry. Production scheduling problems

deal with scheduling jobs on a machine (or a set of machines) in order to optimize a specific

objective function such as total weighted completion time or total weighted tardiness.

A. S. Muhamad (B) S. Deris

Artificial Intelligence and Bioinformatics Group, Faculty of Computer Science and Information System,

Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia

e-mail: [email protected]

123


2/12

A. S. Muhamad, S. Deris

Fig. 1 Job-shop scheduling

problems

1 2 3 4 3 2

2 1 3 1 4 4

3 2 1 3 2 3

2 3 1 3 3 1

Job1

Job2

Job3

Job4

O1 O2 O3 O1 O2 O3

Machine Processing Time

Hermann (2006), offers three important perspectives for the production scheduling. These

are the problem-solving perspective, the decision-making perspective, and the organizational

perspective. The problem solving perspective views scheduling as an optimization problem.

It is the formulation of scheduling as a combinatorial optimization problem isolated from

the manufacturing planning and control system location. Viewed from decision maker per-

spective, scheduling includes decisions which humans must do. The schedule maker would

use official and informal information to establish a schedule capable of fixing a specific task

to be made in that schedule. From an organizational perspective view, scheduling is a com-

plex information flow and decision maker that must decide production planning and system

control. Usually a system is divided into various modules and is done in several different

functions.

In production scheduling, there are three types of scheduling problems most commonly

faced. First is the open shop scheduling problem, where there are no ordering constraints on

operations. Second is the job shop scheduling problem, where the operations of a job aretotally ordered. Third is the flow-shop scheduling problem, where each job has exactly one

operation for every machine and all jobs go through all the machines in the same order. In this

paper, we address the issue of how to solving the job-shop and flexible job-shop scheduling

problems by using an artificial immune system. We also discuss the rescheduling for the

job-shop and flexible scheduling problems to determine how best to overcome the problems

caused by a changing or dynamic environment in the manufacturing industry, problems such

interruptions by equipment failure, changes of the customer requirements and others.

2 Job-shop and flexible job-shop scheduling problems

A job-shop consists of a set of n jobs {j1, j2, . . ., jn} with a number of m machines

{m1, m2, . . ., mm}. For each job there are a series of operations {o1, o2, . . ., oi } with each

operation having a specified processing time {i1, i2, . . ., i m}. All operations are required

to be completed on a specific machine and at a particular time, with one machine being able

to address only one operation. The goal of job-shop scheduling is to produce a schedule that

minimizes the total time taken to complete all the activities. The process constraints will

influence the ability to find the best schedule and determining whether its employment will

be easy or difficult (Pinedo 2002). Figure 1 illustrates the job-shop scheduling problem. Inmost industries, job-shop scheduling is important because it determines the process maps and

process capabilities (Roshanaei 2009). The possible solutions for n jobs on single machine

are n!. When m machines exist, the number of possible solutions is (n!)m .

Flexible job-shop scheduling problem is an extension of the classical job-shop scheduling

problem that allows anoperation to be processed by any machine from a given set of available

machines. Like the job-shop, a flexible job-shop consists of a set ofn jobs {j1, j2, . . ., jn}

123


3/12

An artificial immune system for solving production scheduling problems: a review

Fig. 2 Processing time for

flexible job shop scheduling

problems

Job1

M1

Operation

M2 M3

Machine

O2 5

O3 4 4 4

O4

Job2 O1 6

O2 5 7

O3 7 9

O4 6 3

Job3 O1 5 3 3

O2 4

O3

O4

O1 6 6

Fig. 3 Types of schedules

Feasible Schedule

Semi-active Schedule

Active Schedule

Non-delay Schedule

witha numberofm machines {m1, m2, . . ., mm}.Ineachjob Ji there are a seriesof operations

{oi,1, oi,2, . . ., oi,ni }with each operation having a processing time {i1, i2, . . ., i m}. For the

job-shop each operation only can be processed on one machine. But for the flexible job-shop,

each operation oi,j , i.e. the operation j of job i , can be processed by any among a subset

Mi,j M of compatible machines. Figure 2 illustrates the flexible job-shop schedulingproblem. The symbol in the figure means that a machine cannot execute a corresponding

operation. In other words, it does not belong to the subset of compatible machines for that

operation or any other operation j of job i . Bruker and Schlie (1990) were among the first

to address the flexible job-shop scheduling problem (Fig. 3).

The main problem in job-shop and flexible job-shop scheduling is that of obtaining the

best possible schedules with optimal solutions. The solution to any optimized problem is

evaluated by an objective function, with functions associated with cost, resource and time

minimization. There are several objective functions within job-shop and flexible job-shop

scheduling problem measurement. The common measurements are makespan, flow time,lateness, tardiness and earliness. The makespan is also known as maximum completion

time and indicates the completion time of the last job to be completed. The makespan is

important when having a finite number of jobs and is closely related to the throughput objec-

tive. Flow time is the sum of the completion times for all the jobs scheduled. This function

minimizes the average number of jobs in the system. Lateness is the difference between the

job completion time and the due date, L j = Cj dj , and it may have a positive or a negative

123


4/12


value. Tardiness indicates the time with which the job j is completed after its date. Therefore,

tardiness is positive lateness and is equal to Tj = ma x{0, Cj dj }. Earliness is the time in

which the job j is completed before its due date, Ej = ma x{0, dj Cj }. As French (French

1982) states; when considering minimum makespan at least one of the optimal solutions to

a job-shop problem is semi-active, with a schedule classified as a feasible schedule, a semi-active schedule, an active schedule or a non-delay schedule. An optimal schedule exists in

the set of active schedules.

Recently, in the dynamic environment of the manufacturing industry, to refer to job-shop

or flexible job-shop problems obtained by the best schedules with the optimal solution is

not sufficient. Optimal solutions to problems are often incredibly fragile, and if the original

problem changes slightly, then an optimal solution cannot massaged a match, and a new

one must be produced. In the real-world, such changes happen all the time and hence there

is a great deal of interest in the scheduling communities for generating robust schedules

rather than optimal ones (Jensen 2003). The most common changes in the current solutions

are machine breakdown or new orders received from the customer. For machine breakdown

or new orders received from customers, perhaps the rescheduling of the current solution is

needed and this depend on the type of situation and when changes happened. For example,

if the new order is received while the machine is processing a current job and the new job

(order) is more important than the current job, the uncompleted operation for the current job

needs to be rescheduled.

3 The method for solving job-shop and flexible job-shop scheduling problems

There are several methods to solving the job-shop and flexible job-shop scheduling prob-

lems, and all can be classified into two categories; the exact and approximate methods. For

the exact method, the most significant for the Job-Shop Scheduling Problem is called the

Branch-and-Bound Method. This method was developed by Land and Doig (1960), and used

primarily for the optimization of problems which could be formulated as linear program-

ming problems with additional constraints. The main problem with the exact methods is

cannot always give optimal solutions, especially when resolving scheduling problems. The

exact methodis suitable forsmall size problems (Baptiste and Le Pape 1996) and for job-shop

scheduling problems.

For the approximate methods, it does not always reach an optimal solution, but it can comevery close. There are several techniques in the approximate method that are used to solve the

job-shop and flexible job-shop scheduling problems such as priority dispatch rules, bottle-

neck based heuristics and artificial intelligence. For the priority dispatch rules technique, jobs

can be scheduled on machines taking into consideration certain rules, depending on the final

objective or purpose for which schedule is being generated. Giffler and Thomson (1960),

use some rules in their algorithm for solving production scheduling problems. Adams et al.

(1986), was developed the bottleneck base heuristics algorithm to solving job-shop schedul-

ing problems. This technique starts by establishing partial schedules for each machine, with

the schedules built for each machine individually taking into consideration the ready times

for the jobs on each machine as the completion time on the preceding operation.

Recently, artificial intelligence techniques have become popular for solving various prob-

lems, especially scheduling problems. In thearea of scheduling, artificial intelligencerefers to

the evolutionary algorithm. There are several algorithms for artificial intelligence techniques

designed to solving job-shop and flexible job-shop scheduling problems, These include the

genetic algorithm, artificial neural networks, tabu search techniques, simulated annealing,

123


5/12


J3

J1

J2

J2

J4 J1 J3

J1J4 J2

J4 J3

2 4 6 8 10 12 14

Processing Time

M

achine

M1

M2

M3

Fig. 4 An example of a final solution for the job-shop scheduling problem

J1 (O1,1)

J3 (O3,1)

J1 (O1,2)

J2 (O2,2)

J2 (O2,1) J1 (O1,3) J2 (O2,4

)

J3 (O3,2) J2 (O2,3)

Processing Time

Machine

M3M

2

M1

2 4 6 8 10 12 14 16 18 20 22 24

Fig. 5 An example of a final solution for the flexible job-shop scheduling problem

particle swarm optimization, artificial immune system and others. Which ever technique is

used, the objective is to obtain the best schedule with optimal and most robust solution.Figure 4 illustrates the best schedule for the job-shop problem as Fig. 1 has and Fig. 5 will

illustrate, with the schedule for the flexible job-shop problem shown in Fig. 2.

In a dynamic environment, finding an optimal solution is of the utmost important for real-

world applications. As we see in the research by Wiers (1997), artificial intelligence is the

good technique to finding a solution in the dynamic environment of real-world scheduling

problem applications. In his research he presented the relati9ve applicability of operational

research and artificial intelligence techniques with their shortcomings in practice. These are:

(i) robustness; (ii) complexity; (iii) performance measurement; (iv) fixed versus changeable

input; (v) organizational embedding; (vi) availability and accuracy of data; (vii) interaction

with human scheduler; (viii) learning from experience (artificial intelligence techniques);(ix) availability and reliability of human experts (artificial intelligence techniques). In this

paper we will employ artificial intelligence for solving the job-shop and flexible job-shop

scheduling problems by specifically using an artificial immune system (Figs. 6, 7).

4 The natural immune system

The natural immune system became a subject of research interest due to its powerful infor-

mation processing capabilities. The immune system is a complex of cells, molecules andorgans that function as an identification mechanism capable of perceiving and combating

dysfunction from its own cells (infections self) and from the action of exogenous infec-

tious microorganisms (infectious non-selves) such as viruses, bacteria and other parasites

(so-called invading antigens). The interaction among the immune system and several other

systems and organs allows the regulation of the body, guaranteeing its stable functioning

(Jerne 1973; Janeway 1992).

123


6/12


APC

MHC protein Antigen

Peptide

T-cell

Activated T-cell

B-cell

Lymphokines

Activated B-cell(plasma cell)

( I )

( III )

( IV )

( V )

( VI )

( VII )

( II )

Fig. 6 How human immune system work?

The immune system performs six main tasks. First, Pieces of peptides are joined to the

major histocompatibility complex(MHC) molecules and are displayed on the surface of the

cell. Second, T cells are activated by that recognition divide and secrete lymphokines, or

chemical signals, that mobilize other components of the immune system. Third, the B lym-phocytes, which also have receptor molecules of a single specificity on their surface, respond

to those signals. Fourth, when activated, the B cells divide and differentiate into plasma cells

that secrete antibody proteins, which are soluble forms of their receptors. Fifth, by binding

to the antigens they find, antibodies can neutralize them or sixth precipitate their destruction

by complement enzymes or by scavenging cells.

MHC is one of the most focused components of immune system (Dausset 1980). It plays a

central role in recognizing pathogenic antigens. Lymphocytes are small leukocytes that have

a major responsibility in the immune system. There are two main types of lymphocytes; B

lymphocytes (or B cells), which upon activation, differentiate into plasmocytes (or plasmacells) capable of secreting antibodies; and T lymphocytes (or T cells). The main functions

of the B cells include the production and secretion of antibodies as a response to exogenous

proteins like bacteria, viruses and tumor cells. EachB cell is programmed to produce specific

antibodies. The T lymphocyte is also called a T cell because it matures within the thymus

(Dreher 1995). The functions of T cell include the regulation of other cellular action and

directly attacks the host infecting cells.

123


7/12


Fig. 7 The clonal selection principle

5 Artificial Immune Systems (AIS)

Artificial Immune Systems (AIS) are a set of techniques, which try to algorithmically mimic

the behavior of natural immune systems (Hart 2008). The techniques are naturally used

in pattern recognition, fault detection, diagnosis, and a number of other areas, including

optimization (Costa 2002). AIS also can be defined as a computational system based on

metaphors borrowed from the biological immune system. The work in the field of AIS was

initiated by Farmer (1986). They introduced a dynamic model of the immune system that

was simple enough to be simulated on a computer. In their research, the antibody-antibody

and antibody-antigen reactions are simulated via complementary matching strings.

To develop the AIS model we need to consider the following important factors:

i. Hybrid structures and algorithms that are translated into immune system components;ii. Algorithm calculations based on the immunology principle, distribution processing,

clone selection algorithms, and network theory immunity;

iii. Immunity based on optimization, self-learning, self-organization, artificial life, cog-

nitive models, multi-agent systems, design and scheduling, pattern recognition and

anomaly detection;

iv. The immune tools for engineering.

123


8/12


Hoffman (1986) has constructed a model that incorporates some aspects of the immune sys-

tem into a neural network. The scope of his model in terms of applications is not as extensive

as that proposed by Farmer (1986). However, the unique idea of combining the two promoted

more research into the area and numerous models have been generated since. In other studies

by Ishida (1990, 1993), models of the immune system are developed and applied to areas suchas process diagnosis. In his studies he deals with a model built on the recognition capabilities

of the immune system and how it learns through a specific form of recognition. In other

research, Bersini and Varela (1990, 1991) and Bersini (1991) have developed similar models

of the immune system and applied them to the areas of machine learning, optimization and

adaptive control.

In earlier research, Chueh (2004) introduced an immune algorithm based on the biological

immune system for the functions of optimization and scheduling. In his research, he applies

the terminology of biological immune system to his immune algorithm model and a genetic

algorithm (GA). Genetic algorithms are among the most popular techniques for solving

scheduling problems. They are computational models that area particular class of evolution-

ary algorithms using techniques inspired by evolutionary biology. In another study, Luh and

Chueh (2007) introduce a multi-modal immune algorithm to finding optimal solutions for

job-shop scheduling problems. A study by Fabio and Maurizio (2006) on the comparison of

AIS and GA performance states that in the performance of numerically evaluated functions,

AIS succeed in detecting a larger number of optimal points than GA.

There are several basic of immune system models and algorithm such as Bone Marrow

Models, Negative SelectionAlgorithms, the Clonal Selection Principle, Somatic Hypermuta-

tion and Immune Network Models. In this paper for solving of job-shop and flexible job-shop

scheduling problem, we will employ the Clonal Selection Principle.

6 The clonal selection principle

The clonal selection principle or theory is the algorithm used by the immune system to

describe the basic features of an immune response to antigen stimulus. It establishes the idea

that only those cells that recognize the antigens are able to proliferate, thus being selected

against those which do not. The clonal proliferation ofB cells occurs inside the lymph nodes

(Weissman and Cooper 1993) within a special microenvironment named the germinal center,

which is located in the follicular region of the white pulp and is rich in antigen presentingcells (Tarlinton 1998). When a living body is exposed to an antigen, the B cells will respond

by producing antibodies. Basically,B cells clone themselves into as manyforms as is required

to fight the infection and clone only those cells which are actually capable of fighting the

intruder effectively. During the process of clonal proliferation, a hyper-mutation mechanism

operates on the vulnerable regions of B cells. This hyper-mutation plays a critical role in

creating diverse antibodies, increasing affinity and enhancing specificity of the antibodies.

In the AIS, the number of antibodies produced can be analogized as the number of feasible

solutions, where in the AIS this antibody was produced randomly. For the cloning and mutat-

ing processes for each feasible solution, it is capable of reaching a near optimal solution.

When the number of clones for the mutation is large, the optimal solution can be reached

more quickly. Burnet (1978) state the main features of clonal selection principle:

i. The new cells are copies (clones) of their parents subjected to a mutation mechanism

at high rates;

ii. Elimination of newly differentiated lymphocytes carrying self reactive receptors;

123


9/12


iii. Proliferation and differentiation on contact with mature lymphocytes with antigens;

iv. Restriction of one pattern to one differentiated cell and retention of that pattern by

clonal descendants;

v. Generation of new randomgenetic changes, subsequentlyexpressed as diverseantibody

patterns by a form of accelerated somatic mutation.

7 Applying the AIS to solving the job-shop and flexible job-shop scheduling problem

In past research by Burnet (1978), Hart et al. (1998) and Hart and Ross (1999a) it has been

shown that the AIS model can be used to solve the scheduling problems for industries in a

dynamic environment. In another study by Hart and Ross (1999b), the function of antigens

is defined as a sequence of jobs on a particular machine given a particular scenario and

that of antibodies as a short sequence of jobs that is common to more than one schedule.

In their research, Aickelin et al. (2004) state that the schedules obtained by using AIS

are more robust than those obtained by the GA, and it has been proven that increasing the

number of antigens in an AIS improves the optimality of the schedules obtained. However, it

decreases its fitness. In a study by Tomoyuki (2003), the immune algorithm is used to solve

job-shop scheduling problem, and he has demonstrated that the calculation time used by the

immune algorithm was shorter compared with the GA.

In other research, Chueh (2004) establishes nine steps in his proposed model for solving

job-shop scheduling problems; (i) random initialization of antibody population, where the

initial integer string-encoding antibody population is randomly generated; (ii) antibody rep-

resentation and geneclassification, where an operation-based representation (Gen etal. 1994)is used to represent the genes of an antibody; (iii) calculating combinatorial intensity, where

the antibody-to-antigen affinity value is employed to illustrate the combinatorial intensity

between antigen and antibody/schedules; (iv) clonal proliferation; (v) tournament selection

for donor antibodies; (vi) germ-line DNA library construction; (vii) random gene fragment

rearrangement; (viii) antibody diversification; and (ix) the stopping criterion.

In their research, Ong et al. (2005) proffered an immune algorithm called ClonaFLEX,

which is designed using the clonal selection principle and employed to solve flexible job-

shop scheduling problems. In this study, for the antibody population they take inspiration

from research in applying GA to solving the flexible job-shop scheduling problem by Kacem

et al. (2002) and Tay and Ho (2004). Another study by Bagheri et al. (2010) introduces amodel to solve flexible job-shop scheduling problem by using an artificial immune system.

In their research, they produce the antibody population by follow the procedure proposed by

Pezzella et al. (2008).

From our discussion of means for solving the job-shop and flexible job-shop scheduling

problem using AIS and for developing the AIS model to solve job-shop and flexible job-shop

scheduling problems, we find that the most important is the number of antibody population,

number of clones and the mutation process for the antibody. When the number of antibodies

is large, the feasible solution is close to optimal solution; and when the number of clones is

large, the optimal solution can be reached more quickly. The mutation process is important

in determining when the cloning is near an optimal solution after the mutation process or

is far from the optimal solution. Chueh (2004) was used six types of mutation including

somatic point mutation, somatic recombination, gene inversion, gene conversion and gene

shift and nucleotide addition. Ong et al. (2005) has used two types; operation order mutation

and machine order mutation.

123


10/12


Fig. 8 An integer string

encoding antibody generated at

random

1 4 2 2 3 1 4 4 3 1 3 2

Library 4Library 3Library 2Library 1

1 4 22 3 1

4 4 3

1 3 2

2 4 11 2 3

3 4 4

1 3 2

4 1 22 1 3

4 3 4

2 3 1

4 2 13 2 1

4 4 3

3 1 2

1 4 2 1 2 3 4 3 4 3 1 2

Fig. 9 An integer string encoding antibody generated using a library

(1, 1, 1) (3, 1, 3) (2, 1, 2) (3, 2, 1) (2, 2, 3) (1, 2, 2) (1, 3, 2) (2, 3, 1) (2, 4, 2)

Fig. 10 An antibody representation for flexible job-shop using approach 1

(1, 1, 1) (3, 1, 2) (2, 1, 2) (2, 2, 2) (1, 2, 2) (3, 2, 1) (2, 3, 1) (1, 3, 1) (2, 4, 2)

Fig. 11 An antibody representation for flexible job-shop using approach 2

From another aspect, the way that antibodies are created will effect to most feasible solu-tion. There are two ways to create antibodies for job-shop scheduling problems; first, random

generation; second, generation using libraries. Figures 8 and 9 present examples of antibod-

ies for job-shop scheduling problems based on the problem as Fig. 1. The length of antibody

for the job-shop scheduling problem is equal to m machine multiply by n jobs, where each job

j will appear m times in an antibody. For a flexible job-shop scheduling problem, there are

two approaches to antibody creation; first, the assignment process commencing the operation

with the global minimum processing time in the processing time table, and then performing

the machine workload update in the processing time table; second, the jobs and machines

are randomly permitted before the localization approach is applied. For the flexible job-shop

scheduling problem, the length of the antibody is equal to the number of operations and foreach gene it is formed by triplets (i, j, k) according to the task sequencing list provide by

Kacem et al. (2002), where i is the job that the operation belongs to; j is the progressive

number of operations within job i ; and k is the machine assigned to that operation. Figures

10 and 11 present an example of antibodies for flexible job-shop scheduling problems based

on a specific problem, as in Fig. 2.

8 Conclusion

This paper has introduced the basic concepts of natural immune system and artificial immune

system for the better understanding of the problems created by job-shop and flexible job-

shop scheduling. This paper also introduced a mapping of the natural immune system into an

artificial immune system. It has attempted to illustrate how the AIS can be adapted to tackle

scheduling problems, especially the job-shop and flexible job-shop scheduling problems. To

do so, existing AIS scheduling applications were carefully reviewed. Scheduling is an area

123


11/12


demanding the application of efficient methods to tackle the combinatorial explosion of the

results in real-world applications.

There hasbeen much significant effort and researchundertaken to solve production sched-

uling problems by means of AIS, especially in the field of job-shop and flexible job-shop

scheduling problems. There remain challenging researchareas worthexploring. Themajorityof existing efforts have been directed towards applying the AIS to static scheduling, espe-

cially for job-shop scheduling problems. For flexible job-shop scheduling problems, there

have been only a few attempts directed towards applying AIS to discover solutions. For fur-

ther study, we suggest more investigating for the dynamic scheduling in job-shop scheduling

problem and also to more concentrated investigation of the static and dynamic scheduling on

flexible job-shop scheduling problems. On the other hand, for further study also we suggest

the introduction of the AIS model for solving the job-shop and flexible job-shop scheduling

problems, especially for the purpose of producing optimal and robust scheduling procedures.

References

Adams J, Balas E, Zawack D (1986) The shifting bottleneck procedure for job shop scheduling. Carnegie-

Mellon University Management Science Research Group, Pittsburgh

Aickelin U, Burke E, Mohamed Din A (2004) Investigating artificial immune systems for job shop resched-

uling in changing environments. In: 6th International conference in adaptive computing in design and

manufacture, Bristol, UK

Bagheri A, Zandieh M, Mahdavi I, Yazdani M (2010) An artificial immune algorithm for the flexible job-shop

scheduling problem. Future Generation Comput Syst 26:533541

Baker KR (1974) Introduction to sequencing and scheduling. Wiley, New York

Baptiste P, Le Pape C (1996) A constraint-based branch and bound algorithm for preemptive job-shop sched-uling. In: 5th IEE, international symposium on assembly and task planning, Besanon

Bersini H (1991) Immune network and adaptive control in towards a practice of autonomous systems. In:

Proceedings of the first European conference on artificial life. MIT Press, Cambridge, pp 217226

Bersini H, Varela FJ (1990) Hints for adaptive problem solving gleaned from immune networks. Parallel Prob

Solv Nat pp 343354

Bersini H, Varela FJ (1991) The immune recruitment mechanism: a selective evolutionary strategy. In: Pro-

ceedings of the international conference on genetic algorithm, pp 520526

Bruker P, Schlie R (1990) Job-shop scheduling with multi-purpose machine. Computing 45:369375

Burnet FM (1978) Clonal selection and after. In: Bell GI, Perelson AS, Pimbley GHJr. (eds) Theoretical

immunology. Marcel Dekker Inc, New York pp 6385

Chueh CH (2004) An immune algorithm for engineering optimization. Dissertation Tatung University, Taipei

Costa AM, Vargas PA, Von Zuben FJ, Frabca PM (2002) Makespan minimization on parallel processors:an immune-based approach. In: Proceedings of the 2002 congress on evolutionary computation. IEEE

Press, pp 920925

Dausset J (1980) The major histocompatibality complex in manpast, present and future concepts. Nobel

Lecturer University of Paris, Paris

Dreher H (1995) The immune power personality. Penguin Books, Baltimore

Fabio F, Maurizio R (2006) Comparison of artificial immune systems and genetic algorithms in electrical

engineering. Comput Math Electr Electron Eng 25(4):792811

Farmer JD, Packard NH, Perelson AS (1986) The immune systems, adaptation and machine learning. Phys D

22:87204

French S (1982) Sequencingand scheduling, mathematics and its applications. Ellis Horwood Limited,Chich-

ester

Gen M, Tsujimura Y, Kubota E (1994) Solving job-shop scheduling problem using genetic algorithms. In:Proceedings of the 16th international conferences on computer and industrial engineering, Ashikaga,

Japan, pp 576579

Giffler B, Thomson G (1960) Algorithmsforsolving production scheduling problems.OperResVIII:487503

Hart EJT (2008) Application areas of AIS: the past, the present and the future. Appl Soft Comput 8:191201

123


12/12


Hart E, Ross P (1999a) An immune system approach to scheduling in changing environments. In: Banzhaf

W, Daida J, Eiben AE, Garzon MH, Honavar V, Jakiela M, Smith RE (eds) Proceeding of the GECCO

1999. Morgan Kaufmann, Los Altos, pp 15591565

Hart E, Ross P (1999b) The evolution and analysis of a potential antibody library for job-shop scheduling. In:

Corne D, Dorigo M, Glover F (eds) New ideas in optimisation. McGraw-Hill, London pp 185202

Hart E, Ross P, Nelson J (1998) Producing robust schedules via, an artificial immune system. In: Proceedingof the ICEC 98. IEEE Press, Cambridge, pp 464469

Hermann JW (2006) Improving production scheduling: integrating organizational, decision-making, and

problem-solving perspectives. In: Industrial Engineering Research Conference, Orlando, Florida

Hoffman GW (1986) A neural network model based on the nalogy with the immune system. J Theor Biol

122:3367

Ishida Y (1990) Fully distributed diagnosis by PDP learning algorithm: towards immune network PDP model.

In: Proceedings of the international joint conference on neural networks, pp 777782

Ishida Y (1993) An immune network model and its applications to process diagnosis. Syst Comput Jpn

24(6):646651

Janeway CA Jr (1992) The immune system evolved to discriminate infectious nonself from noninfectious self.

Immunol Today 13(1):1116

Jensen MT (2003) Generating robust and flexible jobshop schedules using genetic algorithms. IEEE TransEvol Comput 7(3):275288

Jerne NK (1973) The immune system. Scientif Am 229(1):5260

Kacem I, Hammadi S, BorneP (2002) Approach by localization and multiobjective evolutionary optimization

for flexible job-shop scheduling problems. IEEE Trans Syst Man Cybern 32(1):113

Land AH, Doig AG (1960) An automatic method of solving discrete programming problems. Econometricca

28(3):497520

Luh GC, Chueh CH (2007) Job shop optimization using multi-modal immune algorithm. In: Okuno HG, Ali

M (eds) IEA/AIE 2007, LNAI 4570. Springer, Berlin, pp 11271137

Ong ZX, Tay JC, Kwoh CK (2005) Applying the clonal selection principle to find flexible job-shop schedules.

LNCS 3627:442455

Pezzella F, Morganti G, Ciaschetti G (2008) A genetic algorithmfor theflexible job-shop scheduling problem.

Comput Oper Res 35(10):32023212Pinedo M (2002) Scheduling: theory, algorithms and systems. Prentice-Hall, Englewood Cliffs

Roshanaei V, Naderi B, Jolai F, Khalili M (2009) A variable neighborhood search for job shop scheduling

with set-up times to minimize Makespan. Future Generation Comput Syst 25:654661

Tarlinton D (1998) Germinal centers: form and function. Curr Oper Immune 10:245251

Tay JC, Ho NB (2004) GENACE: an efficient cultural algorithm for solving the flexible job-shop problem. In:

Proceedings of the IEEE congress of evolutionary computation, pp 17591766

Tomoyuki M (2003) An application of immune algorithms for job-shop scheduling problems. In: Proceedings

of the 5th international symposium on assembly and task planning, pp 146150

Weissman IL, Cooper MD (1993) How the immune system develops. Scientif Am 269(3):3340

Wiers V (1997) Human-computer interaction in production scheduling-Analysis and design of decision

support systems for production scheduling tasks. Dissertation Eindhoven University of Technology,

Eindhoven

123

An Artificial Immune System for Solving Production

Documents

Transcript of An Artificial Immune System for Solving Production