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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
INTERNATIONAL JOURNAL OF ELECTRONICS AND
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME

COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 6, November - December, 2013, pp. 93-106
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IJECET
©IAEME

A GENETIC ALGORITHM APPLICATIONS FOR MULTI-OBJECTIVE
ADVANCED PLANNING AND SCHEDULING PROBLEMS - A REVIEW
Prof. D. L. Bhombe1,

Mr. N. B. Bhawarkar2

1

(Department of Electronics & Telecommunication, SSGMCE Shegaon/
SGB Amravati University, India,)
2
(Department of Electronics & Telecommunication, SSGMCE Shegaon/
SGB Amravati University, India,)

ABSTRACT
This paper gives a review for applications of Genetic algorithm for multi-objective advanced
planning and scheduling problem. At the start, different needs for Multi-objective advanced planning
and scheduling problem is discussed for various applications. Secondly, the brief history of Genetic
algorithm (GA) with its detail structural flow, Problems optimization using Multi-objective GA for
multi-objective scheduling model and advanced planning model is seen. Then different applications
of GA approaches needed for Multi-objective scheduling and advanced planning problems in
different areas are summarized.
Keywords: Genetic Algorithm, Multi-Objective GA, Advanced Planning, Hybrid GA, Moga,
Adaptive GA, GA with Tabu Search.
1. INTRODUCTION
Advanced planning and scheduling (APS) is one of the best solutions for better supply chain
and planning collaboration [1]. The scheduling problems composed of manufacturing problems
having large inventories, difficulties in supply chain costs and promised delivery. It may cause
larger lead times, non availability at promise due dates, and increasing mixed span. Most existing
literature considers minimizing makespan for balancing workloads as one important objective in
scheduling. But in real production more than one objective have to be solved such as minimization
of penalty for tardiness in due date, simultaneously considering precedence constraints, machine
selection, and flexible operation [2], etc.
Advanced planning reduces total makespan, penalty for tardiness in due dates [3]. The
advanced planning with scheduling i.e. APS for multi-objective problems can be achieved by the use
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of Genetic algorithm. Genetic algorithm (GA) is one of the generic population based meta-heuristic
optimization algorithms and the best one for finding a satisfactory solution in an acceptable time for
Advanced planning and scheduling problems [4] [5]. GA is the most popular type of evolutionary
algorithm [6].
In this review, we discuss first about GA and how it is used to find the optimize solution for
problems in section 2. The model of advanced planning and scheduling problems is discussed in
section 3. And the main focus is for different applications of GA used in different areas such as
Hybrid GA for composite problems in manufacturing process, A multistage operation-based genetic
algorithm (moGA) for flexible Job shop scheduling (FJSP), An adaptive genetic algorithm for
advanced planning in Manufacturing Supply Chain (MSC), A genetic algorithm with Tabu Search
for scheduling several machines routed for particular jobs is explained in further sections.
2. GENETIC ALGORITHM
A Genetic Algorithm (GA) is a concept which is developed by Holland with his collegues in
1960s and 1970s [7]. It deals with the nature concept of survival of the fittest i.e. weak and unfit
species within environment do not remain continued with future species. But the stronger species
which can adopt the nature and remain survive undergoes the future generation via reproduction.
The general form of GA was described by Goldberg (1989) and it differs from conventional
algorithms. The GA concept uses a best solution vector i.e. x є X is called as an individual or a
chromosome. The features of chromosomes are controlled by discrete units called genes. It requires
some set of individual or chromosomes as an initial set of random solutions called populations [8]
[9]. To find fitness solution, the process of successive iteration on every individual is called
generation. At start any two individual is required to undergo through iteration process which are
called parents, and the new generation produced after iteration of parent individual is called offspring
chromosomes.
The general structural of Genetic algorithm is shown in fig.1
Where, P(t) and C(t) are considered to be parents and offspring in current generation t.

Fig.1: structure of genetic algorithm (GA)
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The GA in general application follows the flow shown in above structure by considering the
parameters given below:
2.1 Encoding: It is representation of individuals in binary form [10]. Generally two approach of
representation is used. The first approach is bit string representation which is used in many GA
applications [10]. But this representation does not work efficiently during the task having complex
optimization. Hence the second approach i.e. real number representation [11] is used because of the
advantages such as better adapted to complex optimization tasks, higher speeds of search and easy to
develop for hybridized approach.
2.2 Crossover: Crossover is a main genetic operator which selects two individuals at a time to
generate an offspring by combining features of both individuals. A simple way to choose is a
random cut-point as shown in Fig.2

Fig.2: Example of one-cut point crossover operation

Fig.3: Example of mutation operator

2.3

Mutation: Mutation mostly utilizes the background operator to produce spontaneous random
changes in various chromosomes. A simple way to achieve this is to altering one or more genes
as given in figure 3.

2.4

Selection: The best individual is selected according to their fitness value for reproduction. A
different number of selection procedures are used such as proportional selection, tournament
selection and rank based selection [12]

3. PROBLEMS OPTIMIZATION USING MULTI-OBJECTIVE GA
Several objectives when achieved through the GA approach then it is called as multiobjective GA (MOGA). Several ideas have been proposed to solve bi-objective and tri-objective
problems [13]. The multi-objective GA is preferred to achieve multi-objective advanced planning
and scheduling.
3.1 Multi-objective scheduling model
The scheduling model consists of multiple scheduling problems such as minimization of
completion time, make span for several orders, total transportation time from one machine to another
including lateness and tardiness, minimization of cost, total workload, etc. Here every problem is
depends upon each other. These multiple objectives can be achieved using a GA approach so named
as MOGA [14]. The MOGA objective function for multi-objective scheduling problem is given by:

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f(x) = W1.f1(x) + W2.f2(x) + W3.f3(x)+ W4.f4(x) + ………+ Wn.fn(x)
where, f1(x) – Completion time, f2(x) – make span,
f4(x) – total tardiness & fn(x) – total cost

(1)

f3(x) – transportation time,

and W1 , W2, W3, …. Wn are the weights of corresponding objectives that satisfy the conditions
Wi ≥ 0 ; i- 1,2,…n
& W1+ W2+-----+ Wn = 1
Using Pareto Optimal solutions, the objectives can be achieved by considering the following
parameters and performance criteria[15].
Starting time of ith operation for order k i.e.
Unit processing time of operation on machine m
Lot size of order k
Unit load size of order k from operation to operation
Precedence constraint.
Setup time from operation

to operation

Unit shipping time between machine m to machine n
Decision variables:
=
=
=
f1(x) =
f2(x) =
f3(x) =

f4(x) =

Completion time of operation
make span for order k,

=

= max {

+
}

(2)

I

(3)

Total transportation time from machine m to machine n,
=
).
Workload of machine m,

(4)

=

f5(x) =

Total setup time of machine m,

f6(x) =

Total machine idle time,

(5)
=

=

(6)
-

96

-

-

(7)


3.2 Advanced planning model
The advanced planning i.e. APS problem is viewed in literature [16]. The APS problem for
multi-plant also get optimized using mathematical model. It deals with the main objective of
minimizing make span with simultaneously considering precedence constraints, machine selection,
and flexible operational sequence. The APS problem in manufacturing supply chain was studied by
Moon etal [17].
By considering the above parameters, few APS modeling formulation is given below.
1. Machine cannot simultaneously process more than one operation if,
{

-(

+

)}

0

(k,i), (l,j), m

(8)

2. The intermediate transportation instances between machines are ensured if,
{
{ -

-( +

)}
(

+

0

)}

0

i, j, k, m, n

(9)

i, j, k, m, n

(10)

Both above constrained must be satisfied so that the operations can run on one machine
without any interrupt.
3. The capacity restriction is given by,

,

m

4. The assurance about the precedence restrictions are not violated if,
5. For flexible operation sequence,
(13)
(k,i)
6. For flexible machine selection,

= 0,

k, I &

=1,

+

k, i. &

=1

= 0,

(11)
= 0,

i, j, k

(12)

m

(14)

(k,i), (l,j),

(k,i)

Am ,

4. HYBRID GENETIC ALGORITHM FOR JOB SHOP SCHEDULING PROBLEMS
The advance planning and scheduling problems with delivery co-ordination involves three
decisions: Order sequence, order to machine assignment and order to batch assignment. Some
application where orders are processed by either one from several machines and the delivery is also
by using single transportation with co-ordination among production stage and transportation stage
[18]. To achieve the best system performance with proper co-ordination among machines and for
minimization of Advanced planning and scheduling problems, a regular Genetic Algorithm(GA) and
an efficient approach based on Hybrid of GA with parallel scheduling procedure (PSP) is used[19],
this technique is called Hybrid Genetic Algorithm (HGA). The HGA finds the best result within
shorter time than normal GA [20].
The Hybrid GA is developed to solve the composite problems of manufacturing (production)
scheduling problem and or transportation routing problems. First approach is to make sequence of
operations which includes an encoding using improved random keys developed for this part. And the
second approach is to assign resources for each operation.
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4.1 Sequencing operation: The approach is based on the random keys vector which represents the
priority list for performing operations. For example a vector given for sequence as (O1,O2,O3) =
(0,2,1) represents a sequence of operations as O1
O3
O2. All these sequence vectors are
called “permutations”.

(a) Random space

(b) Sequence space

Figure 4: Sequencing operation for given vector.
4.2 Selecting Resources: The approach of combining resources assignment for each operation from
two parents generates better combination of selected resources. So a dynamic programming can be
applied simply if a tentative scheduling is a scalar value. A simple GA based on dynamic
programming approach is applied to this part with the use of uniform crossover to generate
candidates of resource assignment. Thus a Hybrid GA is used to formulate the advanced planning
and composite scheduling [21].
Considering the example to schedule the three jobs having four machines with processing
time given below:
Table1. Job requirements of Example
M1
J1

M2

M3

M4

3

4

1

3

8

2

1

O13

3

5

4

7

O21

4

1

1

4

O22

2

3

9

3

O23

9

1

2

2

O31

8

6

3

5

O32

J3

1

O12

J2

O11

4

5

8

1

The best schedule for the above problem will be as given in table:

98


Table2. Operation index

Table3. Scheduling plan

Machine

Operation performed

J1

M2 M1 M4

M1

O23,O21

J2

M4 M3 M1

M2

O11, O32

J3

M3 M2

M3

O31

M4

5.

O22,
O21

O13

A MULTISTAGE OPERATION-BASED GENETIC ALGORITHM (MOGA) FOR
INTEGRATED DATA STRUCTURE AND SCHEDULING APPROACH

A traditional genetic algorithm (GA) [22] is more complex with more CPU time for finding
solutions. Hence a multistage operation-based GA approach has been proposed. The moGA is used
for designing chromosome to improve the effectiveness for Optimizing Advanced Planning and
scheduling in Flexible Manufacturing System. It deals with objective of optimal resource selection
for assignments, operation sequence and allocation of variable transfer batches to minimize the total
make-span by considering the transportation time. This approach is proposed to make the
chromosomes simpler with improved efficiency after using the new representation.
Most literatures for moGA deals for shop scheduling problem which concentrates on flexible
Job Shop Scheduling (JSP) cases where the transportation problem is considered [23] [24 ] [25]. The
JSP concerns minimization of total makespan with determination of set of jobs on a set of machine.
For flexible Job shop scheduling (FJSP), at least one machine may be capable of performing more
than one type of operation [26]. This flexibility is of two types: Total flexibility where all machines
are available to achieve all operations and Partial flexibility where part of available machines
achieves some operations [22]. The FJSP can be solved efficiently with better result using moGA
compared with other approaches. The objectives of minimizing the makespan, total workloads of the
machines and maximum workloads of the machines can be achieved by moGA which including
k-stages of total number of operations for all jobs with m-state representing total number of
machines [27].
These objectives are achieved by using following fuzzy operators.
(a) The minimization of makespan: min

=

(15)

(b) The minimization of workload: min

=

(16)

(c) The minimization of total workload: min

=

(17)

The moGA approach for F-JSP is shown in fig.5 below which represents 3 jobs operated on 4
machines. Two other nodes are added as starting node and terminal node. Hence the problem can be
formulated as an 8-stage, 4-state problem [27].

99


The feasible schedule can be obtained as:

Fig.5: Example for Multistage Operation-based Representation (mO-R).
ID : 1 2 3
V

=

4 5 6

1 4 1

7 8

2 2 4

3 4

If we consider the same example with two more operations to perform having the
transportation problems as given in table 1. The best schedule will be as shown in figure 6.
Table 4. Manufacturing plan using moGA
Machine
Operation Performed
M1

O22,

M2

O21,

M3
M4

O14,

O25
O15

O13
O12 ,

O11

M5

O24
O23

Fig.6 Grant chart for the best solution
100


6.

ADAPTIVE GENETIC ALGORITHM FOR ADVANCED PLANNING IN MSC

The adaptive genetic algorithm is mostly used for advanced planning model (APS) which is
the important need for process and scheduling problem in manufacturing supply chain (MSC) [28].
The big industries with global manufacturing supply chain needs APS model. Also transportation
associated with manufacturing process becomes an important issue. The normal GA developed to
obtain good solution requires the identification of the correct settings of genetic parameters (such as
population size, crossover and mutation rates). For global MSC, it is a very complex task. Hence to
solve such complex mixed integer programming model, a new Adaptive Genetic algorithm (AGA)
approach with new adaptive scheme is proposed. The AGA adaptively regulates the GA operators
by an adaptive scheme and it also maintains the balance between exploitation and exploration [29] to
prevent the premature convergence and to produce the optimal solution. AGA for advanced planning
problem consists of three main parts.
6.1 Describing feasible solution (Chromosome coding): It states how to represent the feasible
solution which considers all different possible constraints for a given problem. Generally a two
dimensional coding concept is used, this coding significantly affect the generation of effective
solution of a problem [17] [30].
6.2 Determine fitness function: The measure of optimality of chromosomes used to obtain the
probability that the chromosome will appear in the next generation is called the Fitness value. The
for two weights
and
can
integrated fitness functions for fitness objective functions and
be given by:
eval (f) =

/

+

/

6.3 Selection: The genetic operator chooses best chromosomes from the population space to pass to
the next generation. This probability of selection of chromosomes for next generation is given by:
=
Consider the following example for two different plants having three machines each to
perform number of operations for different orders from customers.
Table 5. Transition time between machines
M1
M2
M3
M4
M1

5

6

M2

5

0

7

M3

Plant 1

0

6

7

0

Available
capacity

1000 1000

M5

M6

M4

5

6

M5

5

0

7

M6

Plant 2

0

6

7

0

2000

2000

2000

2000 Available
capacity

101


Table 6. Processing Time for Operations in Alternative Machines
Order 1
Order 2
Order 3
Order 4
Operation

3

4

7

7

-

M2

-

-

M3

-

M4

6

7

8

9

10

11

12

13

14

15

16

17

6 -

3

8

-

10

6

15

-

-

-

-

-

5

6

- 9

5

-

-

-

5

-

6

-

5

-

5

-

-

5

- -

- 12 5

-

-

-

-

6

-

6

-

-

5

6

-

-

8

-

9

-

10

-

6

-

6

-

4

3

-

M5

-

-

8

-

-

6

-

8

-

6

-

5

-

9

-

-

4

M6

Plant 2

2

M1
Plant 1

1

5

-

-

-

5 -

-

8 -

7

-

5

-

8

-

-

5

-

The best schedule using Adaptive GA will be as given in table 7.

Plant d

Table 7. Best schedule
Machine
Operation performed
M1
M2

O21

O42

O44

O31

O13

O43

O11

O12

O34

M5

O33

O35

M6

7.

O45

M4
Plant 2

O23

M3

Plant 1

O22

O41

O32

O14

GENETIC ALGORITHM WITH TABU SEARCH (GATS) FOR JOB SHOP
SCHEDULING

The multistage-operation based G.A. (MOGA) has solved the scheduling problem for flexible
Job-Shop scheduling. But achieving scheduling on m-machines for n jobs and having prescribed
machine route for particular job is a very complex process. Hence to solve this problem a new
approach is given having integrated GA and Tabu search i.e. GATS [31]. The GATS is having main
approach to minimizing the makespan, processing time and the number of iterations with better
result [32]. The job shop scheduling problem is already discussed in section5. A GATS process can
be achieved by applying first a simple G.A. approach and then a Tabu Search approach.
GA approach: This approach is shown in fig.7 and is having its main principle to produce best
chromosomes by crossover and mutation operation [33].

102


Fig.7: A Standard Genetic Algorithm
Tabu-Search (TS) Approach: This approach is used after GA approach and it is nothing but a
meta-heuristic approach used to achieve solutions on combinatorial optimization problems [34]. The
flow of TS search is shown in fig.8.

Fig.8: A standard Tabu Search algorithm
The TS approach basically consists of Tabu list, aspiration criteria, stopping criteria with
proposed algorithm [35].
Tabu list (TL): It is the list of trial solutions in order of their generation. The addition of new
element is added to the ‘bottom’ of list and the element came first on the list is dropped from the
‘top’. The length of TL is assigned initially based on the size of problem and it may vary (i.e.
increase or decrease) during construction of the solution to achieve better search of optimal solution.
Aspiration Criteria (AC): This is a second essential element of TS algorithm used when the move
under consideration has been found to the associated with each entry in TL. This criterion considers
the move when a result in a solution for required objective value is better than the one which present
in TL.
Stopping Criteria (SC): This criterion describes that when to stop the Tabu Search. It is based on
the different scheme used such as,
(i) Stop after a fixed number of iterations.
(ii) Stop after some number of iterations without an improvement in the objective function value.
(iii) Stop when the objective function reaches a pre-specified threshold value.

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If we apply the GATS instead of simple HGA and GA then we get the best optimum result as
shown in following figure 9 and 10.

Fig9. Average makespan values using
different crossover strategie

8.

Fig.10. Average relative error values using
different crossover strategies

CONCLUSION

Even the scheduling model and advanced planning model is having much more optimization
problems for different areas and applications, but the Genetic algorithm have created a optimal
solution for these various problems. Thus, this paper provides a literature review for different
applications of Genetic Algorithm in multi-objective scheduling and advanced planning problems.
Here the multi-objective scheduling and advanced planning is explained in different areas with
different forms of Genetic Algorithms. From this survey we can observe that the Adaptive GA is
more preferable for Broad industries where more complex operations are there with large number of
parameters effecting the final scheduling.
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