Multi Objective Evolutionary Algorithms-Applications of Computer Sciences-Project Presentations, Slides of Applications of Computer Sciences

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Presentation Outline

 Introduction

 Multi-Objective Evolutionary Algorithms

 Techniques for MOEAs

 Results

 Conclusion

 Summary

Introduction

 Objective

◦ To develop a toolbox for solving multi-

objective optimization problems with the help

of genetic algorithms

 Deliverables

◦ GUI for solving MOP

◦ Toolbox for MOP

◦ Complete project report

MOEAs (Contd..)

 Natural choices for solving MOP

 Pareto Optimal solutions captured by EA

populations

 Allows user to find Pareto-Optimal in

single run

 First MOP technique was implemented by

Schaffer

Techniques

 Popular approaches by different researchers

◦ Weighted Sum Approach

◦ Schaffer’s Vector Evaluated Genetic Algorithm

(VEGA)

◦ Srinivas and Deb’s Non-dominated Sorting

Genetic Algorithm (NSGA)

◦ Fonseca and Fleming’s Multi-Objective

Genetic Algorithm (MOGA)

◦ Horn, Nafploitis, and Goldberg’s Niched

Pareto Genetic Algorithm (NPGA)

Techniques (Contd..)

◦ Elitist Non-dominated Sorting Genetic

Algorithm (ENSGA)

◦ Distance Based Pareto Genetic Algorithm

(DBPGA)

◦ Thermodynamical Genetic Algorithm (TGA)

◦ Pareto-Achrived Evolution Strategy (PAES)

VEGA

 Vector Evaluated Genetic Algorithm

 First MOP implemented by Schaffer in

1984 to find set of non-dominated

solution

 Called vector evaluated GA because of

evaluation of the objective vectors instead

of scalar objective function

 Use an extension of SGA

 Only difference b/w VEGA and SGa is in

Selection

VEGA (Contd..)

 Advantages

◦ It uses simple idea and is easy to implement

◦ Only small change is required in simple GA

 Disadvantages

◦ Every solution is not tested for all other

objective functions

NSGA

 Non-dominated Sorting Genetic

Algorithm

 Non-domination idea of Goldberg was

implemented by Deb and Srinivas in 1994

 Non-dominated genetic algorithms vary

from simple genetic algorithms only in the

way selection operator is used.

NSGA (Contd..)

 Ranking individuals on the basis of non-

domination level

◦ Find non-dominated set of solutions

◦ Classified into level of non domination

◦ Number of different non-domination levels

should be varying between 1 to n

NSGA (Contd..)

 Fitness Assignment

◦ Fitness assigned to each individuals according

to its level of non-domination

◦ Performed in two steps

 Assigning same dummy fitness to all the solutions of

a particular non-domination level.

 Applying the Sharing strategy

Test Problem

 Proposed GA as multi-objective optimizer

 Schaffer’s two objective problem

 It is shown as:

Test Problem (contd..)

 Graph for Schaffer’s problem is:

 Range of Pareto-optimal solution is [0,2]

(^0) -5 -4 -3 -2 -1 0 1 2 3 4 5

5

10

15

20

25

30

35

40

45

50

Variable x

Ftiness f1, f

f f

Result of VEGA

Conclusion

Test Functions SCH1 Kursawe

No. of decision variables 3 5 10 3 5 10

No. of Objective Functions

Max. no. of generation 250 250 250 250 250 250

Population size 100 100 100 100 100 100 Time 16.1579 16.8417 17.4043 16.8906 17.5938 20.