This document discusses visualizing the Pareto front in multi-objective optimization problems. It defines key concepts like the Pareto set, Pareto front, and non-dominated solutions. An example is provided of optimizing travel time and ticket price for airplane trips. Common techniques for visualizing the Pareto front include using a genetic algorithm like NSGA-II and dimensionality reduction with PCA. The goal of visualization is to translate multiple objective functions into an intuitive visual representation to identify Pareto optimal solutions. Future work could involve testing on additional problems with more objective functions.

1. Visualization of Pareto
Front for Multi Objective
Optimization
Dawit T.Haile, May 5 2015

2. INTRODUCTION
Multi-objective optimization (also known Pareto
optimization):involving more than one objective function to be
optimized.
Pareto set: all non-dominated solutions are optimal solutions of
the problem.
Pareto front: while its image in objective space.
Visualization of Pareto front in Multi-Objective Optimization:
graphical representation of pareto front.

3. Pareto optimal Solution Example
• Suppose in our airplane-trip example from earlier, we
find the following tickets:
Ticket Travel time (hrs) Ticket Price ($)
A 10 1700
B 9 2000
C 8 1800
D 7.5 2300
E 6 2200

4. Pareto front of the solutions
Plane Ticket Options
0
1000
2000
3000
4000
5000
0 5 10 15 20 25
Flight Time (hrs)
Price($)
B
D
AC
E

5. MATERIALS AND METHODS
Non-dominated Sorting Genetic Algorithm (NSGA-II):
popular non- domination based genetic algorithm.
Principal Component Analysis (PCA): used to reduce the
dimensionality .

6. CONCULUSIONS and FUTURE WORK
• The goal of visualization of pareto front with multi objective function
to translate with more amount of objective functions in to intuitive
visual representation in order to get set of pareto optimal solutions.
• In the future I intend to run more sample test problems for multi-
objective optimization with more objective function to visualize and
interpret the results.

7. THANK YOU!