A Tutorial on Evolutionary Multi-Objective Optimization (EMO)

Abstract

Many real-world search and optimization problems are naturally posed
as non-linear programming problems having multiple objectives. 
Due to lack of suitable solution techniques, such problems are 
artificially converted into a single-objective problem and solved. 
The difficulty arises because such problems give rise to a set 
of Pareto-optimal solutions, instead of a single optimum solution. 
It then becomes important to find not just one Pareto-optimal 
solution but as many of them as possible. Classical methods are 
not quite efficient in solving these problems because they require 
repetitive applications to find multiple Pareto-optimal solutions 
and in some occasions repetitive applications do not guarantee 
finding distinct Pareto-optimal solutions. The population approach 
of evolutionary algorithms (EAs) allows an efficient way to find 
multiple Pareto-optimal solutions simultaneously in a single 
simulation run. 

In this tutorial, we discussed the following aspects related to
EMO:

1. The basic differences in principle of EMO with classical methods.
2. A gentle introduction to evolutionary algorithms with simple
examples. A simple method of handling constraints was also 
discussed.
3. The concept of domination and methods of finding non-dominated
solutions in a population of solutions were discussed. 
4. A brief history of the development of EMO is highlighted. 
5. A number of main EMO methods (NSGA-II, SPEA and PAES) were
discussed. 
6. The advantage of EMO methodologies was discussed by presenting
a number of case studies. They clearly showed the advantage of
finding a number of Pareto-optimal solutions simultaneously.
7. Three advantages of using an EMO methodology were stressed:
 (i)   For a better decision making (in terms of choosing a 
compromised solution) in the presence of multiple solutions
 (ii)  For finding important relationships among decision variables
(useful in design optimization). Some case studies from engineering
demonstrated the importance of such studies. 
 (iii) For solving other optimization problems efficiently. For
example, in solving genetic programming problems, the so-called
`bloating problem of increased program size can be solved by using
a second objective of minimizing the size of the programs. 
8. A number of salient research topics were highlighted. Some of
them are as follows:
 (i) Development of scalable test problems
 (ii) Development of computationally fast EMO methods
 (iii) Performance metrics for evaluating EMO methods
 (iv) Interactive EMO methodologies
 (v) Robust multi-objective optimization procedures
 (vi) Finding knee or other important solutions including partial
Pareto-optimal set
 (vii) Multi-objective scheduling and other optimization problems.
 
It was clear from the discussions that 
evolutionary search methods offers an alternate means of solving
multi-objective optimization problems compared to classical 
approaches. This is why multi-objective optimization using EAs is 
getting a growing attention in the recent years. 
The motivated readers may explore 
current research issues and other important studies from various
texts (Coello et al, 2003; Deb, 2001), conference proceedings 
(EMO-01 and EMO-03 Proceedings) and numerous research papers 
(http://www.lania.mx/~ccoello/EMOO/).

References:
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C. A. C. Coello, D. A. VanVeldhuizen, and G. Lamont.
Evolutionary Algorithms for Solving Multi-Objective Problems.
Boston, MA: Kluwer Academic Publishers, 2002.

K.Deb. Multi-objective optimization using evolutionary algorithms.
Chichester, UK: Wiley, 2001.

C. Fonseca, P. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors.
Proceedings of the Second Evolutionary Multi-Criterion
Optimization (EMO-03) Conference 
(Lecture Notes in Computer Science (LNCS) 2632).
Heidelberg: Springer, 2003.

E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. Corne, 
editors. Proceedings of the First Evolutionary Multi-Criterion
Optimization (EMO-01) Conference 
(Lecture Notes in Computer Science (LNCS) 1993).
Heidelberg: Springer, 2001.