Progressively Interactive Evolutionary Multi-Objective Optimization ...

DM Calls and Func. Evals. (in thousands)
50
40
30
20
10
0
Accuracy
# of DM Calls
Func. Evals./1000
2 5 10
Frequency of DM Calls
20
0.05
0.04
0.02
0
Accuracy
Fig. 9. Three performance measures on modified
ZDT1 problem for different τ values.
DM Calls and Func. Evals. (in thousands)
60
50
40
30
20
10
0
2
Accuracy
# of DM Calls
Func. Evals./1000
5 10
Frequency of DM Calls
20
0.3
0.2
0.1
0
Accuracy
Fig. 10. Three performance measures on threeobjective
modified DTLZ2 problem for different
τ values.
preferred point, thereby causing a large number of generations to satisfy termination
conditions and a large number of DM calls.
Figure 10 shows the same three performance measures on the three-objective modified
DTLZ2 problem. For this problem, the number of DM calls is minimum for τ = 5
and accuracy and the number of function evaluations are also better for τ = 5 generations.
Once again, too small or too large τ is found to be detrimental.
Based on these simulation studies on two and three-objective optimization problems,
one can conclude that a value of τ close to 5 generations is better in terms of
an overall performance of the PI-NSGA-II procedure. This value of τ provides a good
convergence accuracy, requires less function evaluations, and less DM calls to converge
near the most preferred point.
7 Conclusions
In this paper, we have proposed a preference based evolutionary multi-objective optimization
(PI-EMO) procedure which uses a polyhedral cone to modify domination. It
accepts preference information from the decision maker in terms of the best solution
from the archive set. The preference information from the decision maker and information
from the non-dominated set of the parent population of the evolutionary algorithm
have been used together to construct a polyhedral cone. Progressive information from
the population of the evolutionary algorithm as well as the decision maker is used to
modify the polyhedral cone after every few iterations. This approach helps in approaching
towards the most preferred point on the Pareto-front by focussing the search on the
region of interest.
The direction provided by the cone has been used to develop a termination criterion
for the algorithm. The procedure has then been applied to three different test-problems
involving two, three and five objectives. The procedure has been successful in finding
the most preferred solution corresponding to the DM-emulated utility function. A para-
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