Progressively Interactive Evolutionary Multi-Objective Optimization ...

the search is chosen. A scalarizing function is formulated based on the
information and a search is performed with a fixed number of function
evaluations (say nf ). This leads to a progress from point P1 to P2. At this
instant, another decision maker call is made and more questions are asked
from the decision maker. Based on the answers provided, the search direction
is modified to D2, and another scalarizing function is formulated
based on point P2 and new direction D2. With nf number of function evaluations,
further progress is made from P2 to P3. Another decision maker
call is executed and the process is repeated until no further progress is
possible. In the figure it is shown that a satisfactory point is found in four
decision maker calls. The point finally achieved by the algorithm is very
close to the most preferred point. If the step size (P1 to P2, P2 to P3, P3 to
P4 and P4 to P5 are the steps) of the algorithm is reduced, an even higher
accuracy could be obtained, but with a higher number of decision maker
calls. This procedure has potential to get close to the most preferred point
which is, otherwise, difficult in other approaches.
1.6 Motivation
f2
P1
Decision Making Instances
D3
P2 D2
P3
D1
D4 P5
P4
Final
Solution
Most
Preferred
Point
f1
Figure 1.8: Progressively Interactive Approach.
As already pointed out, the target of the EMO algorithms has been to find a
set of well-converged and well diversified Pareto-optimal solutions. Once
the optimization process is started there is no interaction involved with
the decision maker until a set of representative Pareto solutions are found.
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