Progressively Interactive Evolutionary Multi-Objective Optimization ...

the aposteriori approach. This approach makes it necessary for the algorithm to produce
the entire set of approximate Pareto-optimal solutions so that a decision making process
can be executed.
Some EMO researchers adopt a particular multiple criteria decision-making (MCDM)
approach (apriori approach) to avoid the problems associated with finding the entire
front. In such an approach the entire Pareto-optimal set is not aimed at rather a
crowded set of Pareto-optimal solutions near the most preferred solution is targeted. In
this approach the decision maker interacts at the beginning of an EMO run. The conedomination
based EMO [6, 1], biased niching based EMO [7], reference point based
EMO approaches [8, 9], the reference direction based EMO [10], the light beam approach
based EMO [11] are a few attempts in this direction.
In a semi-interactive EMO approach, the decision maker is involved iteratively [13,
14] in the optimization process. Some preference information (in terms of reference
points or reference directions or others) is accepted from the decision maker and an
MCDM-based EMO algorithm is employed to find a set of preferred Pareto-optimal
solutions. Thereafter, a few representative preferred solutions are shown to the DM and
a second set of preference information in terms of new reference points or new reference
directions is obtained and a second MCDM-based EMO run is made. This procedure is
continued till a satisfactory solution is found.
However, the decision maker could be integrated with the optimization run of an
EMO algorithm in a much more effective way, as shown in recent studies [4, 15]. These
approaches require progressive interaction with the decision maker during the intermediate
generations of the optimization process to converge towards the most preferred
solution. Such a progressively interactive EMO approach (PI-EMO), allows the decision
maker to modify her/his preference structure as new solutions evolve, thus making
the process more DM-oriented.
This paper discusses a simple PI-EMO where the decision maker is provided with
a set of points perodically and asked to pick the most preferred solution from the set.
Each time the decision maker is asked to make a choice of the most preferred solution,
we call the instance as a ‘DM call’. With the information obtained from the decision
maker a polyhedral cone is constructed and the domination principle is modified. The
obtained polyhedral cone is further utilized to figure out a direction in which a local
search is performed to determine the termination of the PI-EMO algorithm. The PI-
EMO concept has been integrated with the NSGA-II algorithm [18] and the working
of the algorithm has been demonstrated on three test problems having two, three and
five objectives. A parametric study of the algorithm has also been done to determine the
overall working of the algorithm.
2 Past Studies on Progressively Interactive Methods
Towards the methodologies involving a progressive use of preference information by
involving a decision-maker in an evolutionary multi-objective optimization framework,
there are not many studies yet. Some recent studies periodically presented to the DM
one or more pairs of alternative points found by an EMO algorithm and expected the
DM to provide some preference information about the points. Some of the work in this
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