Progressively Interactive Evolutionary Multi-Objective Optimization ...

of the papers is provided in this section.
1.7.1 An Interactive Evolutionary Multi-Objective Optimization
Method Based on Progressively Approximated Value Functions
The first paper [10] introduces a preference based optimization algorithm
where decision making is incorporated in an evolutionary multi-objective
search procedure. The algorithm requires preference based information
to be elicited from the decision maker after every few generations. The
decision maker is expected to order a given set of alternatives (five in
number) according to preferences and the information is used to model
a value function which emulates the decision maker and drives the algorithm
towards more preferred solutions in the subsequent generations. A
polynomial value function has been proposed which is quasi-concave in
nature and is used to map the decision maker’s preferences by optimally
setting the parameters. The study suggests a simple optimization problem
which is solved to determine the optimal parameters of the value function.
The search of the evolutionary multi-objective optimization algorithm is
focussed in the region of decision maker’s interest by modifying the domination
criteria based on the preference information. Further, a termination
criterion based on preferences is also suggested. The methodology is
evaluated on two to five objective unconstrained test problems, and the
computational expense and decision maker calls required to arrive at the
final solution are reported. The study also presents results obtained by
emulating a decision maker who is prone to make errors while providing
preference information.
1.7.2 Progressively Interactive Evolutionary Multi-Objective Optimization
Method Using Generalized Polynomial Value
Functions
The second paper [28] is an extension of the first paper where the polynomial
value function has been augmented into a generalized polynomial
value function. This equips the approach to fit a wider variety of quasi
concave preference information. Further, the value function fitting procedure
is tested on other commonly used value functions like the Cobb-
Douglas value function and the CES value function, and the generality
of the methodology is shown. Results are computed for constrained test
problems up to five objectives. In this study the efficacy of the algorithm
is also evaluated when the decision maker provides preference informa-
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