  In this study, a nondominated-solution-based multi-objective greedy method is
proposed and applied to a sensor selection problem based on the multiple
indices of the optimal design of experiments. The proposed method
simultaneously considers multiple set functions and applies the idea of Pareto
ranking for the selection of sets. Specifically, a new index is iteratively
added to the nondominated solutions of sets, and the multi-objective functions
are evaluated for new sets. The nondominated solutions are selected from the
examined solutions, and the next sets are then considered. With this procedure,
the multi-objective optimization of multiple set functions can be conducted
with reasonable computational costs. This paper defines a new class of greedy
algorithms which includes the proposed nondominated-solution-based
multi-objective greedy algorithm and the group greedy algorithm, and the
characteristics of those algorithms are theoretically discussed. Then, the
proposed method is applied to the sensor selection problem and its performance
is evaluated. The results of the test case show that the proposed method not
only gives the Pareto-optimal front of the multi-objective optimization problem
but also produces sets of sensors in terms of D-, A-, and E-optimality, that
are superior to the sets selected by pure greedy methods that consider only a
single objective function.
