  General multi-objective optimization problems are often solved by a sequence
of parametric single objective problems, so-called scalarizations. If the set
of nondominated points is finite, and if an appropriate scalarization is
employed, the entire nondominated set can be generated in this way. In the
bicriteria case it is well known that this can be realized by an adaptive
approach which, given an appropriate initial search space, requires the
solution of a number of subproblems which is at most two times the number of
nondominated points. For higher dimensional problems, no linear methods were
known up to now. We present a new procedure for finding the entire nondominated
set of tricriteria optimization problems for which the number of scalarized
subproblems to be solved is at most three times the number of nondominated
points of the underlying problem. The approach includes an iterative update of
the search space that, given a (sub-)set of nondominated points, describes the
area in which additional nondominated points may be located. In particular, we
show that the number of boxes, into which the search space is decomposed,
depends linearly on the number of nondominated points.

Optimization and Control;Data Structures and Algorithms