  Multiobjective optimization problems with heterogeneous objectives are
defined as those that possess significantly different types of objective
function components (not just incommensurable in units or scale). For example,
in a heterogeneous problem the objective function components may differ in
formal computational complexity, practical evaluation effort (time, costs, or
resources), determinism (stochastic vs deterministic), or some combination of
all three. A particularly challenging variety of heterogeneity may occur by the
combination of a time-consuming laboratory-based objective with other
objectives that are evaluated using faster computer-based calculations. Perhaps
more commonly, all objectives may be evaluated computationally, but some may
require a lengthy simulation process while others are computed from a
relatively simple closed-form calculation. In this chapter, we motivate the
need for more work on the topic of heterogeneous objectives (with reference to
real-world examples), expand on a basic taxonomy of heterogeneity types, and
review the state of the art in tackling these problems. We give special
attention to heterogeneity in evaluation time (latency) as this requires
sophisticated approaches. We also present original experimental work on
estimating the amount of heterogeneity in evaluation time expected in
many-objective problems, given reasonable assumptions, and survey related
research threads that could contribute to this area in future.
