Page 89 - 49A Field Guide to Genetic Programming

Chapter 9

Multi-objective

Genetic Programming

The area of multi-objective GP (MO GP) has been very active in the last
decade. In a multi-objective optimisation (MOO) problem, one optimises
with respect to multiple goals or fitness functions f 1 , f 2 , .... The task of a
MOO algorithm is to find solutions that are optimal, or at least acceptable,
according to all the criteria simultaneously.
In most cases changing an algorithm from single-objective to multi-
objective requires some alteration in the way selection is performed. This is
how many MO GP systems deal with multiple objectives. However, there
are other options. We review the main techniques in the following sections.
The complexity of evolved solutions is one of the most difficult things
to control in evolutionary systems such as GP, where the size and shape of
the evolved solutions is under the control of evolution. In some cases, for
example, the size of the evolved solutions may grow rapidly, as if evolution
was actively promoting it, without any clear benefit in terms of fitness. We
will provide a detailed discussion of this phenomenon, which is know as bloat,
and a variety of counter measures for it in Section 11.3. However, in this
chapter we will review work where the size of evolved solutions has been
used as an additional objective in multi-objective GP systems. Of course,
we will also describe work where other objectives were used.

9.1 Combining Multiple Objectives into a
Scalar Fitness Function

When given multiple fitness functions, it is natural to think of combining
them in some way so as to produce an aggregate scalar fitness function. For

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