Computational Intelligence - August 2017 - 68

algorithm and the GEP-PO algorithm,
while Xu et al. [107] presented an Uniform-Constants based GEP (UC-GEP)
for ROPs.The key idea of these methods
is to use multiple genes to represent one
solution of the ROP, with each gene
representing one variable value. They
mainly differ in how to encode a real
value by a gene. For example, in the
HZero algorithm, each gene contains a
tail domain and a Dc domain. Only one
terminal "?" is considered to represent a
real constant. Thus each gene is essentially a formula that consists of different
constant values and functions. The final
result of the formula is assigned to the
corresponding ROP variable. Further, it
is worth noting that a large chromosome
length is required if the high dimensionality ROPs are encountered, which leads
to a huge search space that cannot be
efficiently solved by existing GEPs. It is
an unexplored direction whether the
GEP based methods can outperform
other EAs such as DE and PSO on large
scale ROPs.
VI. Open Research Issues

In this section, several open research
issues of GEP are identified and discussed for further exploration.
A. Advanced Mechanism
Design in GEP

GEP contains several key components,
such as transposition, mutation, constant
creation, and a number of control parameters. The design of these components as
well as the control of the search process
have a great impact on the performance
of GEP. Although many works have been
proposed for dedicated configuration
mechanisms in GEP, further exploration
of advanced designs in GEP is expected.
1) Evolutionary Operator and Parameter
Control Design: In the literature, various
advanced evolutionary operators and
parameter control approaches have been
proposed and verified to be effective in
other EAs, such as the orthogonal design
method [114], [115], the aging concepts
[116], the compact design mechanism
[117], and the opposite-based evolutionary mechanism [118]. In contrast, dedicated designs of evolutionary operators

and parameter settings for GEP are limited, such as the adaptive and self-adaptive GEP designs discussed in Section
III.C. More efficient and effective
designs of the search operators as well as
control approaches of parameter configuration are necessary to achieve advanced
GEP for problem solving.
2) Constant Creation Design: Constant
creation is an important operator in GEP,
which is helpful in finding high quality
GEP solutions. However, the optimization of constants significantly increases
the search space. Existing constant creation techniques are not effective in handling the additional complexity incurred
by constant creation. In particular, Ferreira [32] has compared two commonly
used constant creation methods in GEP
on symbolic regression problems. The
experimental results showed that the
GEPs with a constant creation operator
performed even worse than the GEPs
without a constant creation operator for
checking the solution accuracy. It is therefore desirable to design advanced constant
creation techniques, which can balance
the incurred complexity in a search space
and the efforts made for accurate solution exploration.
3) GEP Design for Solution Complexity
Reduction: The GEP adopts a fixed length
string to represent a computer program.
This enables the GEP to find concise
solutions when the length of chromosome is small. However, when the problems become complicated, especially
with a large number of terminals and
functions, the dimension of the corresponding chromosome will increase
accordingly to ensure the accuracy of the
optimized solution. This, however, can
lead to complicated GEP solutions that
are not general, and difficult for humans
to interpret. Thus, it is necessary to de--
sign effective mechanisms to reduce the
solution complexity of the GEP. One
potential ap--proach is to treat the solution
complexity as another objective and use
multi-objective optimization techniques
[119]-[121] to find solutions that have
trade-offs between the accuracy and the
complexity of solutions.
4) GEP Design for Ill-defined Problems:
Traditional GEP and its variants are usu-

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2017

ally applied to well-defined problems.
However, in many real world applications (e.g., classification problems with
unbalanced data [122]), the problems
encountered may contain specific features, which make GEP inapplicable or
inefficient. In these cases, problem-specific GEP has to be designed based on
the features of the problem encountered.
For example, in the application of determining the water quality and stress on
lakes or rivers as a result of pollutants
found in the wastewater, evaluation systems were installed to measure the
changes of the environment over time in
different perspectives1. Due to the circumstances relating to measurement, the
measurement data may have missing values.This problem can be easily converted
to a symbolic regression problem, which
is the common application of GEP.
However, without an effective method
to deal with the missing data, the GEP
cannot be applied directly to solve it.
B. GEP Meets Machine Learning

Another open research issue relates to
the use of ML techniques to enhance
the search performance of GEP. Specifically, ML can be used to learn highorder or domain-specific knowledge to
enhance the search efficiency of GEP. In
the GP community, some work has
already been done on using ML to learn
high-order or domain-specific knowledge in order to enhance the problemsolving performance of GP [52], [53],
[123]-[126]. As an example, Kameya et
al. [125] used ML to capture the building
blocks (frequently used sub-functions)
from historical search experiences, which
are then reused in an effort to improve
GP. The GEP is an iterative search algorithm that generates a great amount of
history search information during the
search. Thus, it is also possible to learn
useful domain-specific knowledge from
history search information to improve
the search efficiency of GEP.
Furthermore, ML could be used to
define surrogate models aimed at reducing the computational cost of GEP. For
1

The readers are referred to the detailed descriptions of
the application in http://www.spotseven.de/geccochallenge/gecco-challenge-2014

http://www.spotseven.de/gecco

Table of Contents for the Digital Edition of Computational Intelligence - August 2017