The Effect of Building Block Construction on the Behavior of the GA in Dynamic Environments: A Case Study Using the Shaky Ladder Hyperplane-Defined Functions.
ABSTRACT The shaky ladder hyperplane-defined functions (sl-hdf's) are a test suite utilized for exploring the behavior of the genetic algorithm (GA) in dynamic environments. We present three ways of constructing the sl-hdf's by manipulating the way building blocks are constructed, combined, and changed. We examine the eect of the length of elemen- tary building blocks used to create higher building blocks, and the way in which those building blocks are combined. We show that the eects of building block construction on the behavior of the GA are complex. Our results suggest that construction routines which increase the roughness of the changes in the environment allow the GA to perform better by preventing premature convergence. Moreover, short length elementary building blocks permit early rapid progress.
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ABSTRACT: Though recently there has been interest in examining genetic algorithms (GAs) in dynamic environments, work still needs to be done in investigating the fundamental behavior of these algorithms in changing environments. When researching the GA in static environments, it has been useful to use test suites of functions that are designed for the GA so that the performance can be observed under systematic controlled conditions. One example of these suites is the hyperplane-defined functions (hdfs) designed by Holland . We have created an extension of these functions, specifically designed for dynamic environments, which we call the shaky ladder functions. In this paper, we examine the qualities of this suite that facilitate its use in examining the GA in dynamic environments, describe the construction of these functions and present some preliminary results of a GA operating on these functions.Applications of Evolutionary Computing, EvoWorkshops 2005: EvoBIO, EvoCOMNET, EvoHOT, EvoIASP, EvoMUSART, and EvoSTOC, Lausanne, Switzerland, March 30 - April 1, 2005, Proceedings; 01/2005
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ABSTRACT: Building blocks are a ubiquitous feature at all levels of human understanding, froin perception through science and innovation. Genetic algorithms are designed to exploit this prevalence. A new, more robust class of genetic algorithms, cohort genetic algorithms (cGA's), provides substantial advantages in exploring search spaces for building blocks while exploiting building blocks already found. To test these capabilities, a new, general class of test functions, the hyperplane-defined functions (hdf's), has been designed. Hdf's offer the means of tracing the origin of each advance in performance; at the same time hdf's are resistant to reverse engineering, so that algorithms cannot be designed to take advantage of the characteristics of particular examples.Evolutionary Computation 02/2000; 8(4):373-91. · 2.11 Impact Factor
Article: Evaluating evolutionary algorithms[show abstract] [hide abstract]
ABSTRACT: Test functions are commonly used to evaluate the effectiveness of different search algorithms. However, the results of evaluation are as dependent on the test problems as they are on the algorithms that are the subject of comparison. Unfortunately, developing a test suite for evaluating competing search algorithms is difficult without clearly defined evaluation goals. In this paper we discuss some basic principles that can be used to develop test suites and we examine the role of test suites as they have been used to evaluate evolutionary search algorithms. Current test suites include functions that are easily solved by simple search methods such as greedy hill-climbers. Some test functions also have undesirable characteristics that are exaggerated as the dimensionality of the search space is increased. New methods are examined for constructing functions with different degrees of nonlinearity, where the interactions and the cost of evaluation scale with respect to the dimensionality of the search space.Artificial Intelligence. 07/1998;
The Effect of Building Block Construction on
the Behavior of the GA in Dynamic
Environments: A Case Study Using the Shaky
Ladder Hyperplane-Defined Functions
William Rand1and Rick Riolo2
1Northwestern University, Northwestern Institute on Complex Systems, Evanston,
IL, 60208-4057, USA, firstname.lastname@example.org
2University of Michigan, Center for the Study of Complex Systems, Ann Arbor, MI
48109-1120, USA, email@example.com
Abstract. The shaky ladder hyperplane-defined functions (sl-hdf’s) are
a test suite utilized for exploring the behavior of the genetic algorithm
(GA) in dynamic environments. We present three ways of constructing
the sl-hdf’s by manipulating the way building blocks are constructed,
combined, and changed. We examine the effect of the length of elemen-
tary building blocks used to create higher building blocks, and the way
in which those building blocks are combined. We show that the effects of
building block construction on the behavior of the GA are complex. Our
results suggest that construction routines which increase the roughness
of the changes in the environment allow the GA to perform better by
preventing premature convergence. Moreover, short length elementary
building blocks permit early rapid progress.
In order to conduct controlled observations on the GA in dynamic environments,
a test suite of problems is necessary, so that we can control the inputs to the
system and define metrics for the outputs. Moreover, the more parameters of
the system (e.g. time and severity of shakes, difficulty of the problem) that are
controllable, the easier it is to test explanations for the observed behavior.
Other test suites for EAs in dynamic environments exist, such as the dynamic
knapsack problem, the moving peaks problem and more . The test suite and its
variants presented here are similar to the dynamic bit matching functions utilized
by Stanhope and Daida  among others. The test functions that we developed to
explore the GA in dynamic environments, the shaky ladder hyperplane-defined
functions (sl-hdf’s) , are a subset of the hdf’s . Holland created these func-
tions in part to meet criteria developed by Whitley . The hdf’s, designed to
represent the way the GA searches by combining building blocks, are well-suited
for understanding the operation of the GA   . Extending our previous
work on sl-hdf’s   , here we explore the effect of different types of build-
ing blocks on the GA by manipulating the way in which intermediate building
blocks within the sl-hdf’s are constructed. Moreover, whereas in past papers we
often examined the effect of the severity of change within a single environment
type, here we compare the effect of different environment types while holding
the severity of change relatively constant.
We begin by describing the sl-hdf’s and three variants. We then describe the
experiments with these functions, examine the behavior of the GA, discuss the
results and draw some conclusions.
2Shaky Ladder Hyperplane-Defined Functions and the
In this section we describe the sl-hdf’s and the three variants we will be exploring.
For an in-depth explanation of the construction of the sl-hdf’s see .
The sl-hdf’s are a subset of Holland’s hdf’s . To make the hdf’s usable as a
test platform in dynamic environments we place three restrictions on the hdf’s:
(1) The Unique Position Condition (UPC), which requires that all elementary
schemata contain no conflicting bits; (2) The Unified Solution Condition (USC),
which guarantees that all of the specified bits in the positive-valued elementary
level schemata must be present in the highest level schema, and that all inter-
mediate schema are a composition of lower level schema; and (3) The Limited
Pothole Cost Condition (LPCC), which states that the fitness contribution of
any pothole plus the sum of the fitness contributions of all the building blocks
in conflict with that pothole must be greater than zero.
These three conditions guarantee that any string that matches the highest
level schema must be optimally valued. Moreover it gives us an easy way to
create a similar but different sl-hdf by changing the intermediate building blocks.
This process is referred to as “shaking the ladder” , i.e. the intermediate
schemata are changed which alters the reward structure that describes the fitness
landscape. Thus these restrictions allow us to transform the full class of hdf’s
into a class that can be used for exploring the behavior of the GA on dynamic
There are many parameters that control the construction of the sl-hdf’s.
Next we explain and explore the parameters that affect the three variant sl-hdf
construction methods used in this paper.
2.1Elementary Schemata Length
The elementary schemata length (l) is the distance between fixed bits in the
elementary schemata. For the first two variants described below (Cliffs and
Smooth), the elementary schemata length is not specified. When the elementary
schemata length is not specified the fixed bit locations are chosen randomly from
the whole string. On average when the length is unspecified, the actual length
will be large, nearing the length of the string. For the third variant (Weight),
the elementary schemata length is set to l =
length of the string. This relationship is taken from Holland .
10= 50, where ls is the overall
2.2Mean and Variance of Schemata Weight
To create the schemata we need to specify the weight (w) that each schema
contributes to the overall fitness function. Two parameters, mean and variance
of the schemata weight, are used to specify the normal distribution from which
the weight for each intermediate schemata is drawn. There is one caveat to this:
since a normal distribution would allow negative weights to be drawn, and since
the proof of the optimality of the highest level schemata requires that the inter-
mediates always increase the overall value of the schemata, a weight is redrawn
from the same distribution if its value is not positive. In all of the experiments
described herein, the weight of the elementary schemata (2), potholes (−1) and
highest level schemata (3) remains unchanged. In the first two variants (Cliffs
and Smooth), the weight of the intermediate schemata is also held constant at 3.
However in the third variant (Weight) the weight of each intermediate schemata
is drawn from a distribution with mean of 3, and variance of 1.
2.3Restricted vs. Unrestricted Intermediate Construction
In the sl-hdf there are three groups of schemata held constant, the elementary
schemata, the potholes, and the highest level schema. The fourth set of schemata,
the intermediate schemata, is the group of schemata that changes. Thus the in-
termediate schemata could either be constructed out of any of the fixed groups
of schemata, which is called the unrestricted construction method, or the in-
termediate schemata could be constructed out of just the elementary schemata,
which is called the restricted construction method and is more similar to Hol-
land’s original description . The unrestricted construction method is used in
the first variant (Cliffs) below, while the restricted method is used in the other
two variants (Smooth and Weight).
2.4Random vs. Neighbor Intermediate Construction
The schemata utilized for construction of the next level of intermediate schemata
are selected randomly or from a prescribed order from the previous level. The
random construction method creates new intermediate schemata at level n, by
randomly choosing without replacement two schemata from level n − 1 and
combining them. In the neighbor construction method, all of the schemata at
level n − 1 are sorted by the location of their centers, which is the index value
half the distance between their left and right fixed loci. The first two schemata
that are next to each other in this sorted list are combined, and then the next
two, until all pairs have been combined.
If the random construction routine has been used then when the ladder
shakes, all of the intermediate schemata are destroyed and new ones are cre-
ated by randomly combining the lower level schemata to create the intermediate
schemata, and weights are assigned by drawing from the distribution specified
by the intermediate weight mean and variance. If the neighbor construction
routine is specified, then the intermediate schemata are left alone and instead
new weights are drawn for the intermediate schemata. Thus when the neighbor
construction routine is used the only thing that changes during the shakes of
the ladder are the weights, and therefore this is sometimes called “shaking by
weight.” When the random construction routine is used then the whole form of
the ladder changes and thus this is sometimes called “shaking by form.”
2.5The wδ Parameter
wδis the fraction of intermediate schemata weights that are changed when the
ladder is shaken. This parameter only makes sense with the neighbor intermedi-
ate schemata construction method, since in the random method all weights are
changed when the ladder is shaken. However in the first two variants described
below (Cliffs and Smooth), the variance of the weights is 0, thus the weights are
all the same. In the last variant (Weight) wδ= 1 and the neighbor construction
method is utilized, which results in shaking all the weights every time.
3 Variations on the sl-hdf
Given all of the parameters described above, it is necessary to determine how to
explore this space systematically. One of the major choices is to decide whether
to utilize the restricted or unrestricted intermediate construction technique. Ini-
tially we utilized the unrestricted technique, because it increased the amount
of variety in the landscape. One of the properties of this technique is that it
creates a large pool of material to draw from for the creation of the intermediate
schemata. Thus once this decision has been made it is logical to use the shaking
by form technique to sample widely from this pool of building blocks. This cre-
ates the most diverse and unrestrained set of building blocks. This unrestricted,
shaking by form landscape became the Cliffs variant.
This variant does indeed produce interesting results, but we wanted to create
something more similar to the original hdf’s  and the best way to do that was
to restrict the intermediate construction method. This small restriction changes
the composition of the building blocks in a minor way, but does nothing to change
the fact that they are dramatically changed every time the ladder shakes. This
restricted, shaking by form landscape became the Smooth variant.
Finally, in order to move even closer to Holland’s original description we
utilized the neighbor intermediate construction technique. This technique dra-
matically alters the way intermediate building blocks are constructed in this
test suite. However, since this technique fixes the particular schemata that are
combined it is necessary to use a new way to introduce dynamics into the land-
scape. The only property a schema has besides its particular form is the weight
assigned to it. Thus it is clear that if the form of the schema is held constant,
in order to create dynamics the weights must be changed. Moreover, in order to
make this variant as close to Holland’s as possible we also restricted the length
of the elementary building blocks. This restricted, shaking by weight landscape
became the Weight variant.
The main differences between these variants as described in the preceding
paragraphs are detailed in Table 1. We will describe each of these variants in
turn in the following sections.
3.1 Cliffs Variant: Intermediate Schemata are cliffs
Figure 1 illustrates the Cliffs landscape, the base case in this paper.
Fig.1. Illustration of Shaky Ladder Construction and the Process of Shaking the
Ladder for the Cliffs Variant.
The major differences between this variant and the other two are that it
uses the unrestricted construction method. When creating a new intermediate
schemata using the unrestricted method, all of the previous level schemata, plus
the potholes, and the highest level schemata can be used to generate the new
schemata. This has the property of introducing ”cliffs” into the landscape, be-
cause the combination of any schemata and the highest level schemata is the
highest level schemata. Thus many intermediate schemata are replaced by copies
of the highest level schemata. An effect of this is that any string which matches
the highest level schema will have a much higher value relative to the other
strings than it would in the restricted construction method. Moreover, the ef-
fect of having some intermediate schemata combining with potholes or potholes
combining with potholes to create intermediate schemata is interesting and com-
plicated. Essentially, this has the effect of smoothing some transitions since some
of the potholes will not be as detrimental as they could be. On the other hand,
if there is one of these “bridges” in place and the ladder shakes removing the
bridge, an individual making use of that bridge will suffer a sharp decline in fit-
ness because, it loses an intermediate schemata and gains a pothole. In general
the result of all these effects is that the fitness landscape is more sharply defined.
As to the rest of the parameters, the length of the schemata is not specified.
The order of the schemata is set to 8. The length of the string is 500. The number