A Clustering-based Visual Analysis Tool for Genetic Algorithm

Habib Daneshpajouh and Nordin Zakaria

High Performance Computing Center,

Universiti Teknologi Petronas,

Perak, Malaysia

Keywords:

Genetic Algorithm, Cluster Formation, Evolutionary Process, Search Space Analysis, Evolution Visualization.

Abstract:

While Genetic Algorithm (GA) is a powerful tool for combinatorial optimization, the vast population of can-

didate solutions it typically deploys and algorithm’s intrinsic randomness lead to difﬁculty in understanding its

search behavior. We discuss in this paper a clustering-based visualization tool for GA that attempts to mediate

this problem. GA population across its entire generations are clustered, and each cluster and its individuals

are mapped to a visual symbol. The tool enables a GA researcher or user to understand better the behavior

of a GA run, speciﬁcally the local searches it performs in its global exploration to go from one generation to

another.

1 INTRODUCTION

Genetic Algorithm (GA), initially conceived by John

Holland (Holland, 1975), is among the most popular

meta-heuristics for combinatorial optimization prob-

lems these days. GA typically generates a huge num-

ber of candidate solutions (individuals) to a problem

in a search process inspired by Darwinian natural evo-

lution, involving concepts such as selection, crossover

and mutation. While a powerful paradigm, the vast

amount of data semi-randomly evolved by GA eludes

an intuitive interpretation, leading to difﬁculty in un-

derstanding its search behavior.

The main approach pursued in this paper to ad-

dress the above-mentioned problem is visualization.

The mainstay of big data analysis (Fan and Bifet,

2013), visualization can serve users with different lev-

els of expertise (Gelman and Unwin, 2013). Applied

to GA, it can potentially be used to analyze its inner

working (Hart and Ross, 2001).

Speciﬁcally, this paper describes a clustering-

based visualization tool for GA. The proposed tool

performs an ofﬂine visualization on the GA data. The

clustering structures the population visited by GA

across its generations, allowing a GA researcher to

make sense of the local searches performed by GA in

its global exploration. Individuals within a cluster are

mapped in a certain way to a certain symbol, allow-

ing the researcher to make statements about the way

in which the GA has been progressing.

While there have been various tools for the visual-

ization of GA, the one proposed in this paper is unique

due to its emphasis. Prior work in general focuses on

the visualization of high-dimensional individuals in

GA, while our proposed tool concerns more on visu-

alizing the dynamics of cluster formations in GA. In

particular, this tool enables us:

1. To study the search space explored by GA and an-

alyze the behavior of the operators and parameters

deployed for the search.

2. To obtain useful information that can be used later

by the GA researcher to interactively manipulate

the search space.

The rest of this paper is organized as follows: In

section 2, work related to the visualization of GA

is reviewed. The details of the visualization imple-

mented in our proposed tool is elaborated in section

3. An example analysis is presented in section 4, fol-

lowed by a comparison with the existent tools in sec-

tion 5. Finally in section 6, the conclusion is drawn

along with suggestions for future work.

2 RELATED WORK

In the following, existent tools and methods for ofﬂine

visualization of GA are reviewed. Early works in the

90s were mostly published by Collins. In (Collins,

1996), Collins proposed a mapping method called

Genotypic-Space Mapping based on the direct lin-

ear two-way relationship between high-dimensional

Daneshpajouh H. and Zakaria N.

A Clustering-based Visual Analysis Tool for Genetic Algorithm.

DOI: 10.5220/0006135902330240

In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), pages 233-240

ISBN: 978-989-758-228-8

233

Figure 1: (a) Tool developed by Collins; (b) ELICIT tool; (c) Tool developed by He and Yen; (d) Tool developed by Craven

and Jimbo; (e) Tool developed by Kudo and Yoshikawa; (f) FOM tool; (g) Tool developed by Kramer and Luckehe; (h)

GAVEL tool; (i) VIS tool.

strings and two or three dimensional co-ordinates

for visualization of GA population. Although this

was the ﬁrst dedicated work on visualization of high-

dimensional individuals, it only offers a single view

into the GA population and also insufﬁcient level of

user interactivity.

A tool developed by Wu et al. (Wu et al., 1999)

called VIS to analyze the details of an Evolutionary

Algorithm (EA) run. For visualization of individuals,

ﬁve different graphical representations are offered by

this tool, namely: Genotype, Zebra, Neapolitan, Four

Color, and Gene Location, each of which is suitable

for a speciﬁc chromosome representation. Also, it of-

fers a view named Family Format to show the parents

and offspring of a particular individual. However, it

does not provide any view for the visualization of in-

dividuals in objective space, and also for individuals

phenotype.

GAVEL introduced by Hart and Ross (Hart and

Ross, 2001), is another analysis tool for GA. The

main idea of this tool is to start from the best solu-

tion found at the end of a GA run and trace back its

evolution by ﬁnding the parents and parents of par-

ents, etc., all the way back to the initial generation

of individuals. The aim of this process is to produce a

complete ancestry tree of the best solution. Moreover,

this tool tracks the history of every single gene in the

best individual’s chromosome to ﬁnd the individual it

originated in. GAVEL visualizes the individuals using

three graphical representations, namely: Alleles Val-

ues, Gene Origins, and Operator Origins. Like the

VIS tool, this tool has the disadvantage of not provid-

ing any view for the individuals phenotype.

Parejo et al. (Parejo et al., 2003) developed

a framework for meta-heuristic optimization called

FOM. This tool includes the implementation of sev-

eral meta-heuristics such as Steepest Descent, Iter-

ative Steepest Descent, Tabu Search, Simulated An-

nealing, GRASP, Variable Neighbourhood Search

and GA. FOM provides visualization and some sta-

tistical information of the individuals ﬁtness values.

However, no view is provided for representing indi-

viduals in parameter space and also for individuals

phenotype.

Kudo and Yoshikawa (Kudo and Yoshikawa,

2012) proposed a visualization method using an idea

of Isomap. They applied the proposed method to

data came from a Multi-Objective Genetic Algorithm

(MOGA), which was used to solve a problem in engi-

neering design ﬁeld, i.e. conceptual design optimiza-

tion problem of hybrid rocket engine. The focus of

this method is to analyze the distribution of Pareto in-

dividuals by visualizing the manifold embedded in the

high dimensional objective space, and in fact, this is

the only view provided by this method.

Craven and Jimbo (Craven and Jimbo, 2014) in-

troduced a hybrid visualization scheme to determine

the stability of an EA with regards to changes of its

control parameters. In this method, the EA stabil-

ity is measured according to two perturbation metrics,

and will result a different visual representation of lo-

cal neighborhoods in parameter space for each met-

ric. However, the visualization using this method is

limited to parameter space, and objective space is not

considered.

Kramer and Luckehe (Kramer and L

uckehe,

2015) presented a visualization approach for con-

tinues evolutionary runs, using isometric mapping

(ISOMAP) for mapping high-dimensional individu-

als to a two-dimensional representation. By perform-

ing some experiments, they claimed that ISOMAP re-

sults equally or better locally linear embedding than

IVAPP 2017 - International Conference on Information Visualization Theory and Applications

234

Principal Component Analysis (PCA) in maintaining

neighborhoods of high-dimensional individuals.

A tool called ELICIT was developed by Cruz and

Machado (Cruz et al., 2015) to enable the visual

exploration of evolutionary computation algorithms.

Two levels of view is provided by ELICIT, namely

General View to cover the whole population, and In-

dividual View to cover a particular individual. For an

individual, both genotype and phenotype can be visu-

alized. However, this tool lacks in providing enough

statistical information beside the visualizations.

In a recent effort, He and Yen (He and Yen, 2016)

proposed a new method to visualize the population of

Many-Objective Evolutionary Algorithms (MaOEAs)

in high-dimensional objective space. They claimed

that their proposed method maps individuals from a

high-dimensional objective space into a 2D polar co-

ordinate graph while preserving Pareto dominance re-

lationship, retaining shape and location of the Pareto

front, and maintaining distribution of individuals. Al-

though effective in visualizing the high-dimensional

objective space, this tool only provides a single view

into the EA population which might not be sufﬁcient

for gaining a comprehensive insight.

A screenshot from each of the reviewed works is

presented in Fig. 1. Although all these works have

their own strengths and weaknesses which some are

already mentioned, each of them has at least one of

the following limitations:

• Poor level of user-interactivity.

• Expert knowledge required on the context in or-

der to digest the visualization result, which makes

it unsuitable for users with less knowledge in evo-

lutionary computation.

In contrast, by taking into consideration the above

limitations, the tool proposed in this paper provides

the user with a high level of interactivity in a 3-D en-

vironment to move inside and in between views with

different levels of granularity. However, it is notewor-

thy that the 3-D environment is merely used to orga-

nize the information space, and the third dimension

itself contains no information.

3 VISUALIZATION APPROACH

3.1 Overview

The data produced by the evolutionary process of GA

including all the individuals genotypes and their ob-

jective values will be given to the visualizer as in-

put. The process pipeline includes a clustering algo-

rithm to perform a (global) clustering across all gen-

erations of a GA run based on the distribution (simi-

larity) of individuals in parameter space. Then, clus-

ters will pass through a symbol mapping process, to

be described in subsections to follow. Finally, all the

clusters and their mapped symbols will be passed to

an interactive visualization interface. Since the infor-

mation to be visualized is over multiple generations,

clusters and sub-clusters, the visualization interface

contains square-walls to ease the organization, parti-

tioning and positioning of this information. Symbols

to be used in the elaboration are listed below:

• N: total number of individuals in all generations

of a GA run

• M: number of generations

• K: number of clusters

• I = {i

| 1 < n <= N } is the set of all individuals

• C

, 1 < k <= K,C

⊆ I is a cluster of individuals

across all generations

• C = {C

, ...,C

} is the set of all clusters

• c

, 1 < k <= K, 1 < m <= M, c

⊆ C

is a part

of cluster C

in generation m (sub-cluster)

Fig. 2 gives a bird’s-eye view of the visualization

interface where the whole population of N individuals

are placed on a tower, with each column representing

a cluster, each row representing a generation and each

square-wall representing a sub-cluster.

There is a control panel at right side of the inter-

face (Fig. 2), which not only provides some statistics

of clustering and information about the individuals,

but also enables the user to choose between three op-

tions from different families of clustering algorithms,

set their associated parameters and re-run the cluster-

ing (i.e. restart the whole process pipeline). The op-

tions for clustering algorithm are as follows:

• Centroid-based: k-means

• Density-based: DBSCAN

• Connectivity-based: Hierarchical agglomerative

The user is able to move the camera in six direc-

tions to have a look from an arbitrary angle. More-

over, different walls, ﬂoors and towers (multiple tow-

ers in case of multi-population visualization) can be

chosen by a mouse click to get the related statistics

in the control panel. As shown in Fig. 2, the wall on

down-left corner of the tower is currently being ac-

tivated. In fact, blue color indicates the active wall

(sub-cluster) and red border indicates the active ﬂoor

(generation). The ”Next” and ”Previous” buttons in

the control panel can be used to navigate through in-

dividuals of the active wall to see their gene values,

A Clustering-based Visual Analysis Tool for Genetic Algorithm

235

Figure 2: A bird’s-eye view of the visualization interface.

Figure 3: An example set of reference shapes with 16 ver-

tices in their graph structures.

scaled aggregate ﬁtness values and objective scores.

The active individual is always presented by a red

color. To gain a rich insight, the visualization inter-

face provides three levels of view into the GA popu-

lation which are described in the following.

3.2 Symbol-view

This is a high-level view in which a unique visual

symbol is assigned to each cluster. Then, a represen-

tative individual from each sub-cluster is mapped to

the symbol of the cluster it belongs to, so that shape

transformation of the symbol in each generation de-

picts the evolution of the representative individual.

Fig. 3 shows a set of ﬁve shapes drawn by our simple

shape-drawer program to be used as symbols. Each

of these shapes will be used as symbol of a partic-

ular cluster. Two methods of symbol mapping are

presented here. First, is Isomorphic Graph-Mapping

which is a genotypic-based method and is mainly use-

ful in case of combinatorial problems. Second, is

Polygon-Morphing which is a ﬁtness-based method

and can be used for any kind of problem given to GA.

3.2.1 Isomorphic Graph-mapping

Let G={V, E} and G

= {V

, E

} be graphs. G and

are said to be isomorphic (G

∼

) if there is a

bijection ϕ = V → V

which preserves adjacency and

nonadjacency (with xy ∈ E ⇔ ϕ(x)ϕ(y) ∈ E

for all

x, y ∈ V ) (Diestel, 2000). Such a mapping ϕ is called

an isomorphism. Although two isomorphic graphs

might have different shapes, their structures are ex-

actly the same.

Algorithm 1 describes the assignment of a symbol

to each cluster, using Isomorphic Graph-Mapping. In

step 4 of the algorithm, we are facing with an opti-

mization problem to ﬁnd the best mapping from the

graph produced by the representative individual (e.g.

in the case of Vehicle Routing Problem (VRP), the

graph includes customer nodes as its vertices and ve-

hicle routes as its edges) to the graph of its corre-

sponding symbol. A genetic algorithm is used here

to handle the optimization problem. The GA being

used tries to ﬁnd the best mapping from the vertex-set

of the representative individual to the vertex-set of its

symbol. In order to measure the quality of mappings

found by the GA chromosomes, Hausdorff distance

is being used in the ﬁtness function. This distance

measures the extent to which each point of a model

set lies near some point of another set and vice versa

(Huttenlocher et al., 1993). The Hausdorff distance is

presented as the function in Algorithm 2.

After assigning a symbol to each cluster (step 2 to

5 of Algorithm 1), each sub-cluster is taken to map its

representative to the symbol of the cluster it belongs

to, based on the mapping found in step 4.

3.2.2 Polygon-morphing

This method uses ﬁtness values to assign symbols,

hence it is neither dependent on the type of prob-

lem nor the representation of individuals. Basically, it

generates a range of morphed shapes for each symbol.

The process begins by generating a random mapping

of vertex-list for the original symbol to get an ugly

instance of it. Then, the generated shape will be mor-

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236

Algorithm 1: Assigning symbols based on Isomorphic

Graph-Mapping.

1: procedure ASSIGN ISO SYMBOLS(C, shapes)

2: for k ← 1 to K do

3: ClRepIndv ← get rep indiv(C

)

4: ϕ

← best mapping(ClRepIndv, shapes

)

5: end for

6: for m ← 1 to M do

7: for k ← 1 to K do

8: SubClRepIndv ← get rep indv(c

)

9: map(SubClRepIndv, shapes

, ϕ

)

10: end for

11: end for

12: end procedure

Algorithm 2: Finding Hausdorff distance between two

graphs G and G

1: function HAUSDORFF DIST(G, G

)

2: hausDist ← 0

3: for each vertex (v in G and ϕ(v) in G

) do

4: longestDist ← 0

5: for each neighbor n o f v in G do

6: shortestDist ← +∞

7: for each neighbor n

o f ϕ(v) in G

8: d ← euclidean

Dist(n, n

)

9: if d < shortestDist then

10: shortestDist ← d

11: end if

12: end for

13: if shortestDist > longestDist then

14: longestDist ← shortestDist

15: end if

16: end for

17: hausDist ← hausDist + longestDist

18: end for

19: return hausDist

20: end function

phed towards the original shape in multiple steps.

The number of steps depends on deﬁned length of

the morphing range by the user. Obviously, longer

length of the range results in a more accurate map-

ping while needing more computational time and re-

sources. Again by using Hausdorff distance, each

morphed shape will be compared to its original shape

and given a similarity score. Finally, representatives

of each sub-cluster will be associated with one of the

morphed shapes based on the closeness of their aggre-

gate ﬁtness values to the similarity score of the mor-

phed shapes.

Figure 4: Phenotype-View.

Figure 5: Result of Isomorphic Graph-Mapping.

3.3 Individual-distribution View

This is a middle-level view which shows the distribu-

tion of individuals in clusters by placing circles (as in-

dividuals) on a square-wall. While a unique color (for

the circles) is assigned to each cluster, the positioning

of individuals on 2-D walls is based on their scaled

objective scores. The control panel enables the user

to choose between three options of individual rank-

ing that results different positioning on the walls: in

sub-cluster, in cluster, and in generation.

A Clustering-based Visual Analysis Tool for Genetic Algorithm

237

Figure 6: Result of Polygon-Morphing.

3.4 Phenotype-view

The lowest-level view of the visualizer provides phe-

notype of the individuals in a sub-cluster chosen by

the user (Fig. 4). The individuals are sorted from

highest to lowest aggregate ﬁtness in a row. The cam-

era is placed on the 45-degree angle from the individ-

uals to provide a more dominant view of the whole

row, so the user is able to compare the most-front in-

dividual with some of those behind in one look. Nev-

ertheless, the active individual is always highlighted

by a different color. In addition, the control panel

includes a checkbox which enables the user to link

the camera to the active individual, so each time the

user switch to another individual, camera will auto-

matically be placed at a close position to the active

individual.

4 EXAMPLE ANALYSIS

A test application of the proposed approach is per-

formed in the following context: We applied Non-

dominated Sorting Genetic Algorithm II (NSGA-II)

(Deb et al., 2002) to an instance of VRP. The VRP in-

stance being used is a smaller version (15 customer

nodes) of C101 instance from Solomon’s bench-

Figure 7: Result of Individual-Distribution View.

marks. The maximum number of generations for GA

was set to 10 (which proved to be enough for a good

convergence as C101 has a clustered structure) with

50 individuals per generations.

Fig. 5 shows the result when Isomorphic Graph-

Mapping is chosen to map the symbols. In the ﬁrst

few generations down there, all the symbols are seen

to be messy that is a proper representation of the weak

individuals. By each generational step, symbols tend

to be more similar to the perfect shape. For instance,

the left-most cluster with a ﬁsh as its symbol lasts un-

til sixth generation and it had no improvement from

ﬁfth to sixth generation, because its symbols at these

generations are identical. However, second cluster

with a star symbol, despite of being absent in gen-

eration 3, lasts up to the end of evolutionary process

which obviously represents the place in ﬁtness land-

scape where GA is converged in. The reason that sec-

ond cluster with a star symbol disappears in genera-

tion 3 is due to the fact that none of its individuals

belongs to this generation. In other words, GA left

this cluster in generation 3 and went back to it in gen-

eration 4 onward. Same goes to empty sub-clusters in

Fig. 2, Fig. 6 and Fig. 7.

Fig. 6 illustrates the results for the Polygon-

Morphing method of mapping symbols. Unlike the

previous method which takes care of similarity in

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238

Figure 8: Number of individuals in different clusters during

each generation.

parameter space, Polygon-Morphing visualizes the

changes in objective space. As an example, the

square-symbol cluster on the middle of tower expe-

rienced two jumps in its ﬁtness from ﬁrst generation

to third, but form generation 4 onwards, the changes

are little.

Moving one level deeper, the Individual-

Distribution View is experimented with. One of the

useful insights given by this view is the diversity level

of the population. In Fig. 7, individuals are placed

on the walls based on their scaled objective scores

in sub-cluster for total traveled distance (horizontal

axes, left to right) and number of routes (vertical

axes, down to up). Further, at each ﬂoor, the best and

worst individuals in generation are presented with

black and white color respectively. When comparing

blue cluster with yellow, it can be seen that yellow

is much more diverse while blue is the one which

contains the best-in-generation individual for half of

the generations. Fig. 8 illustrates how GA converges

in the blue cluster. By referring to statistics given

by our visualization tool, we see that the variance of

the blue cluster is almost 28, which is the minimum

among all, together with the chart in Fig. 8, one can

conclude that GA tries to gradually ﬁnd and climb

the global optima (i.e. the blue cluster) in the ﬁtness

landscape while at the same time tests different places

(i.e. other clusters that might be around local optima).

In other words, by having a holistic look at the tower,

it is clear that GA tends to globally explore the ﬁtness

landscape by hanging around different optima and

trying to evolve them using its local searches. Also,

it shows that at each generational step, depending

on competitiveness of the local optima compared to

others, GA might clone more individuals around it or

conversely, take out (some) individuals from there.

Last but not least, lowest-level view of the visual-

izer is presented in Fig. 4, which provides a close look

at the individual’s phenotype. As can be seen, the

active individual is presented with a different color,

which in the case of VRP, each route has a unique

color. By traversing the individuals in the row, it can

be seen that ﬁtter individuals are less colorful due to

their superiority in the number of routes objective.

5 COMPARISON WITH OTHER

TOOLS

This section presents a comparison between the fea-

tures offered by our proposed tool and the tools pre-

viously discussed in section 2. The choice of the

characteristics for this comparison was based on three

main factors: the ability to visualize the evolutionary

process and individuals from various perspectives, the

suitability for users with different levels of expertise,

and the level of user-interactivity. This comparison

is shown in Table 1. As we can observe, the ability

of visualizing cluster formations in GA evolutionary

process is offered by none of the tools except our pro-

posed tool. Moreover, all other features provided by

the existent tools are also offered by our tool with the

exception of the feature to visualize many-objective

problems. This feature is planned to be integrated into

the current tool in the near future.

6 CONCLUSION AND FUTURE

WORK

A clustering-based visualization tool for GA has been

presented in this paper. The tool has the potential of

providing useful information on the dynamics of clus-

ter formations in GA. Since cluster formations corre-

spond to local searches performed by the GA, it can

provide insight on how effectively the GA is behav-

ing in its search effort. The proposed tool particularly

enables us to analyze the behavior of GA operators

and parameters, and also obtain useful information

that can be used later to interactively manipulate the

search space.

More work of course remains to be done to en-

hance the usefulness or usability of the tool and its

underlying paradigm. In the near term, we intend to

investigate the following:

• Full analysis of the clusters found by different

clustering algorithms.

• Using different distance measures for clustering

to possibly get different insights into the ﬁtness

landscape.

A Clustering-based Visual Analysis Tool for Genetic Algorithm

239

Table 1: A comparison between the features provided by the existent tools and our proposed tool.

• Incorporating dimensionality reduction tech-

niques into the visualizer to handle the case of

problems with many objectives.

ACKNOWLEDGEMENTS

This work is partially supported by FRGS Grant,

Malaysia.

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