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Large Network Analysis for Fisheries Management using
Coevolutionary Genetic Algorithms
Garnett Wilson
Department of Computer
Science
Memorial University of
Newfoundland
St. John’s, NL, Canada
gwilson@mun.ca
Simon Harding
Department of Computer
Science
Memorial University of
Newfoundland
St. John’s, NL, Canada
simonh@mun.ca
Orland Hoeber
Department of Computer
Science
Memorial University of
Newfoundland
St. John’s, NL, Canada
hoeber@mun.ca
Rodolphe Devillers
Department of Geography
Memorial University of
Newfoundland
St. John’s, NL, Canada
rdeville@mun.ca
Wolfgang Banzhaf
Department of Computer
Science
Memorial University of
Newfoundland
St. John’s, NL, Canada
banzhaf@mun.ca
ABSTRACT
Traditionally, a genetic algorithm is used to analyze net-
works by maximizing the modularity (Q) measure to create
a favorable community. A coevolutionary algorithm is used
here to not only find the appropriate community division for
a network, but to find interesting networks containing sub-
stantial changes in data within a very large network space.
The network is one of the largest, if not the largest, analyzed
by evolutionary computation techniques to date and is cre-
ated using a real world data set consisting of fisheries catch
data in the north Atlantic Ocean off the coast of Canada.
This work examines the quantitative performance of two
types of coevolutionary algorithms against both a standard
GA that uses a natural (but not necessarily optimal) division
of the data set into communities, and simulated annealing.
The goal for all search algorithms was to automatically find
anomalies (differences in catch) within the data. To measure
practical usefulness of the system, a fisheries expert analyzed
the best networks located by the search algorithms using an
existing visualization software prototype. The expert indi-
cated that a refined version of coevolutionary GA known as
PAMDGA was found to most reliably locate subnetworks
containing catch differences of biological relevance.
Categories and Subject Descriptors
I.2.8 [Artificial Intelligence]: Problem Solving, Control
Methods, and Search—Heuristic methods
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General Terms
Algorithms, Performance, Experimentation
Keywords
coevolution; genetic algorithm; Q modularity; spatiotempo-
ral visualization; fisheries
1. INTRODUCTION
In most works that employ the use of genetic algorithms
(GA) to analyze the structure of a network, researchers use
community membership as a fitness function. In particular,
the community membership function that is optimized by
the GA is the modularity metric, also called the “Q metric.”
The Q metric rewards networks of densely connected nodes
within communities and sparse connections between commu-
nities. The goal of evolution is to determine the community
structure of a network with an optimal Qvalue. The fit-
ness function typically only optimizes community structure;
it does not look for anomalies within a network.
To the authors’ knowledge, we present the first instance
of a coevolutionary GA used for the analysis of community
structure of a network in this work. Two coevolutionary
GA-based algorithms are examined, where both algorithms
determine not only community structure (as in other liter-
ature), but also simultaneously determine solutions. Using
actual data obtained from the Department of Fisheries and
Oceans in Atlantic Canada, a software tool called GTdiff
[3] was developed that could analyze differences in bottom
trawl survey data for the northern cod (Gadus morhua )in
the form of a very large network [8]. A network is of interest
due to one or more anomalies (or large changes in average
catch data over time and geographical location). These large
differences in catch between time and space are of interest
to fisheries observers as they could indicate overfishing or bi-
ological phenomena that should be more closely examined,
and as such they are considered good solutions to be located
by the GA. In particular, the network nodes each correspond
to an x, y point on an NxNgrid for a particular span of
years. The edges in the GA solution network correspond to
differences between the time spans, which are visualized in
GTdiff as difference graphs that highlight changes between
time spans (additional details and figure in Section 3). The
GA algorithms described in this work represent an attempt
to aid fisheries scientists using the visualization tool through
partial automation of the search for anomalies in substantial
amounts of catch data.
The size of this network is greater than any networks ex-
amined in the evolutionary computation literature that is
known to the authors. The use of this large real world net-
work poses a new challenge in that a known community
structure does not exist in the network. A search thus can
be conducted to establish a community structure. Given
the context of a community structure for the network pro-
vided by one population, a second population of poten-
tially anomalous networks is also evaluated using coevolu-
tion based on a community-based fitness metric.
Section 2 describes previous work in the evolutionary com-
putation literature related to establishing community struc-
ture in networks. Section 3 describes the spatiotemporal
fisheries catch data set used in this work, including its repre-
sentation as a large network and the Q-based fitness function
used by the GA for evaluation of its subnetworks. Section
4 describes the four search algorithms that are compared,
namely genetic algorithm (GA), simulated annealing (SA),
coevolutionary GA, and a refined coevolutionary GA called
“Probabilistic Adaptive Mapping Development Genetic Al-
gorithm (PAMDGA)”. Section 5 describes quantitative per-
formance analysis of the algorithms, with expert analysis of
the networks located by the search algorithms following in
Section 6. Section 7 provides conclusions.
2. PREVIOUS WORK
Genetic algorithms are often chosen as a search algorithm
for optimizing the modularity metric Qof a network. The
individuals evolved by the GA are typically a particular divi-
sion of a network into communities, which can be considered
a mapping of the network’s nodes into communities. Tas-
gin et al. [7] applied a genetic algorithm to individuals that
were a mapping of each node to a community, where the fit-
ness function was the straightforward optimization of the Q
metric. Tasgin et al. use the GA to decide the community
structure of the network for two smaller (karate club and
football matches) and one larger (email dataset) network
that are often used as benchmarks in the literature. Their
results indicate that the GA search is scalable for potentially
large networks. Gog et al. [1] also use a GA algorithm to
evolve individuals that are mappings of network nodes to
communities. The GA is enhanced slightly in that the GA
individuals are aware of the current optimum solution of the
search and a best ancestor. Nicosia et al. [6] use a GA with
overlapping community structure in the modularity-based
fitness function (as in this work). Genotypes consisted of
a mapping of nodes to communities for the network, with
each element of the mapping representing the strength of
community membership for each node. The authors exam-
ined evolved networks for two benchmarks and two newly
introduced networks of varying size.
In the existing literature, if there is an ideal or known
community structure for a network under investigation, au-
thors typically attempt to show that an evolution-based al-
gorithm is able to discover a network reasonably close to
the known structure. If there is not a known community
structure for the network (as in this work), authors will typ-
ically try to show that their solution can outperform other
machine learning techniques in its ability to maximize the
Q metric. In previous work [8], the authors presented a
standard GA to search for anomalous networks given a nat-
ural, assumed community structure based on a year-based
temporal ordering of nodes in the fisheries catch data net-
work. While the assumption of temporally ordered years as
a community structure is a natural one, there is the oppor-
tunity to expand the power of the search for anomalies by
also allowing a search through the community space in ad-
dition to a search for a solution. In this work two types of
coevolutionary GA are applied to the fisheries data set to
provide improved networks that better represent anomalies
that would be interesting to a domain expert. In order to
search for both solution and appropriate underlying com-
munity structure simultaneously, we present two algorithms
that coevolve two populations: one population of network
solutions and another population of mappings that indicate
node community membership.
3. SPATIOTEMPORAL CATCH DATA
3.1 Dataset as a Very Large Network
The very large network used in this work is based on a
spatiotemporal data set of annual bottom trawl survey catch
data for the Atlantic cod (Gadus morhua) conducted by the
Canadian Department of Fisheries and Oceans (DFO) for
the Newfoundland and Labrador, Canada region. To the
authors’ knowledge, this data set as described herein repre-
sents the largest network data set analyzed in the evolution-
ary computation literature to date. Nodes represent catch
amounts at a particular geographical location and an associ-
ated time span, where the mean catch over all data points in
the given span of years is calculated to determine the level
of catch for the node (see leftmost two girds of Figure 1).
Edges in the network represent differences in the mean catch
between locations over two time spans, and are shown in the
rightmost grid of Figure 1. Edges in the network using two
nodes with the same time span are excluded, since they do
not reflect any difference because the entire geographical
area is viewed at once in the visualization tool (application
of the tool is discussed in Section 5). In virtue of not allow-
ing the same time span (regardless of locations) in an edge,
loops (reflexive ties) are prohibited in the large graph.
The data collected covers an area of 1,000,000 km2and
a temporal range of 1980 to 2005. The data set produces
a very large network to be evaluated: The search space in-
volves a node for every pair of locations x, y in an N x N grid
and two year time span. The number of unique, unordered
two year time spans for the 26 year period we examine (1980
to 2005, inclusive) is 26
2, or 325 possibilities. The span of
one year (e.g. 1996 to 1996) is also considered a possible time
span of interest, so the number of possible time spans is thus
a total of 325 + 26 = 351. The area covered by the data set
is divided as a 30 x 30 grid (selected as an appropriate reso-
lution for viewing changes in preliminary experiments with
an expert). Given the number of possible time spans, there
will thus be 302x 351 = 315,900 possible nodes to consider.
Nodes are average catch data over a particular area dur-
ing a time span. We wish to consider the difference be-
tween nodes as absolute differences in those mean catches.
1995-2002,
mean catch: 2950kg
2001-2003,
mean catch: 2000kg
1999-2002 vs. 2001-2003,
mean catch dierence: 950kg
node 1 node 2 edge
catch: 5500kg
year:1997
catch: 400kg
year:2001
catch: 2000kg
year:2002
sample catches
Figure 1: Relationship between network structure
and spatiotemporal visualization. Catch amounts
are hypothetical for purposes of illustration.
Thus, the network to be considered consists of an undirected,
weighted graph. The number of all unique edges existing in
this search space is the number of possible pairings of nodes,
with no time span compared to itself, giving n(n−1)/2tpos-
sibilities for nnodes and ttime spans, or approximately 1.5
x10
8edges.
3.2 The Q Metric
The modularity (or Q)metricisappliedinthisworktoa
network where a strength is associated with the connection
between nodes. Newman adapted the modularity metric for
weighted networks in [5], which is used here and is defined
as
Qw=1
2m
ij Aij −kikj
2mδf(ci,c
j)(1)
where Aij is the weight of the edge from ito j,kiof a node
iin a weighted network is the sum of the weights of the
edges connected to it (ki=
j
Aij ), and m=1
2
ij
Aij is the
total weight of the edges in the network. Qwhas an absolute
value between 0 and 1, where a value of over 0.3 is typically
considered to indicate favorable community division [5].
The typical community membership function is denoted as
δf(ci,c
j), where ciis the community to which a node iis as-
signed. In the traditional community membership function,
a node cannot be a member of more than one community
(communities cannot overlap). In this work, the members
of a community are time spans of two years. The Qmet-
ric is thus modified to allow for the more natural choice of
overlapping community membership, detailed in [2]. We cal-
culate overlapping community membership as the degree of
overlap between time spans (communities) within each of
two nodes:
δf(ci,c
j)= |Yi∩Yj|
|Yi∪Yj|(2)
where Yiis the enumeration of all years (inclusive) for the
node itime span. Similarly, Yjis the enumeration of years
for the node jtime span. The function δfyields a decimal
value between 0 and 1, conforming to the traditional range
of possible values for Qw.Inpractice,theδffunction pro-
vides large values of Qwfor networks with edges with large
differences within overlapping time frames. For instance, the
user may see that two years out of a five year span reflect
abnormally large (or low) catches on average.
In addition to traditional community overlap, we exam-
ine a variant of (1) where δfis replaced by 1 −δfto em-
phasize non-overlapping time spans. In this instance, large
differences in catch for non-overlapping time spans will be
highlighted by the GA search. As an example, a three year
span containing high (low) catch compared to a six year
span starting after the end of the three year span could be
identified.
In the case of either variant of (1), there can be a trade-off
between maximizing overlap (or reducing overlap) of partic-
ular time spans and the largeness of the catch differences
within those time spans. Also, one large difference between
time spans (edge weight) can sometimes come at the ex-
pense of other lower differences (edge weights) in the same
network. These trade-offs are effected by the differences de-
tected by search in the network, the number of time spans
(communities) in the network, and the associated lengths of
those time spans. All of these aspects will be examined in
greater detail as they relate to individual algorithms in Sec-
tion 5. In particular, we compare the results of a GA, two
coevolutionary GAs, and simulated annealing. Each of these
algorithms is considered using each of the two Qwvariants.
4. SEARCH ALGORITHMS
4.1 GA Algorithm
Each GA individual genotype is a chromosome of 20 gene
sequences, where each sequence is an ordered set of 8 integers
(genes) that correspond to an edge in the network. Each
individual is thus a list of edges, or a network that should be
of interest to the user. The first 4 integers correspond to the
first node in the edge, while the last 4 integers correspond
to the second node of the edge. In each set of 4 integers
identifying a node, the first two integers provide the xand
ycoordinates in the N x N grid and the second two integers
provide the two years of a time span in the data set and
are always ordered. There is an added restriction on the 8
integers of the edge that the time spans (integers 3,4 and 7,8)
cannot be the same. The absolute difference between the
average catch over all years for the time span and location
pair in each node is considered to be the weight of the edge.
The gene sequence representing an edge is shown in Figure 2.
x1, y1 t1, t2 x2, y2 t3, t4
location 1 location 2
timespan 1 timespan 2
node 1 node 2
edge
where t2 ≥ t1 , t4 ≥ t3 and t1,t2 ≠ t3,t4
Figure 2: Gene structure representing two nodes
and their joining edge.
The GA involves a steady state tournament of 100,000
rounds using a population of 10. The small population size
has been found to improve evolutionary search and will guide
the construction of interesting networks rather than relying
on the discovery of randomly generated material in a larger
initial population that must be found using extensive search.
The algorithm for the GA tournament is
for each tournament round
randomly select 4 genotypes
determine fitness (Q value) of 4 genotypes
keep best two genotypes as parents
replace worst two genotypes with parents
mutation on children
crossover on children
Four individuals are selected for evaluation for each tour-
nament round. The top two individuals become “parents”
and are left unchanged (in virtue of this aspect of selec-
tion, the best individuals are left unchanged). The last two
individuals are replaced by copies of the parents and thus
become “children.” The children then have mutation and
crossover applied to them. The mutation operator is applied
to the children always, and the operation involves each edge-
based sequence of 8 genes having a 50% (rate of 0.5) chance
of being mutated. In practice, on average half of the nodes
and edges in the childrens’ network are replaced with newly
generated edges to more efficiently explore the search space.
Standard two-point crossover is used to exchange sections
of edge-based gene sequences, also at rate of 0.5. The fit-
ness function is (1), either with a preference for overlap (δf)
or no overlap (1 −δf). The mutation and crossover rates
were found to provide fast real-time search progress in our
experiments when the best individuals in each round were
retained.
4.2 Coevolutionary GA Algorithm
While the standard GA algorithm provides a means of
searching for an anomalous subnetwork involving large catch
differences from a larger network, there is no search occur-
ring to attempt to refine a community structure for the large
network. Most GAs only perform the search for an optimal
community structure for a single network. We now present
the first usage of a coevolutionary GA to search for both an
optimized solution (subnetwork) and an appropriate com-
munity structure for the general problem space.
The coevolutionary GA maintains and performs a search
on two populations: a genotype and a mapping population.
The genotype structure is as described for the general GA,
but there is also the evolution of the underlying mapping
structure as a separate population. That is, the second pop-
ulation consists of potential mappings of all time spans of
two years to a community. As described in Section 3, there
are 351 time spans that are each considered a community
in the standard GA. A mapping individual consists of all
ordered year pairings that constitute a time span. Upon
initialization, each ordered pairing of years are given a ran-
domly assigned community number from 1...351. As such,
the mapping is redundant because more than one ordered
pair of years (time span) can be a member of the same
community and there will be 351 or less communities. By
allowing the mapping of time span to community to be re-
dundant, the GA search on the mapping population will
emphasize particular sets of time spans (not necessarily se-
quential). That is, instead of each time span being its own
community by definition (as in the standard GA), a num-
ber of collectively interesting time spans can be grouped in
a community by the coevolutionary search in the mapping
population. The coevolutionary GA operates as follows
for each tournament round
if round % 2 == 0
randomly select 4 genotypes
determine genotype, best mapping fitnesses
keep best two genotypes as parents
replace worst two genotypes with parent copy
mutation on children genotypes
crossover on children genotypes
if round % 2 != 0
randomly select 4 mappings
determine mapping, best genotype fitnesses
keep best two mappings as parents
replace worst two mappings with parent copy
mutation on children mappings
The coevolutionary GA operates in somewhat the same man-
ner as the standard GA, except there are alternating rounds
for evaluation of genotype individuals and mapping individ-
uals. In the genotype evaluation rounds (even numbered
rounds), each of the four genotype individuals chosen are
paired with the current best mapping individual (chosen
randomly in the initial round) for fitness evaluation. No
genotype individual can be evaluated in the absence of a
mapping individual in the coevolutionary algorithm: there
is no default association of community with each time span.
The two losing genotype individuals are subjected to muta-
tion and crossover based on the established thresholds. In
the mapping evaluation rounds, 4 mapping individuals are
chosen and are evaluated by pairing with the current best
genotype individual. As before, the best two mapping indi-
viduals are retained as parents and the worst two mappings
become copies of the parents and are potentially subjected
to the operation of mutation. The rate of mutation is kept
low (rate of 0.1) so that there is a more consistent context
against which the genotypes will evolve (found to be ben-
eficial in initial experiments). Since the mappings are an
ordered list of year time spans, crossover is not appropriate.
4.3 PAMDGA Algorithm
The PAMDGA (Probabilistic Adaptive Mapping Develop-
mental Genetic Algorithm) algorithm is a genetic algorithm
version of the PAMDGP (Probabilistic Adaptive Mapping
Developmental Genetic Programming) algorithm introduced
in [9]. The algorithm is designed to overcome known diffi-
culties of more standard coevolutionary algorithms, in par-
ticular loss of context and fitness spiking due to a sudden
change in one of the current best individuals grouped for co-
evolution (known as the “Red Queen Effect”), lack of explo-
ration of the search space, and general lack of fitness-based
performance. These drawbacks are mitigated or eliminated
through the use of slight elitism (not allowing the best geno-
type or mapping in the best pairing to be altered by muta-
tion or crossover), and exploration of the search space using
a selection table that enables any grouping to be selected at
any time (see [9] for additional background).
The algorithm begins with initialization of genotype and
mapping populations of size gand m, respectively. A prob-
ability table of size gxmis then created with cells initial-
ized to 1/m. For each round of a steady state tournament,
4 cells of the probability table are selected using roulette
selection on the maxis. The selected cells correspond to
four genotype/mapping pairings that are selected where the
genotypes must be unique but the mappings can be chosen
more than once. The pairings are evaluated for fitness, and
the best two pairings are considered parents and are left
unaltered. The best two pairings are also checked against
the current best genotype/mapping pairing found so far in
the tournament to determine if they will be identified as the
new best. Once the current best genotype/mapping pair-
ing is identified, the table cell corresponding to the two best
genotype/mapping pairings is updated according to
P(g,m)new =P(g,m)old +α(1 −P(g,m)old)(3)
and the other combinations in the same column are updated
according to
P(g,m)new =P(g,m)old +α(P(g,m)old)(4)
where gis the index of the genotype, mis the index of
the mapping, αis the learning rate (corresponding to the
emphasis of current table values over previous values), and
P(g,m) is the probability in cell [g,m] of the table. Updates
by equations 3 and 4 result in all values in a column always
having a sum of unity. A threshold value of γis used to
prevent premature convergence on a sub-optimal solution:
Following the table update, if any cell in the probability
table column corresponding to the winning genotypes exceed
γ, all values in that column are then reset to 1/m so they
sum to unity. The effect of noise addition and normalization
is to effectively reset the chances of selection of all mappings
with respect to the genotype handled by that table column.
The last two ranked pairings are considered the children and
are subject to genetic operations based on their respective
associated thresholds. However, if either the genotype or
mapping of the losing pairings is identified as the current
best genotype or mapping found so far in the tournament,
they are protected from both mutation and crossover.
initialize genoPopSize x mapPopSize probTable
for each tournament round
use roulette selection on probTable mapping rows
choose 4 geno/mapping pairs (unique geno)
rank 4 geno/mapping pairs
verify or replace bestGeno/bestMapping pair
update probability table by Eq. (1) & (2)
if (cell in bestGeno column >= gamma)
set column values to 1 / mapPopSize
leave best 2 geno/mapping pairs as parents
for worst 2 geno/mapping pairs
if (geno != bestGeno)
replace genotype with parent
mutation of genotypes
crossover of genotypes
if (mapping != bestMapping)
replace mapping with parent
mutation of mapping
For the purposes of this work, the number of tournaments
was kept the same as GA and coevolutionary GA (100,000
rounds). The rate of mutation and crossover for genotypes,
and mutation for mappings is the same as the coevolution-
ary GA described in the previous section. The αlearning
rate is set at 0.1 (found to be a good value in preliminary
experiments), and γis set at 0.9 to indicate that for a partic-
ular genotype column in the probability table no particular
mapping should have a chance to be selected that exceeds
90%.
4.4 Simulated Annealing
Simulated Annealing (SA) is often considered to be the
prominent search algorithm for determining large Qdivi-
sions of a network [4]. As such, we use it as a benchmark
algorithm against which to compare the performance of the
standard GA and the coevolutionary GA. Each GA algo-
rithm is run for 100,000 rounds with 4 individuals evalu-
ated per round, so 400,000 individual evaluations are con-
ducted. For equivalent computational effort, the SA is run
for 400,000 evaluations.
The SA algorithm tracks both the best state located so
far in the search and the current state in the search. For
each cycle of the SA, the current state can be replaced with
the new candidate state with probability eΔE/Twhere ΔE
is the change in value of Qand Tis the current temperature
of the system. The temperature of the system is reduced
with each completed cycle. The SA then updates the best
state located so far with the the new current state if it has
ahigherQ(energy) than the current best state.
5. PERFORMANCE RESULTS
All algorithms were examined with respect to four met-
rics: fitness achieved (highest Qvalue of network located),
number of timespans in the best network, maximum differ-
ence in the best community generated, and mean length of
time spans. The results are shown in the boxplots of Fig-
ures 3 to 7 below for 50 trials (of 400,000 evaluations each).
The bottom, middle, and top lines of boxes indicate lower
quartile, median, and upper quartile values, respectively. If
there is no overlap in the notches of two boxes around the
medians, the medians of the two data sets are different at
the 0.95 confidence interval. Whiskers extend from the boxes
to 1.5 times the interquartile range. The symbol ‘+’ corre-
sponds to points from 1.5 to 3 times the interquartile range,
and the symbol ‘o’ corresponds to points outside 3 times the
interquartile range.
In Figure 3 it is evident that for the overlap-favored fitness
function, the coevolutionary algorithm provided the high-
est Q values. A more precise plot of its Q values is given
in Figure 4. The tendency for the coevolutionary GA to
switch mappings (to jump from one overlapping time span
pair to another) likely yielded these results. However, our
domain expert (fourth author) found the non-overlapping
fitness function to provide the most worthwhile information
(discussed in greater detail in the next section). For the
non-overlap favored fitness type, PAMDGA and GA pro-
vided significantly higher Q values. However, we can see
from a higher precision view of the best performing algo-
rithms in 4 that there is no difference between PAMDGA
and GA at 95% confidence with respect to the median.
As mentioned in Section 3.2, the Q-value of the network
is a result of the length of time spans (related to community
membership and overlap), number of time spans considered
(related to number of communities), and the differences in
catch between times (value of network edges). Figures 5
to 7 consider these aspects of the Q modularity in turn.
In Figure 5 it is evident that for the overlap-favoring fit-
Figure 3: Modularity (Q) of the best networks for
given fitness function over 50 trials.
Figure 4: Modularity (Q) of the best networks for
given fitness function over 50 trials at greater preci-
sion for best algorithms.
Figure 5: Number of time spans within the best
networks for given fitness function over 50 trials.
ness function, the standard coevolution and PAMDGA al-
gorithms produce the lowest number of time spans but are
not different with any statistical significance. Lower num-
ber of time spans given equal network sizes will yield higher
modularity, so lower number of time spans is better. For the
non-overlap favored fitness, there is very little difference in
the number of time spans in the best networks produced by
every algorithm (notches overlap).
Closely related to the number of time spans represented
by the networks is the length of the time spans used, as
seen in Figure 6. For the overlap favored fitness function,
the coevolutionary GA and PAMDGA had the smallest time
span lengths being compared when overlapped and GA had
the largest time spans. Conversely, given the non-overlap fa-
vored fitness function, the coevolutionary GA and PAMDGA
produced the largest time span lengths. This is significant
because the coevolutionary algorithms aim, in their evo-
lution of the mapping population, to emphasize particular
time spans. In particular, using a fitness function reward-
ing overlapping time spans, shorter time spans were em-
Figure 6: Average length of time spans within nodes
of the best networks for given fitness function over
50 trials.
Figure 7: Maximum difference within the best net-
works for given fitness function over 50 trials.
phasized in coevolution. For a fitness function emphasizing
non-overlapping time spans, coevolution emphasized longer
time spans.
In Figure 7, examining overall spread of the maximum
catch difference in each network, we can see that for the
overlap-favored fitness function the coevolutionary GA actu-
ally identified the lowest average differences throughout the
networks. Coupled with the fact that it produced the highest
modularity networks (Figure 3), we can conclude that coevo-
lutionary GA traded off large differences for higher overlap
in years. Paired with shorter time spans considered (recall
Figure 6), this trade off would naturally not produce the
most interesting networks for fisheries experts. For the non-
overlap favored network, in terms of overall spread of the
data, PAMDGA consistently produced large maximum av-
erage differences within its network when noting reach of
whisker and outliers (but its results in this respect are not
statistically different than GA around the median and are
generally comparable to GA). However, for non-overlapping
time spans, PAMDGA dominates the other algorithms when
considering both longer time span lengths (Figure 6) and
large average differences (Figure 7) together. By maximiz-
ing both the time span length and catch difference metrics,
PAMDGA produces high modularity networks (Figure 3)
that were chosen as most useful by a fisheries expert for the
geographical area under study.
6. EXPERT EXAMINATION
OF VISUALIZATIONS
A fisheries expert, the fourth author, examined the best
networks located by all algorithms (GA, SA, Coevolution-
ary GA, and PAMDGA). He was asked to rate each network
edge of the best networks. Network edges were visualized
using GTdiff as two temporal bins and one corresponding
difference graph. The first two grids are the temporal bins
in GTdiff, and display average catch in kilograms in each
spatial grid element. The two temporal bins are ordered se-
quentially based on the last year of the time spans; if the
last year is the same, the temporal bins are ordered by the
first year. The colour scale spans from light yellow (lowest
average catch) to brown (largest average catch). The third
grid is the difference graph, where the difference in average
catch between the two time spans is displayed as a positive
(green) or negative (red) change. No change in catch is rep-
resented by white, and the degree of saturation of green and
red is used to represent positive and negative differences,
respectively. The visualization tool was used to change the
resolution of the final networks to 10 x 10. The resolution
does not change the content of the networks and allowed for
viewing of trends by the expert and presentation in publica-
tion rather than examination on the high resolution display
used in the study.
During the time period examined (1980 to 2005), there
were known anomalies (large differences in catch over time):
Fisheries scientists reported that the population levels of
cod dropped suddenly in the early 1990s, which prompted
a moratorium on cod fisheries starting in 1992. In addition,
other smaller changes known to fisheries scientists occurred
during particular years. The three options for the rating
of each difference graph by the expert were: No (meaning
no difference relevant to fisheries scientists appeared), Rel-
evant (a difference relevant to fisheries scientists appeared),
or Salient (a special case of Relevant indicating that an im-
portant biological shift was identified). The ratings of each
of the difference graphs (individual edges) in the final best
network of each algorithm out of 50 trials are summarized
in Table 1 as the number of responses for each rating and
total differences rated.
Our expert found that for almost all results for every algo-
rithm using the overlap favored fitness function, differences
were not emphasized appropriately. In particular, there were
many instances of small changes in catch between two time
spans with a very large degree of overlap in the final net-
works. Despite this, the expert indicated that PAMDGA
provided the largest number of relevant differences, with
both coevolutionary algorithms significantly outperforming
the standard GA and SA algorithms.
The expert found that for non-overlap favored fitness, SA
had the largest proportion of relevant differences. However,
there were only 10 differences in the best SA network. The
expert also indicated that none of the differences located in
the SA were of particular interest; they simply presented
known overall trends with no particular anomalous changes
identified. In contrast, PAMDGA presented the highest pro-
portion of salient anomalies in the data. PAMDGA gleaned
from the dataset a remarkably higher percentage of salient
differences than any other algorithm (3/16, or 18.75%). We
present all three difference graphs for PAMDGA that repre-
sented salient differences for the expert in Figure 8.
The top difference graph in Figure 8 clearly shows the
decline of cod stocks from the decade leading up to the
moratorium of 1992 to 1993 on northern cod compared to
a sample later year in the future. In the middle graph of
Figure 8, the darker red across the region indicates that cod
stocks dropped considerably after the years 1983 to 1991,
which were prior to the moratorium on cod (1992 to 1993).
This difference graph nicely contrasts those previous years
of abundance with post moratorium levels of 1994 to 1997.
In the bottom difference graph of Figure 8, years mostly
covering the time period of the moratorium (1991 to 1994)
are compared to years following the moratorium by several
years (2000 to 2004). The interesting aspect of these data
for the expert was the red in the difference graph depicting
the decline in cod stocks post-moratorium in the northeast
of the grid with the exception of a place southwest of New-
foundland (light green portion of grid). This area actually
corresponds to known areas where levels of cod during the
moratorium were lower than the current levels.
Table 1: Ranking of Difference Graphs
Overlap Favored
No Relevant Salient Differences
GA 5 2 0 7
SA 6 1 0 7
CoEvGA 611 017
PAMD G A 2 5 0 7
Overlap Not Favored
No Relevant Salient Differences
GA 10 6 1 17
SA 3 7 0 10
CoEvGA 6 6 1 13
PAMD G A 6 7 3 16
7. CONCLUSIONS
This work described the application of coevolutionary GA
algorithms to the simultaneous discovery of problem solution
(interesting network containing anomalous large changes in
catch data) and underlying community structure. A large
real-world network based on geospatial fisheries catch data
over a 25 year span in Atlantic Canada was used as the basis
for performance comparisons. The fitness function for the
analysis of the networks used modularity (the Qmetric) with
a community membership function that either did or did
not favor overlapping of communities to emphasize different
relationships between time periods. Four search algorithms
were compared: GA, SA, standard coevolutionary GA, and
PAM DGA (refined coevolutionary GA). The best networks
found by all algorithms were examined using a prototype
visualization tool designed for fisheries scientists.
Results indicated that the coevolutionary algorithm pro-
duced superior Q-based fitness results for overlap-favored
fitness. However, the fisheries expert indicated that non-
overlap favoring fitness provided more interesting final net-
works. With respect to the non-overlap favored fitness func-
tion, PAMDGA provided high fitness networks that com-
bined both large differences and extended time spans in its
chosen networks to a greater degree than the other algo-
rithms. Upon examination of the final networks by the ex-
pert, he found that PAMDGA located the largest number
of interesting known trends in the catch data.
Figure 8: Salient difference graphs selected by ex-
pert from the highest Q, no overlap favored network
produced by PAMDGA. Catches are shown in thou-
sands of kg.
8. ACKNOWLEDGMENTS
The authors wish to thank Fisheries and Oceans Canada
(DFO) for making available the data used in the case study.
This work was supported by a Strategic Projects Grant from
the Natural Sciences and Engineering Research Council of
Canada (NSERC) held by O.H., R.D., and W.B.
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