Binary Ant Algorithm
Carlos M. Fernandes
LaSEEB, Technical Univ. of Lisbon
Av. Rovisco Pais, 1, TN 6.21, 1049-
001, Lisbon, PORTUGAL
cfernandes@laseeb.org
Agostinho C. Rosa
LaSEEB, Technical Univ. of Lisbon
Av. Rovisco Pais, 1, TN 6.21, 1049-
001, Lisbon, PORTUGAL
acrosa@isr.ist.utl.pt
Vitorino Ramos
LaSEEB, Technical Univ. of Lisbon
Av. Rovisco Pais, 1, TN 6.21, 1049-
001, Lisbon, PORTUGAL
vramos@laseeb.org


ABSTRACT
When facing dynamic optimization problems the goal is no longer
to find the extrema, but to track their progression through the
space as closely as possible. Over these kind of over changing,
complex and ubiquitous real-world problems, the explorative-
exploitive subtle counterbalance character of our current state-of-
the-art search algorithms should be biased towards an increased
explorative behavior. While counterproductive in classic
problems, the main and obvious reason of using it in severe
dynamic problems is simple: while we engage ourselves in
exploiting the extrema, the extrema moves elsewhere. In order to
tackle this subtle compromise, we propose a novel algorithm for
optimization in dynamic binary landscapes, stressing the role of
negative feedback mechanisms. The Binary Ant Algorithm
(BAA) mimics some aspects of social insects’ behavior. Like Ant
Colony Optimization (ACO), BAA acts by building pheromone
maps over a graph of possible trails representing pseudo-solutions
of increasing quality to a specific optimization problem. Main
differences rely on the way this search space is represented and
provided to the colony in order to explore/exploit it, while and
more important, we enrol in providing strong evaporation to the
problem-habitat. By a process of pheromone reinforcement and
evaporation the artificial insect’s trails over the graph converge to
regions near the ideal solution of the optimization problem. Over
each generation, positive feedbacks made available by pheromone
reinforcement consolidate the best solutions found so far, while
enhanced negative feedbacks given by the evaporation
mechanism provided the system with population diversity and fast
self-adaptive characteristics, allowing BAA to be particularly
suitable for severe complex dynamic optimization problems.
Experiments made with some well known test functions
frequently used in the Evolutionary Algorithms’ research field
illustrate the efficiency of the proposed method. BAA was also
compared with other algorithms, proving to be more able to track
fast moving extrema on several test problems.
Categories and Subject Descriptors
I.2.8 [Artificial Intelligence]: Problem Solving, Control Methods
and Search – Heuristic methods.
General Terms: Algorithms, Experimentation.
Keywords: Ant algorithms, Swarm Intelligence, Stigmergy,
Dynamic Optimization.
1. INTRODUCTION
Swarm Intelligence [8,12] refers to systems where unsophisticated
distributed entities evolve by interacting locally with their
environment or search landscape. The communication between
entities via the environment causes the emergence of coherent
global patterns and the formation of a social collective
intelligence that easily lead to bio-inspired computational
paradigms and Stigmergic Optimization [8, 12]. Ant Colony
Optimization (ACO) [6], Particle Swarm Optimization (PSO) [9]
and other algorithms inspired by the behavior of bees [22] or
bacteria [16], for instance, are examples of self-adaptive multi-
agent systems based on natural organisms.
ACO algorithms have proven to be suitable for several hard
combinatorial optimization problems. Based on the ability of
natural ants to find the shortest paths to food sources, ACO
simulates the ants’ process of pheromone deposition and their
stochastic tendency to walk in the direction of sensed pheromone.
Together with a constant pheromone evaporation rate, these
stigmergic mechanisms lead to the emergence of pheromone trails
which are found to represent valuable solutions to combinatorial
problems. ACO was first applied to the Traveling Salesman
Problem and since then it has proved to be efficient in a large
range of problems, like the quadratic assignment problem [14],
vehicle routing problem [5] or scheduling [7] and timetabling
problems [21]. Other Swarm Intelligent variations using discrete
3D grid representations instead of graphs as well as different local
heuristics were also applied to Clustering, Data or Text Mining
[17] and Image Processing and Pattern Recognition [10].
Following the eusocial insect foraging natural strategy of past
works our proposal also mimics the ants’ ability to create trails by
depositing and following pheromone in the environment. Our
objective is to build an algorithm suitable for the optimization of
binary coded functions via stigmergy by pheromonal
communication. Thus, the ants evolve in a binary landscape
(graph in Fig. 1) composed of two interconnected sequences of 0s
and 1s, moving in the environment along a chosen trail, creating a
solution or path (binary string) to the problem constituted by the
0s and 1s that are found along the trail (nodes). The ants act upon
the environment by depositing (a posteriori), on the visited
connections, an amount of pheromone directly proportional to the
quality of the solution represented by this binary string. Like so,
pheromone laying in those trails that represent higher fitness

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solutions is, eventually attracting other ants in the following
iterations. The necessary negative feedback is given by an
evaporation process avoiding the system to become trapped in
local optima as well as allowing the system to be highly adaptive
when dramatic changes occur. While the signal reinforcement
works as a dynamic distributed memory, the evaporation allows
for self-organized innovation and adaptation.
At each iteration, a certain number of ants go through this process
of pheromone reinforcement and evaporation, and path-solution
creation. The pheromone maps, created by the interaction
between all the ants and the fitness landscape, evolve to a state
where ants start to be attracted to regions near the optima of the
problem. The self-adaptive and stigmergic nature of the model
suggests that BAA may be an efficient strategy to deal with the
problem of tracking extrema in dynamic landscapes.
In Dynamic Optimization Problems, the fitness function and the
constraints of the problem are not constant [4, 1, 19]. When
changes occur, the solutions already found may be no longer
valuable and the process must engage in a new search effort
(check [4] for enhanced analysis). Traditional Evolutionary
Algorithms [2], for instance, may encounter some difficulties
while solving dynamic problems, when the first convergence
stage reduces population diversity, thus decreasing its capability
to react to sudden changes. The crucial and delicate equilibrium
needed between exploration and exploitation in static
environments becomes even more important and complex when
dealing with Dynamic Optimization Problems. Swarm
Intelligence and Stigmergic Optimization major characteristics
point toward promising research paths covering the field of
optimization in dynamic environments. Previous results on
different high-demanding areas like image processing between
two altering images [10] or mobile wireless networking using SI
[20] supports this general idea. Also, specific ACO algorithms
were designed to tackle dynamic Traveling Salesman Problems
[11] and dynamic real-world industrial problems [23], amongst
other applications. This paper will show that the proposed swarm
algorithm efficiently tracks the extrema in a set of dynamic binary
test problems and outperforms the Standard Genetic Algorithm
(SGA) when facing the same task. Also, results will show that
BAA is more able than a co-evolutionary model of Genotype
Editing (ABMGE) [20] when evolving on the dynamic landscapes
of the test set.
2. ANT ALGORITHMS
Ant algorithms are one of the most successful examples of Swarm
Intelligence. They have been applied to a wide set of problems,
ranging from the Traveling Salesman Problem [8] to clustering
problems [17]. We will briefly describe the ACO meta-heuristic
which defines a particular class of ant algorithms. There are
several ACO algorithms, each one designed for a specific problem
and differing in the transition, reinforcement and evaporation
rules, amongst other properties. In general, an ACO algorithm
comprises the following steps: pheromone trail initialization,
solution construction using pheromone trails and pheromone
update (evaporation and reinforcement). A state transition rule is
essential to guide the ants through the environment until a
complete solution is built. The process of solution construction
and pheromone update continues until a termination criterion is
reached. Since the Traveling Salesman Problem was the first
problem to be attacked by these methods we will take a closer
look at the heuristics of that particular ACO algorithm.
Starting from a city (node), an ant moves from one another until
all cities have been visited. When being at a node, the ant decides
to go to an unvisited node with a certain probability that depends
on two factors: the pheromone level of the connection and local
heuristic information (the distance between the two cities). After
all the ants have completed their tour, each one deposits an
amount of pheromone on each connection that is used in its trail.
The amount of pheromone is a function of the ant’s performance
since the shorter the tour, the greater the amount of pheromone
deposited. After updating the pheromone levels, evaporation takes
place by reducing the amount of pheromone in each connection.
This simple method of indirect stigmergic communication based
on the behavior of natural ant colonies proved to be effective not
only in the Traveling Salesman Problem but also in a wide range
of applications. Since its first use on the Traveling Salesman
Problem, ACO has experienced numerous modifications in order
to improve its performance or adapt itself to other types of
problems - see [8] for a survey.

Figure 1. The Binary Ant Algorithm (BAA) environment and
search space.
3. THE BINARY ANT ALGORITHM: BAA
In this section we describe BAA’s heuristics and analyze its
components and expected global behavior. This way, we look
forward to identify the strengths and weaknesses of the model, an
effort that not only guides further research in order to improve
some of its limitations, but also allow us to determine possible
areas of application. The model starts by building the
environment where our ant-like agents will evolve. This
environment is represented in fig. 1 and consists of two connected
sequences of 0s and 1s. Starting from the root, the ant has two
possible entries to the field.

initialize pheromone field τi,j = γ
do while stop criterion NOT TRUE
for all N ants do
for each bit do
compute transition probabilities /*Eq. 1 and 2*/
decide where to go and move to the next node
end for
evaluate the solution
end for
evaporate pheromone at all edges /*Eq. 3*/
for all ants do
if fitness is above average reinforce trail /*Eq. 4*/
end for
end do
Figure 2. Pseudo-code of the Binary Ant Algorithm (BAA).
After that point, each 0 or 1 has two connections, each leading
again to a 0 or a 1. These trails are unidirectional, since a solution
0 0 0
1 1 1
0
1
0
1
Solution Dimension
ROOT
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