Stigmergic Optimization in Dynamic Binary Landscapes
Carlos Fernandesi
LaSEEB, Technical Univ. of Lisbon
Av. Rovisco Pais, 1, TN 6.21, 1049-001,
Lisbon, PORTUGAL
cfernandes@laseeb.org
Vitorino Ramos
LaSEEB, Technical Univ. of Lisbon
Av. Rovisco Pais, 1, TN 6.21, 1049-001,
Lisbon, PORTUGAL
vitorino.ramos@alfa.ist.utl.pt
Agostinho C. Rosa
LaSEEB, Technical Univ. of Lisbon
Av. Rovisco Pais, 1, TN 6.21, 1049-001,
Lisbon, PORTUGAL
acrosa@laseeb.org


ABSTRACT
Hereafter we introduce a novel algorithm for optimization in
dynamic binary landscapes. The Binary Ant Algorithm (BAA)
mimics some aspects of real social insects’ behavior. Like Ant
Colony Optimization (ACO), BAA acts by building pheromone
maps over a grid of possible trails that represent solutions to an
optimization problem. Main differences rely on the way this
search space is represented and provided to the colony in order to
explore/exploit it. Then, by a process of pheromone reinforcement
and evaporation the artificial insect trails converge to regions near
the problem solution or extrema. The negative feedback granted
by the evaporation mechanism provides the self-organized system
with population diversity and self-adaptive characteristics,
allowing BAA to be particularly suitable for hard Dynamic
Optimization Problems (DOP), where extrema continuously
changes at severe speeds.
Categories and Subject Descriptors: I.2.8 [Artificial
Intelligence]: Problem Solving, Control Methods and Search –
Heuristic methods.
General Terms: Algorithms, Experimentation.
Keywords: Ant algorithms, Stigmergy, Dynamic Optimization.
1. INTRODUCTION
Ant algorithms [2] are one of the most successful examples of
Swarm Intelligence and Stigmergic Optimization [1]. They have
been applied to a wide set of problems, ranging from TSP to
clustering – see [2] for a survey. ACO meta-heuristic [2] defines a
particular class of ant algorithms. 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. 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). These stigmergic
mechanisms lead to the emergence of pheromone trails which are
found to represent valuable solutions to combinatorial problems.
Following the eusocial insect foraging natural strategy of past
works [3,1], and the implicit adaptive ability of Self-Regulated
Swarms and Bacterial Foraging Optimization Algorithms [5] our
proposal also mimics ants ability to create trails by depositing and


Figure 1. The BAA environment and search space.
following pheromone in the environment. Our objective is to
build an algorithm suitable for the optimization of binary coded
functions via stigmergy [2,1] by pheromonal communication.
Having that aim in mind, our ant-like agents evolve in a binary
landscape (graph in fig. 1) composed of two interconnected
sequences of 0s and 1s, moving around the environment along a
chosen trail, creating a solution or path (binary string) to the
problem constituted by those bits found along the trail (nodes).
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. Thus, pheromone laying at those higher fitness trails
(best-so-far solutions) are reinforced, yielding the probability of
attracting other agents in the following iterations to exploit them
(snow-ball effect or positive feedback). The necessary counter-
balanced negative feedback is given by evaporation, avoiding the
system to become trapped in local optima as well as allowing it to
be highly adaptive when dramatic changes occur.
2. THE BINARY ANT ALGORITHM - BAA
This environment where ants evolve 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. 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 pseudo-solution to
the problem at hands at a given time should be represented by a
finite binary string visiting those Boolean values at this precise
left-to-right order. Any ant enters the field (left side) and stops on
the other edge, creating a binary string along the way, as it passes
trough the nodes. The search process is described in fig. 2. The
pheromone (deposited at the connections between the nodes) is
initialize pheromone field
i,j = 
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 for the Binary Ant Algorithm (BAA).
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SAC’07, March 11-15, 2007, Seoul, Korea.
Copyright 2007 ACM 1-59593-480-4/07/0003…$5.00.


 

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