COMPUTATIONAL INTELLIGENCE
Robin Wikström, IAMSR/Åbo Akademi University
Liebowitz [appropriate references can be found in the state-of-the-art documents] wrote in a
famous editorial “If you are a dog lover, build expert systems; if you are a cat lover, build
neural networks”. Expert systems require a lot of human input, so the user should be knowledgeable and fond of interacting with the system. Cats are more independent than dogs and
seldom in need of any attention. Systems built around neural networks basically handle themselves and need very little human input. Many would probably argue that even though dogs
require more care and interaction, they also produce more value.
There are quite a few definitions of Computational Intelligences:
A system is computational intelligent when it: deals with only numerical (low-level) data, has
pattern recognition components, does not use knowledge in the artificial intelligence sense;
and additionally when it (begins to) exhibit (i) computational adaptivity, (ii) computational
fault tolerance, (iii) speed approaching human-like turnaround, and (iv) error rates that approximate human performance. [Bezdek]
Computational intelligence is defined as a methodology involving computing (whether with a
computer, wetware, etc.) that exhibits an ability to learn and/or deal with new situations such
that the system is perceived to possess one or more attributes of reason, such as generalisation, discovery, association, and abstraction.[Eberhart]
Computational intelligence is a branch of science studying problems for which there are no
effective computational algorithms.[Duch]
In the following a brief summary of some newer, not commonly known CI methods [for a full
account of CI methods, cf. the state-of-the-art reports]
Swarm Intelligence
Swarm intelligence is a collection of CI techniques based upon the collective behaviour in
decentralized, self-organized systems. The expression was coined by Beni andWang in the
late 1980`s]. They studied cellular robotic systems, where self-organization trough interactions with the closest neighbour are common. The overall interest for Swarm Intelligence has
increased dramatically since the beginning of the century, when studies of Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) became popular.
The general idea behind Swarm Intelligence is that a population of agents interact locally with
each other and with the environment. This leads to a behaviour which exceeds the capability
of a single agent; they are capable of performing tasks together in a collective that would be
impossible to perform by them individually. The interesting factor is that these tasks are undertaken automatically - the agents in a population instinctively react and perform the tasks,
by reacting to the agents that are close to them. A flock of birds moving is a good example on
how single agents (a bird) react to the closest agents (other birds) and perform a collective
movement (moving together in formation).
Ant Colony Optimization
Ant Colony Optimization (ACO) is inspired by the behaviour of ants. The ants use pheromone
to signal to the others ants which roads are favourable and should attract more ants. As more
ants start following the initial ant, it means that the amount of positive pheromone will increase, which in turn attracts even more ants to that path. Researchers studying ants in real
life, notice that this method is very effective when the ants determine the best path to use
when collecting food. If they have to choose from two different roads, they quickly rule out
the longer one. However, if the roads are equally good, the random fluctuation will, in time,
tip the amount of pheromone over to one side, with the result that more ants will be attracted
to that path, which in turn attracts even more ants, continuing until the other paths is empty.
The same principle is applied for algorithms; the possible solutions are assigned with amounts
of “pheromone”, these values are changed as the solutions are evaluated, the ones who seem
promising are given more attention. As the iterations are performed, the possible solutions
will be narrowed down to a few.
ACO has been applied for a number of different applications; most of the problems have been
NP-hard. This has attracted a lot of attention from the business sector, specifically from telecommunication network companies. ACO are useful for solving routing problems, where the
factors influencing the routing changes all the time (price and parts) but the general goal still
remains the same; to minimize the cost and increase productivity. A concrete example is
AntNet, which outperforms other routing algorithms available today.
ACO has been successfully applied to find the most beneficial routes for the delivery trucks to
take, for industrial scheduling problems and for assembly line problems; Parpinelli et al have
tested ACO algorithms for data mining problems. ACO is promising as researchers continue
to apply the optimisation algorithms on NP-hard problems and to constantly figure out how
ACO can best be used.
Bee Colony Optimization
Lucic and Teodorovic developed Bee Colony Optimization (BCO) which is based on the behaviour of bees in nature; BCO creates multi-agent systems, similar to the colonies of bees
that exist in nature.
Bees are highly organized when they are collecting and processing nectar. Similar to the ants,
the individual bees learn from other bees where to find good sources of nectar. The bees do
not follow pheromones but they use a “dance stage” to communicate. When a bee has found a
source of nectar it goes to the dance stage and tries to attract the attention of other bees; if the
dance is successful, new bees will join the original bee and collect nectar from that particular
source; all new bees joining the original bee will go at least one trip to the source and collect
some nectar; as the bee returns to the hive, it has three choices to decide between: (i) abandon
the food source and join another “dancing bee”; (ii) continue collecting nectar from that
source, without encouraging other bees to join; (iii) go via the “dance floor” before returning
to the source, thus recruiting more collectors to that particular source.
Even though it is not understood how the bees decide between the different dancing bees, it is
assumed to be based on the quality of the food source - the bees’ dance differs based on the
quality of the food; a better food source would attract more bees.
The BCO is a population-based algorithm - artificial bees are used to generate the optimal
solution. Every generated individual will create a solution for the problem that should be
solved; the solutions will then be eliminated one by one, until the best solution remains. The
algorithm is based on two alternating phases: forward pass and backward pass. The forward
pass is for exploration and testing of new solutions and the backward pass is for information
sharing. After each forward pass, the artificial bees present their solutions after which they
decide if they should abandon that solution or if they should try to recruit more followers.
These passes are repeated until some predefined stopping conditions are met.
BCO has enjoyed a lot of success, which actually seems to be quite normal for Swarm Intelligence techniques, and a number of success stories have been reported
Chaos Theory
Chaos Theory is actually a combination of several research areas: physics, engineering, economics, biology and philosophy. However, the unpredictability of chaos is the central theme
for all the areas. Chaos Theory states that chaotic systems are unpredictable, at least when
compared to deterministic systems. Chaos theory allows the study of nonlinear phenomena in
a determinist manner, focusing on strange relations among several types of variables and
providing mathematical models to analyse changing behaviour. Chaos theory is especially
interesting for organisations and businesses as the theory has been successfully applied to
organizational problems and it has been found that many financial indicators are of a chaotic
nature.
The butterfly result from the Lorenz attractor
One of the interesting topics of the Chaos Theory is the butterfly effect. It was coined by Edward Lorenz and deals with the sensitive dependence on initial conditions, meaning that even
a small change somewhere in a nonlinear system could cause a huge effect elsewhere in the
system; the result of the butterfly effect in a Lorenz attractor is shown in the above figure that
resembles a butterfly.
Firefly Algorithm
The Firefly Algorithm [FA] is one of several new optimization models that emerged over the
past years. Originally proposed by Yang in 2009] it has since then been applied in several
applications; the FA has superior performance compared to the older techniques.
The FA is based on the behaviour of fireflies flying around using flashing patterns to communicate to each other. Yang did not mimic their behaviour in full detail, but created a simplified algorithm based on the following rules: (i) all fireflies are unisex so that one firefly will
be attracted to other fireflies regardless of their sex; (ii) attractiveness is proportional to firefly
brightness; for any couple of flashing fireflies, the less bright one will move towards the
brighter one; attractiveness is proportional to the brightness which decreases with increasing
distance between fireflies; if there are no brighter fireflies than a particular firefly, this individual will move randomly in the space; (iii) the brightness of a firefly is somehow related to
the analytical form of a cost function; for a maximization problem, brightness can be proportional to the value of the cost function; other forms of brightness can be defined in a similar
way to the fitness function in genetic algorithms.
The FA has been modified and rearranged quite a lot. This is because of the original algorithm
was simple which made it possible to add features and adapt the algorithm to specific problems. The following list presents some of the more interesting modifications available:
* The Discrete Firefly Algorithm (DFA) is adapted for solving NP-hard problems; Sayadi
et.al found that DFA outperforms existing algorithms, such as ACO. DFA has also been successfully applied for QAPs by Durkota.
* Apostolopoulos and Vlachos found that FA could be used for multi-objective load and dispatch problems.
* The Lagrangian FA (LFA) has been used in power system optimization. The LFAcan be
used to minimize the cost of power supply and to calculate how the power should be divided
to maximise the return for the company.
* The CFA (Chaotic Firefly Algorithm) was proposed by Santos Coelho et.al. for reliabilityredundancy optimization problems and multi-objective optimisation. The problem is a mixedinteger programming problem and it was proved that both the original Firefly Algorithm and
the Chaotic version show superior results compared to other algorithms.
* The building of Hybrid Algorithms is probably one of the presently most interesting research areas. It studies the possibility to combine different algorithms for solving NP-hard
problems. A hybrid scheme combining ACO and FA was proposed by Giannakouris et.al.
who stated that they can prove that this hybrid algorithm can produce better results than traditional techniques and that by combining two algorithms their combined result is better than
their individual results.