BIO INSPIRED COMPUTING

Transcription

1 BIO INSPIRED COMPUTING SEMINAR REPORT Submitted by ULLAS MOHAN In partial fulfillment of the award of the degree Of BACHELOR OF TECHNOLOGY In COMPUTER SCIENCE AND ENGINEERING SCHOOL OF ENGINEERING COCHIN UNIVERSITY OF SCIENCE & TECHNOLOGY COCHIN JULY 2008

2 DIVISION OF COMPUTER ENGINEERING SCHOOL OF ENGINEERING COCHIN UNIVERSITY OF SCIENCE & TECHNOLOGY, COCHIN Certificate Certified that this is a bonafide record of the Seminar Entitled BIO-INSPIRED COMPUTING Done by the following Student Ullas Mohan Of the VIIth semester,computer Science and Engineering in the year 2008 in partial fulfillment of the requirements to the award of Degree Of Bachelor Of Technology in Computer Science and Engineering of Cochin University of Science and Technology Mr Pramod Pavithran Dr David Peter.S Seminar Guide Head of Division Date

3 ACKNOWLEDGEMENT At the outset, I thank the Lord Almighty for the grace, strength and hope to make my endeavor a success. I also express my gratitude to Dr. David Peter S, Head of the Division and my Seminar Guide for providing me with adequate facilities, ways and means by which I was able to complete this seminar. I express my sincere gratitude to him for his constant support and valuable suggestions without which the successful completion of this seminar would not have been possible. I thank Mr. Pramod Pavithran, my seminar guide for his boundless cooperation and helps extended for this seminar. I express my immense pleasure and thankfulness to all the teachers and staff of the Division of Computer Engineering, CUSAT for their cooperation and support. Last but not the least, I thank all others, and especially my classmates and my family members who in one way or another helped me in the successful completion of this work ULLAS MOHAN

4 ABSTRACT Biologically inspired (often hyphenated as biologically-inspired) computing (also bio-inspired computing) is a field of study that loosely knits together subfields related to the topics of connectionism, social behaviour and emergence. It is often closely related to the field of artificial intelligence, as many of its pursuits can be linked to machine learning. It relies heavily on the fields of biology, computer science and mathematics. Briefly put, it is the use of computers to model nature, and simultaneously the study of nature to improve the usage of computers. Biologically inspired computing is a major subset of natural computation. Some areas of study encompassed under the canon of biologically inspired computing, and their biological counterparts: genetic algorithms evolution emergent systems ants, termites, bees, wasps artificial immune systems immune system The way in which bio-inspired computing differs from traditional artificial intelligence (AI) is in how it takes a more evolutionary approach to learning, as opposed to the what could be described as 'creationist' methods used in traditional AI. In traditional AI, intelligence is often programmed from above: the programmer is the creator, and makes something and imbues it with its intelligence. Bio-inspired computing, on the other hand, takes a more bottom-up, decentralised approach; bio-inspired techniques often involve the method of specifying a set of simple rules, a set of simple organisms which adhere to those rules, and a method of iteratively applying

5 those rules. After several generations of rule application it is usually the case that some forms of complex behaviour arise. Complexity gets built upon complexity until the end result is something markedly complex, and quite often completely counterintuitive from what the original rules would be expected to produce.

6 TABLE OF CONTENTS CHAPTER NO TITLE PAGE NO: LIST OF FIGURES iii 1. INTRODUCTION 1 2. EVOLUTION ALGORITHMS Components of Algorithm Representation Evaluation Function Population Parent Selection Mechanism Mutation Recombination Replacement Initialization Termination SWARM INTELLIGENCE Introduction Techniques Ant Colony Optimization Particle Swarm Optimization Stochastic Diffusion Search Applications Ant Colony Optimization Particle Swarm Optimization 19

7 4. ARTIFICIAL IMMUNE SYSTEM Immune Algorithms CONCLUSION REFERENCES 29

8 LIST OF FIGURES NO: NAME PAGE 1. Examples Of Swarm Intelligence Example for ant colony optimization Particle Swarm Optimization 22 -iii-

9 1.INTRODUCTION Biologically inspired computing (also bio-inspired computing) is a field of study that loosely knits together subfields related to the topics of connectionism, social behavior and emergence. It is often closely related to the field of artificial intelligence, as many of its pursuits can be linked to machine learning. It relies heavily on the fields of biology, computer science and mathematics. Biologically inspired computing is a major subset of natural computation. The field of biocomputation has a twofold definition: the use of biology or biological processes as metaphor, inspiration, or enabler in developing new computing technologies and new areas of computer science; and conversely, the use of information science concepts and tools to explore biology from a different theoretical perspective. In addition to its potential applications, such as DNA computation, nanofabrication, storage devices, sensing, and health care, biocomputation also has implications for basic scientific research. It can provide biologists, for example, with an IT-oriented paradigm for looking at how cells compute or process information, or help computer scientists construct algorithms based on natural systems, such as evolutionary and genetic algorithms. Biocomputing has the potential to be a very powerful tool. Division Of computer science, SOE, CUSAT 1

10 2. EVOLUTION ALGORITHMS As the history of the field suggests there are many different variants of Evolutionary Algorithms. The common underlying idea behind all these techniques is the same given a population of individuals the environmental pressure causes natural selection (survival of the fittest) and this causes a rise in the fitness of the population. Given a quality function to be maximised we can randomly create a set of candidate solutions, i.e., elements of the function s domain, and apply the quality function as an abstract fitness measure the higher the better. Based on this fitness, some of the better candidates are chosen to seed the next generation by applying recombination and/or mutation to them. Recombination is an operator applied to two or more selected candidates (the so-called parents) and results one or more new candidates (the children).mutation is applied to one candidate and results in one new candidate. Executing recombination and mutation leads to a set of new candidates (the offspring) that compete based on their fitness (and possibly age) with the old ones for a place in the next generation. This process can be iterated until a candidate with sufficient quality (a solution) is found or a previously set computational limit is reached. In artificial intelligence, an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses some mechanisms inspired by biological evolution: reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the cost function determines the environment within which the solutions "live". Evolution of the population then takes place after the repeated application of the above operators. Artificial evolution (AE) describes a process involving individual evolutionary algorithms; EAs are individual components that participate in an AE. Evolutionary algorithms consistently perform well approximating solutions to all types of problems because they do not make any assumption about the underlying fitness landscape. Division Of computer science, SOE, CUSAT 2

11 Apart from their use as mathematical optimizers, evolutionary computation and algorithms have also been used as an experimental framework within which to validate theories about biological evolution and natural selection, particularly through work in the field of artificial life. Techniques from evolutionary algorithms applied to the modelling of biological evolution are generally limited to explorations of microevolutionary processes, however some computer simulations, such as Tierra and Avida, attempt to model macroevolutionary dynamics. A limitation of evolutionary algorithms is their lack of a clear genotype-phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature phenotype. This indirect encoding is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the evolvability of the organism. Genetic algorithm - This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved - these are not normally binary), virtually always applying recombination operators in addition to selection and mutation. This type of EA is often used in optimization problems. Genetic programming - Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem. Evolutionary programming - Like genetic programming, only the structure of the program is fixed and its numerical parameters are allowed to evolve; Evolution strategy - Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates; Basically,there are two fundamental forces that form the basis of evolutionary systems: Variation operators (recombination and mutation) create the necessary diversity and thereby facilitate novelty, while selection acts as a force pushing quality. Division Of computer science, SOE, CUSAT 3

12 The combined application of variation and selection generally leads to improving fitness values in consecutive populations. It is easy (although somewhat misleading) to see such a process as if the evolution is optimising, or atleast approximising, by approaching optimal values closer and closer over its course. Alternatively, evolution it is often seen as a process of adaptation. From this perspective, the fitness is not seen as an objective function to be optimised, but as an expression of environmental requirements. Matching these requirements more closely implies an increased viability, reflected in a higher number of offspring. The evolutionary process makes the population adapt to the environment better and better. Many components of such an evolutionary process are stochastic. During selection fitter individuals have a higher chance to be selected than less fit ones, but typically even the weak individuals have a chance to become a parent or to survive.for recombination of individuals the choice of which pieces will be recombined is random. Similarly for mutation, the pieces that will be mutated within a candidate solution, and the new pieces replacing them, are chosen randomly. The general scheme of an Evolutionary Algorithm can is given in a pseudo-code fashion; BEGIN INITIALISE population with random candidate solutions; EVALUATE each candidate; REPEAT UNTIL ( TERMINATION CONDITION is satisfied ) DO 1 SELECT parents; 2 RECOMBINE pairs of parents; 3 MUTATE the resulting offspring; 4 EVALUATE new candidates; 5 SELECT individuals for the next generation; END The representation of a candidate solution is often used to characterise different streams. Typically, the candidates are represented by (i.e., the data structure encoding a solution has the form of) strings over a finite alphabet in Genetic Algorithms (GA), real- Division Of computer science, SOE, CUSAT 4

13 valued vectors in Evolution Strategies (ES), finite state machines in classical Evolutionary Programming (EP) and trees in Genetic Programming (GP). Technically, a given representation might be preferable over others if it matches the given problem better, that is, it makes the encoding of candidate solutions easier or more natural. For instance, for solving a satisfiability problem the straightforward choice is to use bit-strings of length n, where n is the number of logical variables, hence the appropriate EA would be a Genetic Algorithm. For evolving a computer program that can play checkers trees are well-suited (namely, the parse trees of the syntactic expressions forming the programs), thus a GP approach is likely. It is important to note that the recombination and mutation operators working on candidates must match the given representation. Thus for instance in GP the recombination operator works on trees, while in GAs it operates on strings. As opposed to variation operators,selection takes only the fitness information into account, hence it works independently from the actual representation. Differences in the commonly applied selection mechanisms in each stream are therefore rather a tradition than a technical necessity. 2.1 COMPONENTS OF ALGORITHM EAs have a number of components, procedures or operators that must be specified in order to define a particular EA. The most important components are: representation (definition of individuals) evaluation function (or fitness function) population parent selection mechanism variation operators, recombination and mutation survivor selection mechanism (replacement) Each of these components must be specified in order to define a particular EA. Furthermore, to obtain a running algorithm the initialisation procedure and a termination condition must be also defined. Division Of computer science, SOE, CUSAT 5

14 2.1.1 Representation (Definition of Individuals) The first step in defining an EA is to link the real world to the EA world, that is to set up a bridge between the original problem context and the problem solving space where evolution will take place. Objects forming possible solutions within the original problem context are referred to as phenotypes, their encoding, the individuals within the EA, are called genotypes. The first design step is commonly called representation, as it amounts to specifying a mapping from the phenotypes onto a set of genotypes that are said to represent these phenotypes. For instance, given an optimisation problem on integers, the given set of integers would form the set of phenotypes. Then one could decide to represent them by their binary code, hence 18 would be seen as a phenotype and as a genotype representing it. It is important to understand that the phenotype space can be very different from the genotype space, and that the whole evolutionary search takes place in the genotype space. A solution a good phenotype is obtained by decoding the best genotype after termination. To this end, it should hold that the (optimal) solution to the problem at hand a phenotype is represented in the given genotype space. The common EC terminology uses many synonyms for naming the elements of these two spaces. On the side of the original problem context, candidate solution, phenotype, and individual are used to denote points of the space of possible solutions. This space itself is commonly called the phenotype space. On the side of the EA, genotype, chromosome, and again individual can be used for points in the space where the evolutionary search will actually take place. This space is often termed the genotype space. Also for the elements of individuals there are many synonymous terms. A place-holder is commonly called a variable, a locus (plural: loci), a position, or in a biology oriented terminology a gene. An object on such a place can be called a value or an allele. It should be noted that the word representation is used in two slightly different ways. Sometimes it stands for the mapping from the phenotype to the genotype space. In this sense it is synonymous with encoding, e.g., one could mention binary Division Of computer science, SOE, CUSAT 6

15 representation or binary encoding of candidate solutions. The inverse mapping from genotypes to phenotypes is usually called decoding and it is required that the representation be invertible: to each genotype there has to be at most one corresponding phenotype. The word representation can also be used in a slightly different sense, where the emphasis is not on the mapping itself, but on the data structure of the genotype space. This interpretation is behind speaking about mutation operators for binary representation, for instance Evaluation Function (Fitness Function) The role of the evaluation function is to represent the requirements to adapt to. It forms the basis for selection, and thereby it facilitates improvements. More accurately, it defines what improvement means. From the problem solving perspective, it represents the task to solve in the evolutionary context. Technically, it is a function or procedure that assigns a quality measure to genotypes. Typically, this function is composed from a quality measure in the phenotype space and the inverse representation. To remain with the above example, if we were to maximise x2 on integers, the fitness of the genotype could be defined as the square of its corresponding phenotype: 182 = 324.The evaluation function is commonly called the fitness function in EC.This might cause a counterintuitive terminology if the original problem requires minimisation for fitness is usually associated with maximisation. Mathematically, however, it is trivial to change minimisation into maximisation and vice versa. Quite often, the original problem to be solved by an EA is an optimization problem In this case the name objective function is often used in the original problem context and the evaluation (fitness) function can be identical to, or a simple transformation of, the given objective function. Division Of computer science, SOE, CUSAT 7

16 2.1.3 Population The role of the population is to hold (the representation of) possible solutions. A population is a multiset1 of genotypes. The population forms the unit of evolution. Individuals are static objects not changing or adapting, it is the population that does. Given a representation, defining a population can be as simple as specifying how many individuals are in it, that is, setting the population size. In some sophisticated EAs a population has an additional spatial structure, with a distance measure or a neighbourhood relation. In such cases the additional structure has to be defined as well to fully specify a population. As opposed to variation operators that act on the one or two parent individuals, the selection operators (parent selection and survivor selection) work at population level. In general, they take the whole current population into account and choices are always made relative to what we have. For instance, the best individual of the given population is chosen to seed the next generation, or the worst individual of the given population is chosen to be replaced by a new one. In almost all EA applications the population size is constant, not changing during the evolutionary search. The diversity of a population is a measure of the number of different solutions present. No single measure for diversity exists, typically people might refer to the number of different fitness values present, the number of different phenotypes present, or the number of different genotypes. Other statistical measures, such as entropy, are also used. Note that only one fitness value does not necessarily imply only one phenotype is present, and in turn only one phenotype does not necessarily imply only one genotype. The reverse is however not true: one genotype implies only one phenotype and fitness value Parent Selection Mechanism The role of parent selection or mating selection is to distinguish among individuals based on their quality, in particular, to allow the better individuals to become parents of the next generation. An individual is a parent if it has been selected to undergo variation in order Division Of computer science, SOE, CUSAT 8

17 to create offspring. Together with the survivor selection mechanism, parent selection is responsible for pushing quality improvements. In EC, parent selection is typically probabilistic. Thus, high quality individuals get a higher chance to become parents than those with low quality. Nevertheless, low quality individuals are often given a small, but positive chance, otherwise the whole search could become too greedy and get stuck in a local optimum.the role of variation operators is to create new individuals from old ones. In the corresponding phenotype space this amounts to generating new candidate solutions. From the generate-and-test search perspective, variation operators perform the generate step. Variation operators in EC are divided into two types based on their activity Mutation A unary3 variation operator is commonly called mutation. It is applied to one genotype and delivers a (slightly) modified mutant, the child or offspring of it. A mutation operator is always stochastic: its output the child depends on the outcomes of a series of random choices. It should be noted that an arbitrary unary operator is not necessarily seen as mutation. A problem specific heuristic operator acting on one individual could be termed as mutation for being unary. However, in general mutation is supposed to cause a random, unbiased change. For this reason it might be more appropriate not to call heuristic unary operators mutation. The role of mutation in EC is different in various ECdialects, for instance in Genetic Programming it is often not used at all, in Genetic Algorithms it has traditionally been seen as a background operator to fill the gene pool with fresh blood, while in Evolutionary Pro- gramming it is the one and only variation operator doing the whole search work. It is worth noting that variation operators form the evolutionary implementation of the elementary steps within the search space. Generating a child amounts to stepping to a new point in this space. From this perspective, mutation has a theoretical role too: it can guarantee that the space is connected. This is important since theorems stating that an EA will (given sufficient time) discover the global optimum of a given problem often rely on Division Of computer science, SOE, CUSAT 9

18 the property that each genotype representing a possible solution can be reached by the variation operators. The simplest way to satisfy this condition is to allow the mutation operator to jump everywhere, for example, by allowing that any allele can be mutated into any other allele with a non-zero probability. However it should also be noted that many researchers feel these proofs The arity of an operator is the number of objects that it takes as inputs An operator is unary if it applies to one object as input. Usually these will consist of using a pseudo-random number generator to generate a series of values from some given probability distribution. We will refer to these as random drawings have limited practical importance, and many implementations of EAs do not in fact possess this property Recombination A binary variation operator5 is called recombination or crossover. As the names indicate such an operator merges information from two parent genotypes into one or two offspring genotypes. Similarly to mutation, recombination is a stochastic operator: the choice of what parts of each parent are combined, and the way these parts are combined, depend on random drawings. Again, the role of recombination is different in EC dialects: in Genetic Programming it is often the only variation operator, in Genetic Algorithms it is seen as the main search operator, and in Evolutionary Programming it is never used. Recombination operators with a higher arity (using more than two parents) are mathematically possible and easy to implement, but have no biological equivalent. Perhaps this is why they are not commonly used, although several studies indicate that they have positive effects on the evolution. The principal behind recombination is simple that by mating two individuals with different but desirable features, we can produce an offspring which combines both of those features. This principal has a strong supporting case it is one which has been successfully applied for millennia by breeders ofplants and livestock, to produce species which give Division Of computer science, SOE, CUSAT 10

19 higher yields or have other desirable features. Evolutionary Algorithms create a number of offspring by random recombination, accept that some will have undesirable combinations of traits, most may be no better or worse than their parents, and hope that some have improved characteristics. Although the biology of the planet earth, (where with a very few exceptions lower organisms reproduce asexually, and higher organisms reproduce sexually suggests that recombination is the superior form of reproduction, recombination operators in EAsare usually applied probabilistically, that is, with an existing chance of notbeing performed.it is important to note that variation operators are representation dependent. That is, for different representations different variation operators have to defined. For example, if genotypes are bit-strings, then inverting a 0 to a 1 (1 to a 0) can be used as a mutation operator. However, if we represent possible solutions by tree-like structures another mutation operator is required Survivor Selection Mechanism (Replacement) The role of survivor selection or environmental selection is to distinguish among individuals based on their quality. In that it is similar to parent selection, but it is used in a different stage of the evolutionary cycle. The survivor selection mechanism is called after having having created the offspring of the selected parents. In EC the population size is (almost always) constant, thus a choice has to to be made on which individuals will be allowed in the next generation. This decision is usually based on their fitness values, favouring those with higher quality, although the concept of age is also frequently used. As opposed to parent selection which is typically stochastic, survivor selection is often deterministic, for instance ranking the unified multiset of parents and offspring and selecting the top segment (fitness biased), or selecting only from the offspring (agebiased). Survivor selection is also often called replacement or replacement strategy. In many cases the two terms can be used interchangeably. The choice between the two is thus often arbitrary. A good reason to use the name survivor selection is to keep terminology consistent. A preference for using replacement can be motivated by the skewed proportion of the number of individuals in the population and the number of Division Of computer science, SOE, CUSAT 11

20 newly created children. In particular, if the number of children is very small with respect to the population size, e.g., 2 children and a population of 100. In this case, the survivor selection step is as simple as to chose the two old individuals that are to be deleted to make place for the new ones. In other words, it is more efficient to declare that everybody survives unless deleted, and to choose whom to replace. If the proportion is not skewed like this, e.g., 500 children made from a population of 100, then this is not an option, so using the term survivor selection is appropriate Initialisation Initialisation is kept simple in most EA applications: The first population is seeded by randomly generated individuals. In principle, problem specific heuristics can be used in this step aiming at an initial population with higher fitness. Whether this is worth the extra computational effort or lot is very much depending on the application at hand. There are, however, some general observations concerning this issue based on the socalled anytime behaviour of EAs Termination Condition As for a suitable termination condition we can distinguish two cases. If the problem has a known optimal fitness level, probably coming from a known optimum of the given objective function, then reaching this level (perhaps only with a given precision > 0) should be used as stopping condition. However, EAs are stochastic and mostly there are no guarantees to reach an optimum, hence this condition might never get satisfied and the algorithm may never stop. This requires that this condition is extended with one that certainly stops the algorithm. Commonly used options for this purpose are the following: 1. the maximally allowed CPU time elapses; 2. the total number of fitness evaluations reaches a given limit; 3. for a given period of time (i.e, for a number of generations or fitness evaluations), the fitness improvement remains under a threshold value; 4. the population diversity drops under a given threshold. Division Of computer science, SOE, CUSAT 12

21 The actual termination criterion in such cases is a disjunction: optimum value hit or condition x satisfied. If the problem does not have a known optimum, then we need no disjunction, simply a condition from the above list or a similar one that is guaranteed to stop the algorithm Division Of computer science, SOE, CUSAT 13

22 3.SWARM INTELLIGENCE 3.1 INTRODUCTION Swarm intelligence (SI) is artificial intelligence based on the collective behavior of decentralized, self-organized systems. The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems. SI systems are typically made up of a population of simple agents interacting locally with one another and with their environment. The agents follow very simple rules, and although there is no centralized control structure dictating how individual agents should behave, local interactions between such agents lead to the emergence of complex global behavior. Natural examples of SI include ant colonies, bird flocking, animal herding, bacterial growth, and fish schooling. The application of swarm principles to robots is called swarm robotics, while 'swarm intelligence' refers to the more general set of algorithms. Figure 3.1 Examples of Swarm Intelligence Swarm intelligence is the emergent collective intelligence of groups of simple autonomous agents. Here, an autonomous agent is a subsystem that interacts with its environment, which probably consists of other agents, but acts relatively independently from all other agents. The autonomous agent does not follow commands from a leader, or Division Of computer science, SOE, CUSAT 14

23 some global plan. For example, for a bird to participate in a flock, it only adjusts its movements to coordinate with the movements of its fock mates, typically its neighbors that are close to it in the fock. A bird in a flock simply tries to stay close to its neighbors, but avoid collisions with them. Each bird does not take commands from any leader bird since there is no lead bird. Any bird can be in the front, center and back of the swarm. Swarm behavior helps birds take advantage of several things including protection from predators (especially for birds in the middle of the flock), and searching for food (essentially each bird is exploiting the eyes of every other bird). 3.2 TECHNIQUES Some of the techniques in swarm intelligence are illustrated below: ANT COLONY OPTIMIZATION Ant colony optimization is a class of optimization algorithms modeled on the actions of an ant colony. Artificial 'ants' - simulation agents - locate optimal solutions by moving through a parameter space representing all possible solutions. Real ants lay down pheromones directing each other to resources while exploring their environment. The simulated 'ants' similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions. One variation on this approach is the bees algorithm, which is more analogous to the foraging patterns of the honey bee PARTICLE SWARM OPTIMIZATION Particle swarm optimization or PSO is a global optimization algorithm for dealing with problems in which a best solution can be represented as a point or surface in an n- dimensional space. Hypotheses are plotted in this space and seeded with an initial velocity, as well as a communication channel between the particles [3][4]. Particles then move through the solution space, and are evaluated according to some fitness criterion after each timestep. Over time, particles are accelerated towards those particles within their communication grouping which have better fitness values. The main advantage of Division Of computer science, SOE, CUSAT 15

24 such an approach over other global minimization strategies such as simulated annealing is that the large number of members that make up the particle swarm make the technique impressively resilient to the problem of local minima STOCHASTIC DIFFUSION SEARCH Stochastic Diffusion Search or SDS is an agent based on probabilistic global search and optimization technique best suited to problems where the objective function can be decomposed into multiple independent partial-functions. Each agent maintains a hypothesis which is iteratively tested by evaluating a randomly selected partial objective function parameterised by the agent's current hypothesis. In the standard version of SDS such partial function evaluations are binary resulting in each agent becoming active or inactive. Information on hypotheses is diffused across the population via inter-agent communication. Unlike the stigmergic communication used in ACO, in SDS agents communicate hypotheses via a one-to-one communication strategy analogous to the tandem running procedure observed in some species of ant. A positive feedback mechanism ensures that, over time, a population of agents stabilise around the global-best solution. SDS is both an efficient and robust search and optimisation algorithm, which has been extensively mathematically described. 3.3 APPLICATIONS Swarm Intelligence-based techniques can be used in a number of applications. The U.S. military is investigating swarm techniques for controlling unmanned vehicles. The European Space Agency is thinking about an orbital swarm for self assembly and interferometry. NASA is investigating the use of swarm technology for planetary mapping. A 1992 paper by M. Anthony Lewis and George A. Bekey [5] discusses the possibility of using swarm intelligence to control nanobots within the body for the purpose of killing cancer tumors. Artists are using swarm technology as a means of creating complex interactive systems or simulating crowds. Tim Burton's Batman Returns was the first movie to make use of swarm technology for rendering, realistically depicting the movements of a group of penguins using the Boids system. The Lord of the Division Of computer science, SOE, CUSAT 16

25 Rings film trilogy made use of similar technology, known as Massive, during battle scenes. Swarm technology is particularly attractive because it is cheap, robust, and simple. The inherent intelligence of swarms has inspired many social and political philosophers, in that the collective movements of an aggregate often derive from independent decision making on the part of a single individual. A common example is how the unaided decision of a person in a crowd to start clapping will often encourage others to follow suit, culminating in widespread applause. Such knowledge, an individualist advocate might argue, should encourage individual decision making (however mundane) as an effective tool in bringing about widespread social change. The use of Swarm Intelligence in Telecommunication Networks has also been researched, in the form of Ant Based Routing. This was pioneered separately by Dorigo et al and Hewlett Packard in the mid-1990s, with a number of variations since. Basically this uses a probabilistic routing table rewarding/reinforcing the route successfully traversed by each "ant" (a small control packet) which flood the network. Reinforcement of the route in the forwards, reverse direction and both simultaneously have been researched: backwards reinforcement requires a symmetric network and couples the two directions together; forwards reinforcement rewards a route before the outcome is known (but then you pay for the cinema before you know how good the film is). As the system behaves stochastically and is therefore lacking repeatability, there are large hurdles to commercial deployment. 3.4 ANT COLONY OPTIMIZATION The ant colony optimization algorithm (ACO), introduced by Marco Dorigo in 1992 in his PhD thesis, is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. They are inspired by the behavior of ants in finding paths from the colony to food.in the real world, ants (initially) wander randomly, and upon finding food return to their colony while laying down pheromone trails. If other ants find such a path, they are likely not to keep traveling Division Of computer science, SOE, CUSAT 17

26 at random, but to instead follow the trail, returning and reinforcing it if they eventually find food. Over time, however, the pheromone trail starts to evaporate, thus reducing its attractive strength. The more time it takes for an ant to travel down the path and back again, more time the pheromones have to evaporate. A short path, by comparison, gets marched over faster, and thus the pheromone density remains high as it is laid on the path as fast as it can evaporate. Pheromone evaporation has also the advantage of avoiding the convergence to a locally optimal solution. If there were no evaporation at all, the paths chosen by the first ants would tend to be excessively attractive to the following ones. In that case, the exploration of the solution space would be constrained.thus, when one ant finds a good (i.e. short) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads all the ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with "simulated ants" walking around the graph representing the problem to solve. Figure 3.2 Example for Ant colony optimization Ant colony optimization algorithms have been used to produce near-optimal solutions to the traveling salesman problem. They have an advantage over simulated Division Of computer science, SOE, CUSAT 18

27 annealing and genetic algorithm approaches when the graph may change dynamically; the ant colony algorithm can be run continuously and adapt to changes in real time. This is of interest in network routing and urban transportation systems. ACO algorithms are usually applied to discrete (combinatorial) optimization problems. Assuming that the problem to be optimized can be represented by a graph, the general ACO algorithm can be described as given below:. 1. Initialization: assign the same initial pheromone value to each edge of the graph, and randomly place an ant in a location of the search space. 2. Population loop: for each ant, do: 2.1 Probabilistic transition rule: according to a given probabilistic transition rule, move ant over the space so that a solution to the problem is built. 2.2 Goodness evaluation: evaluate the goodness of the solution obtained by this ant. 2.3 Pheromone updating: update the pheromone level of each edge by reinforcing good solutions.reduce the pheromone level of each edge (evaporation). 3. Cycle: repeat Step 2 until a given convergence criterion is met. 3.5 PARTICLE SWARM OPTIMIZATION The particle swarm optimization algorithm was introduced to study social and cognitive behavior, but it has been largely applied as a problem-solving technique in engineering and computer science. There are two main versions of the PSO algorithm: a binary and a real-valued version. With the exception of the representation, the two versions of the algorithm are very much the same, thus only the real-valued (most popular) version will be discussed here. The particle swarm approach assumes a population of individuals represented as binary strings or real-valued vectors particles, which suffer an iterative procedure of adaptation to their environment. It also assumes that these individuals are social, what implies that they are capable of interacting with other individuals within a given neighborhood. There are two main types of information available to each individual of the population. The first is their own past experiences, and the second is the Division Of computer science, SOE, CUSAT 19

28 knowledge about how individuals around them have performed. The authors likened these two types of information to the individual learning and cultural transmission. Individuals tend to be influenced by its success along its past history and also by the success of any individual in its neighborhood, i.e., with which it interacts. To these schemes of interactions between individuals, the authors termed sociometric principles. Individuals can interact with each other in a number of ways. The simplest form is a binary interaction, where the individual interacts with its two nearest neighbors. Any number k of nearest neighbors can be used. If the number of nearest neighbors is less than the total number of individuals in the population, then this sociometric principle is called lbest, else (if k = N) it is called gbest. Conceptually, gbest connects all the individuals together, what means that its social interaction is maximal. In contrast, lbest results in a local neighborhood for the individual. The authors claim that the binary particle swarm algorithm can be interpreted as a qualitative or quantitative social optimization algorithm, while the real valued (continuous) version of PSO is a truly numeric optimization algorithm. In the latter version, the PSO searches for optima in Rn, where n is the dimension of the search space. The continuous version of PSO assumes individuals as points in a space, and the change over time is represented as movements of the points, now defined as particles. A psychological system is viewed as an information processing function, and each coordinate of a particle in the search space corresponds to a psychological measure. Forgetting and learning are viewed respectively, as an increase or a decrease in the value of a given coordinate. Assume that the position of a particle i is given by xi and its velocity by vi. The velocity is a vector of numbers that are added to the position coordinates of the particle in order to move it throughout the search space along the iterations (t is the time index): xi(t) = xi(t 1) + vi(t) (1) The social-psychological theory used as inspiration to envelop the PSO algorithm suggests that individuals oving along a sociocognitive space should be influenced by their own previous behavior and by the successes of its neighbors. It is important to note that neighborhood is related to the topologic space that defines the sociometric structure of the population, not to the distance between individuals in the parameter space. In both versions (binary and continuous) of the Division Of computer science, SOE, CUSAT 20

29 algorithm, a neighborhood is defined for each individual based on its position in the topological population array. The population array is usually implemented as a ring structure, with the last member being a neighbor of the first one. As the particles are moving in the space, the direction of movement is a function of its current position and velocity, the location of the individual s current best success pi, and the best position found by any member of the neighborhood pg: xi(t) = f(xi(t 1), vi(t 1), pi, pg) The change vi in the trajectory of a particle is a function of the difference between the individual s previous best and current positions, and the difference between the neighborhood s best and the current individual s position. The formula for changing velocity assumes continuous variables: vi(t) = vi(t 1) + ϕ1(pi xi(t 1)) + ϕ2(pg xi(t 1)) (3) In order to avoid that this system explodes when the particles oscillations become too large, the velocity of the particles is damped by a factor Vmax: if vid > Vmax, then vid = Vmax. (4) if vid < Vmax, then vid = Vmax. (5) The general PSO algorithm is summarized below:. 1. Initialization: randomly initialize a population of particles. 2. Population loop: for each particle, do: 2.1 Goodness evaluation and update: evaluate the goodness of the particle. If its goodness is greater than its best goodness so far, then this particle becomes the best particle found so far. 2.2 Neighborhood evaluation: if the goodness of this particle is the best among all its neighbors, then this particle becomes the best particle of the whole neighborhood. 2.3 Determine vi: apply equation (3). 2.4 Particle update: apply the updating rule given by equation (1). 3. Cycle: repeat Step 2 until a given convergence criterion is met Division Of computer science, SOE, CUSAT 21

30 Figure 3.3 Particle Swarm Optimization Division Of computer science, SOE, CUSAT 22

31 4.ARTIFICIAL IMMUNE SYSTEM Artificial immune systems (AIS) have been defined as adaptive systems inspired by the immune system and applied to problem solving. In a simplified form, to design an AIS it is necessary to choose an appropriate shape-space for the components of the system, one or more affinity measure(s), and an immune algorithm. The shape-space is a formalism used to create abstract ( artificial ) representations for the components of the immune system. The shape of an immune cell or molecule corresponds to all the features required to quantify interactions between the cell or molecule and the environment, and also with other elements of the system. There are four main types of shape-spaces: Euclidean or realvalued, Hamming, Integer, and Symbolic. In Euclidean shape-spaces the elements of the system are represented as real-valued vectors. In Hamming shapespaces the elements of the system are attribute strings built out of a finite alphabet. In Integer shape-spaces, cells and molecules are represented as integer values. (Note that Integer shape-spaces are a particular case of Hamming shape-spaces.) Symbolic shape-spaces use different types of attributes to represent a single element, for example, an integer value and a string such as color. There are two main types of interactions that can be performed by an element of an artificial immune system. One is the interaction with the environment. For example, an AIS can be used as a pattern recognition tool, thus the artificial immune cells are used to recognize a set (or sets) of artificial antigens (patterns). In this case, the degree of recognition, known as the affinity between the immune cell and the antigen, is measured via a function that quantifies the strength of the match between the two. If we assume that two cells interact to the extent their shapes are similar, then a similarity measure can be used according to the shape-space adopted. As an example, assume an immune cell with the following shape Ab = [1,0,0,0,1] in a binary Hamming shape-space, and an antigen with the following shape Ag = [0,1,1,1,1]. If affinity is directly proportional to their similarity, then the expression L Hamming distance is a suitable measure to quantify immune recognition, where L is the length of the string. Their Division Of computer science, SOE, CUSAT 23

32 affinity in this case is Aff = 5 4 = 1. There are several types of affinity measures, which usually vary according to the shape-space adopted, which by itself is usually defined by the problem in hand. The last building block of artificial immune systems corresponds to the immune algorithms. There are a number of different algorithms that can be applied to many domains, from data analysis to autonomous navigation. These immune algorithms were inspired by works on theoretical immunology and several processes that occur within the immune system. They can be classified as population-based and network-based immune algorithms. In population-based algorithms, the elements of the system are not connected with each other, meaning that they only interact directly with the environment. Interactions with other elements of the system can only be performed indirectly, via, for example, a reproductive operator. In network-based AIS by contrast, some (or all) elements of the system are interconnected. This way, there are two levels of interaction within this system: with the environment and with other elements in the system IMMUNE ALGORITHMS In order not to overload the text with descriptions of several immune algorithms, the focus will be given to two population-based AIS (negative and clonal selection algorithms), and to two types of network-based AIS (continuous and discrete immune networks). The main role played by the immune system is to protect our organisms against infectious diseases (caused by viruses, bacteria, etc.), and to eliminate debris and malfunctioning cells. To perform these functions, the immune system has to be able to distinguish between our own cells (known as self) and those elements that do not belong to the organism itself (known as nonself). One of the processes by which the immune system differentiates self from nonself (self/nonself discrimination) is termed negative selection. This gave rise to the negative selection algorithm. After distinguishing between self and nonself, the immune system has to perform an immune response in order to eliminate the nonself substances. Clonal selection is the name given to a theory Division Of computer science, SOE, CUSAT 24