Swarm intelligence theory: A snapshot of the state of the art

Nature offers us many interesting and surprising examples in which the behaviour of a group of organisms seems to have some fundamentally distinct characteristics, not shared by the individuals in that group. Different species of birds flock together, and species of fish form schools, in groups that vary in size from a handful to many millions. Meanwhile it is wellknown thatmost species of ants, bees and termites form swarms that performmany functions collectively, including hunting and gathering food, and building complex structures. In different scenarios, these groupsmay be called herds, flocks, schools, and so forth, but the convenient term that stands for all such cases is ‘swarm’. The concept of ‘swarm intelligence’ captures the interest of many groups of (indeed, swarms of) academics and scientists, encapsulating the idea that the behaviour of a swarm often exhibits useful, functional and intelligent behaviours which seem well beyond the ability, as far as we know, of any of the individuals that together constitute the swarm. Swarm intelligence therefore concerns systems in which a group of similar ‘agents’, each of which is relatively simple in its behavioural repertoire, is somehow coordinated in a way that leads to useful (‘emergent’) behaviour of the swarm itself. Certain structural aspects of swarms are commonly assumed when swarm intelligence is discussed: apart from the aforementioned ‘simplicity’ of the constituent agents, we also expect that a swarmhas no central controller or ‘master’ agent that conducts the activities of others. Each agent is independent, but interacts with its fellow swarm-members (and other aspects of its environment) in simpleways. The fact that such a system can lead to interesting, useful and robust behaviour is in itself one of the appealing points that makes swarm intelligence an area of intense current study. This is partly because it suggests howwemight build real-world systems of various types, that aremore robust to damage and/or easier to construct or deploy than alternatives that rely on sophisticated central controllers. Meanwhile, of course, some swarm intelligence studies are undertaken with the goal of better understanding swarms in nature. Some of the most useful outcomes from swarm intelligence research for computer science are a collection of novel optimization algorithms. Inspired in turn by the flocking behaviour of birds, and the pheromone-trail following behaviour of ants, particle swarm optimization (PSO) and ant colony optimization (ACO) have both found considerable success in addressing a wide range of optimization problems. The growth of interest in these algorithms, as well as other themes in swarm intelligence (such as collective robotics, foraging algorithms, swarm simulation, and more), presents a number of specific challenges for theoretical work. We can conveniently class the theoretical challenges into two kinds. First, given specific new algorithm designs, we need to develop an understanding of their scalability, their convergence properties, the interactions between their parameters, and so forth — i.e., the typical range of issues that face us when a new algorithm is mooted, irrespective of its origins. Naturally, wemay object that suchwork is really necessary orworthwhile formany algorithms, but in the case of algorithms that have proven excellent in practical and empirical work on real problems – which is certainly the case here – such work is clearly warranted, and has a lot to contribute when done well. The second kind of challenge concerns understanding the special features of swarm-intelligence-based methods in particular. Examples of questions in this area are: What is special about the nature-inspired interactions in particle swarm optimization that seems to accelerate and improve search on some problems?What particular role does (an abstraction of) pheromone laying/following in social insects play, in the context of an optimization algorithm that integrates this with heuristics and local search? The present state of understanding, with regard to both kinds of questions, is still relatively immature. There have been many attempts already to undertake (for example) runtime analyses of simplified versions of ant colony optimization, for simple optimization landscapes. For ant colony optimization in particular, Dorigo and Blum [1] provides a comprehensive recent account of theoretical progress. However much remains to be done before we have built up a strong backbone of such theoretical results that underpin a real understanding of ant colony optimization’s capabilities, and of how to set its parameters for particular cases. Similar things can be said of particle swarm optimization, and there is very little theoretical understanding so far of other algorithms in the swarm intelligence community.When it comes to understanding the specific benefits that arise from the novel features of swarm intelligence algorithms, again there has been very little progress so far overall. However there have been clear notable developments, such as Poli [3,4], which studies