A non-local model for a swarm

 This paper describes continuum models for swarming behavior based on non-local interactions. The interactions are assumed to influence the velocity of the organisms. The model consists of integro-differential advection-diffusion equations, with convolution terms that describe long range attraction and repulsion. We find that if density dependence in the repulsion term is of a higher order than in the attraction term, then the swarm profile is realistic: i.e. the swarm has a constant interior density, with sharp edges, as observed in biological examples. This is our main result. Linear stability analysis, singular perturbation theory, and numerical experiments reveal that weak, density-independent diffusion leads to disintegration of the swarm, but only on an exponentially large time scale. When density dependence is put into the diffusion term, we find that true, locally stable traveling band solutions occur. We further explore the effects of local and non-local density dependent drift and unequal ranges of attraction and repulsion. We compare our results with results of some local models, and find that such models cannot account for cohesive, finite swarms with realistic density profiles. Received: 17 September 1997 / Revised version: 17 March 1998     

Modeling multi-robot task allocation with limited information as global game

Continuous response threshold functions to coordinate collaborative tasks in multi-agent systems are commonly employed models in a number of fields including ethology, economics, and swarm robotics. Although empirical evidence exists for the response threshold model in predicting and matching swarm behavior for social insects, there has been no formal argument as to why natural swarms use this approach and why it should be used for engineering artificial ones. In this paper, we show, by formulating task allocation as a global game, that continuous response threshold functions used for communication-free task assignment result in system level Bayesian Nash equilibria. Building up on these results, we show that individual agents not only do not need to communicate with each other, but also do not need to model each other’s behavior, which makes this coordination mechanism accessible to very simple agents, suggesting a reason for their prevalence in nature and motivating their use in an engineering context.     

Modelling a wireless connected swarm of mobile robots

It is a characteristic of swarm robotics that modelling the overall swarm behaviour in terms of the low-level behaviours of individual robots is very difficult. Yet if swarm robotics is to make the transition from the laboratory to real-world engineering realisation such models would be critical for both overall validation of algorithm correctness and detailed parameter optimisation. We seek models with predictive power: models that allow us to determine the effect of modifying parameters in individual robots on the overall swarm behaviour. This paper presents results from a study to apply the probabilistic modelling approach to a class of wireless connected swarms operating in unbounded environments. The paper proposes a probabilistic finite state machine (PFSM) that describes the network connectivity and overall macroscopic behaviour of the swarm, then develops a novel robot-centric approach to the estimation of the state transition probabilities within the PFSM. Using measured data from simulation the paper then carefully validates the PFSM model step by step, allowing us to assess the accuracy and hence the utility of the model.     

Artificial pheromone for path selection by a foraging swarm of robots

Foraging robots involved in a search and retrieval task may create paths to navigate faster in their environment. In this context, a swarm of robots that has found several resources and created different paths may benefit strongly from path selection. Path selection enhances the foraging behavior by allowing the swarm to focus on the most profitable resource with the possibility for unused robots to stop participating in the path maintenance and to switch to another task. In order to achieve path selection, we implement virtual ants that lay artificial pheromone inside a network of robots. Virtual ants are local messages transmitted by robots; they travel along chains of robots and deposit artificial pheromone on the robots that are literally forming the chain and indicating the path. The concentration of artificial pheromone on the robots allows them to decide whether they are part of a selected path. We parameterize the mechanism with a mathematical model and provide an experimental validation using a swarm of 20 real robots. We show that our mechanism favors the selection of the closest resource is able to select a new path if a selected resource becomes unavailable and selects a newly detected and better resource when possible. As robots use very simple messages and behaviors, the system would be particularly well suited for swarms of microrobots with minimal abilities.     

Collective behaviors of two-component swarms

We present a particle-based simulation study on two-component swarms where there exist two different types of groups in a swarm. Effects of different parameters between the two groups are studied systematically based on Langevin's equation. It is shown that the mass difference can introduce a protective behavior for the lighter members of the swarm in a vortex state. When the self-propelling strength is allowed to differ between two groups, it is observed that the swarm becomes spatially segregated and finally separated into two components at a certain critical value. We also investigate effects of different preferences for shelters on their collective decision making. In particular, it is found that the probability of selecting a shelter from the other varies sigmoidally as a function of the number ratio. The model is shown to describe the dynamics of the shelter choosing process of the cockroach–robot mixed group satisfactorily. It raises the possibility that the present model can be applied to the problems of pest control and fishing using robots and decoys.     

Spatial swarm segregation and reproductive isolation between the molecular forms of Anopheles gambiae

Anopheles gambiae, the major malaria vector in Africa, can be divided into two subgroups based on genetic and ecological criteria. These two subgroups, termed the M and S molecular forms, are believed to be incipient species. Although they display differences in the ecological niches they occupy in the field, they are often sympatric and readily hybridize in the laboratory to produce viable and fertile offspring. Evidence for assortative mating in the field was recently reported, but the underlying mechanisms awaited discovery. We studied swarming behaviour of the molecular forms and investigated the role of swarm segregation in mediating assortative mating. Molecular identification of 1145 males collected from 68 swarms in Donéguébougou, Mali, over 2 years revealed a strict pattern of spatial segregation, resulting in almost exclusively monotypic swarms with respect to molecular form. We found evidence of clustering of swarms composed of individuals of a single molecular form within the village. Tethered M and S females were introduced into natural swarms of the M form to verify the existence of possible mate recognition operating within-swarm. Both M and S females were inseminated regardless of their form under these conditions, suggesting no within-mate recognition. We argue that our results provide evidence that swarm spatial segregation strongly contributes to reproductive isolation between the molecular forms in Mali. However this does not exclude the possibility of additional mate recognition operating across the range distribution of the forms. We discuss the importance of spatial segregation in the context of possible geographic variation in mechanisms of reproductive isolation.     

Turing learning: a metric-free approach to inferring behavior and its application to swarms

We propose Turing Learning, a novel system identification method for inferring the behavior of natural or artificial systems. Turing Learning simultaneously optimizes two populations of computer programs, one representing models of the behavior of the system under investigation, and the other representing classifiers. By observing the behavior of the system as well as the behaviors produced by the models, two sets of data samples are obtained. The classifiers are rewarded for discriminating between these two sets, that is, for correctly categorizing data samples as either genuine or counterfeit. Conversely, the models are rewarded for ‘tricking’ the classifiers into categorizing their data samples as genuine. Unlike other methods for system identification, Turing Learning does not require predefined metrics to quantify the difference between the system and its models. We present two case studies with swarms of simulated robots and prove that the underlying behaviors cannot be inferred by a metric-based system identification method. By contrast, Turing Learning infers the behaviors with high accuracy. It also produces a useful by-product—the classifiers—that can be used to detect abnormal behavior in the swarm. Moreover, we show that Turing Learning also successfully infers the behavior of physical robot swarms. The results show that collective behaviors can be directly inferred from motion trajectories of individuals in the swarm, which may have significant implications for the study of animal collectives. Furthermore, Turing Learning could prove useful whenever a behavior is not easily characterizable using metrics, making it suitable for a wide range of applications.     

Stop-Signaling Reduces Split Decisions without Impairing Accuracy in the Honeybee Nest-Site Selection Process

In the honeybee swarm nest-site selection process, individual bees gather information about available candidate sites and communicate the information to other bees. The swarm makes an agreement for a candidate site when the number of bees that supports the site reaches a threshold. This threshold is usually referred to as the quorum threshold and it is shown by many studies as a key parameter that is a compromise between the accuracy and speed of decisions. In the present work, we use a model of the honeybee Apis mellifera nest-site selection process to study how the quorum threshold and discovery time of candidate sites have major impact on two unfavorable situations in selecting a nest site: decision deadlock and decision split. We show that cross-inhibitory stop-signaling, delivered among bees supporting different sites, enables swarms to avoid the decision split problem in addition to avoiding the decision deadlock problem that has been previously proposed. We also show that stop-signaling improves decision speed, but compromises decision accuracy in swarms using high quorum thresholds by causing the swarms to be trapped in local optima (e.g., choosing a sub-optimal option that is encountered first). On the other hand, we demonstrate that stop-signaling can reduce split decisions without compromising decision accuracy in swarms using low quorum thresholds when it is compared to the accuracy of swarms using the same threshold values but not exhibiting stop-signaling. Based on our simulations, we suggest that swarms using low quorum thresholds (as well as swarms with large population sizes) would benefit more from exhibiting the stop-signaling activity than not exhibiting it.     

Designing pheromone communication in swarm robotics: Group foraging behavior mediated by chemical substance

In swarm robotics, communication among the robots is essential. Inspired by biological swarms using pheromones, we propose the use of chemical compounds to realize group foraging behavior in robot swarms. We designed a fully autonomous robot, and then created a swarm using ethanol as the trail pheromone allowing the robots to communicate with one another indirectly via pheromone trails. Our group recruitment and cooperative transport algorithms provide the robots with the required swarm behavior. We conducted both simulations and experiments with real robot swarms, and analyzed the data statistically to investigate any changes caused by pheromone communication in the performance of the swarm in solving foraging recruitment and cooperative transport tasks. The results show that the robots can communicate using pheromone trails, and that the improvement due to pheromone communication may be non-linear, depending on the size of the robot swarm.     

Evolution of swarm robotics systems with novelty search

Novelty search is a recent artificial evolution technique that challenges traditional evolutionary approaches. In novelty search, solutions are rewarded based on their novelty, rather than their quality with respect to a predefined objective. The lack of a predefined objective precludes premature convergence caused by a deceptive fitness function. In this paper, we apply novelty search combined with NEAT to the evolution of neural controllers for homogeneous swarms of robots. Our empirical study is conducted in simulation, and we use a common swarm robotics task—aggregation, and a more challenging task—sharing of an energy recharging station. Our results show that novelty search is unaffected by deception, is notably effective in bootstrapping evolution, can find solutions with lower complexity than fitness-based evolution, and can find a broad diversity of solutions for the same task. Even in non-deceptive setups, novelty search achieves solution qualities similar to those obtained in traditional fitness-based evolution. Our study also encompasses variants of novelty search that work in concert with fitness-based evolution to combine the exploratory character of novelty search with the exploitatory character of objective-based evolution. We show that these variants can further improve the performance of novelty search. Overall, our study shows that novelty search is a promising alternative for the evolution of controllers for robotic swarms.     

Predicting krill swarm characteristics important for marine predators foraging off East Antarctica

Open ocean predator‐prey interactions are often difficult to interpret because of a lack of information on prey fields at scales relevant to predator behaviour. Hence, there is strong interest in identifying the biological and physical factors influencing the distribution and abundance of prey species, which may be of broad predictive use for conservation planning and evaluating effects of environmental change. This study focuses on a key Southern Ocean prey species, Antarctic krill Euphausia superba, using acoustic observations of individual swarms (aggregations) from a large‐scale survey off East Antarctica. We developed two sets of statistical models describing swarm characteristics, one set using underway survey data for the explanatory variables, and the other using their satellite remotely sensed analogues. While survey data are in situ and contemporaneous with the swarm data, remotely sensed data are all that is available for prediction and inference about prey distribution in other areas or at other times. The fitted models showed that the primary biophysical influences on krill swarm characteristics included daylight (solar elevation/radiation) and proximity to the Antarctic continental slope, but there were also complex relationships with current velocities and gradients. Overall model performance was similar regardless of whether underway or remotely sensed predictors were used. We applied the latter models to generate regional‐scale spatial predictions using a 10‐yr remotely‐sensed time series. This retrospective modelling identified areas off east Antarctica where relatively dense krill swarms were consistently predicted during austral mid‐summers, which may underpin key foraging areas for marine predators. Spatiotemporal predictions along Antarctic predator satellite tracks, from independent studies, illustrate the potential for uptake into further quantitative modelling of predator movements and foraging. The approach is widely applicable to other krill‐dependent ecosystems, and our findings are relevant to similar efforts examining biophysical linkages elsewhere in the Southern Ocean and beyond.     

Termites as models of swarm cognition

Eusociality has evolved independently at least twice among the insects: among the Hymenoptera (ants and bees), and earlier among the Isoptera (termites). Studies of swarm intelligence, and by inference, swarm cognition, have focused largely on the bees and ants, while the termites have been relatively neglected. Yet, termites are among the world’s premier animal architects, and this betokens a sophisticated swarm intelligence capability. In this article, I review new findings on the workings of the mound of Macrotermes which clarify how these remarkable structures work, and how they come to be built. Swarm cognition in these termites is in the form of “extended” cognition, whereby the swarm’s cognitive abilities arise both from interaction amongst the individual agents within a swarm, and from the interaction of the swarm with the environment, mediated by the mound’s dynamic architecture. The latter provides large scale “cognitive maps” which enable termite swarms to assess the functional state of their structure and to guide repair efforts where necessary. The crucial role of the built environment in termite swarm cognition also points to certain “swarm cognitive disorders”, where swarms can be pushed into anomalous activities by manipulating crucial structural and functional attributes of the termite system of “extended cognition.”     

Nest‐Site Defense by Competing Honey Bee Swarms During House‐Hunting

Cavity‐nesting animals must often defend their homes against intruders, especially when the availability of suitable cavities is limited. Competition for nest sites is particularly strong when multiple groups of the same species migrate synchronously to found a new home. This may be the case for honey bees during the reproductive season, because neighboring colonies often cast swarms simultaneously, leading to potential competition for high‐quality nesting cavities. To test the idea that honey bee swarms may compete for and defend potential nest sites as they search for a new home, we observed pairs of artificial swarms that were house‐hunting concurrently. Workers from one swarm in each pair carried a gene influencing body color, so that the bees from the two swarms were easily distinguished. We set up a high‐quality nest box and waited for nest‐site scouts from each swarm to explore and recruit swarm mates to it. We recorded all the interactions between competing scouts at the nest box and found that when scouts from both swarms explored the box simultaneously they behaved agonistically toward bees from the other swarm. The level of aggression depended on the number of scouts from each swarm present at the nest box. When only one to three scouts from each swarm were at the box, they rarely fought. But when the scouts from one swarm outnumbered those from the other swarm (4–20 vs. one to three bees), those in the majority advertised their presence with a buzzing behavior at the entrance opening, and started mobbing and killing those in the minority. When one swarm gained clear control of the nest box (20+ vs. zero to one bees), some of its scouts guarded the box’s entrance, preventing entry by foreign scouts. Our study exemplifies how cavity‐nesting animals may compete for and defend suitable nesting sites.     

Predicting species distributions for conservation decisions

Species distribution models (SDMs) are increasingly proposed to support conservation decision making. However, evidence of SDMs supporting solutions for on‐ground conservation problems is still scarce in the scientific literature. Here, we show that successful examples exist but are still largely hidden in the grey literature, and thus less accessible for analysis and learning. Furthermore, the decision framework within which SDMs are used is rarely made explicit. Using case studies from biological invasions, identification of critical habitats, reserve selection and translocation of endangered species, we propose that SDMs may be tailored to suit a range of decision‐making contexts when used within a structured and transparent decision‐making process. To construct appropriate SDMs to more effectively guide conservation actions, modellers need to better understand the decision process, and decision makers need to provide feedback to modellers regarding the actual use of SDMs to support conservation decisions. This could be facilitated by individuals or institutions playing the role of ‘translators’ between modellers and decision makers. We encourage species distribution modellers to get involved in real decision‐making processes that will benefit from their technical input; this strategy has the potential to better bridge theory and practice, and contribute to improve both scientific knowledge and conservation outcomes.     

A biologically inspired neural network for dynamic programming

An artificial neural network with a two-layer feedback topology and generalized recurrent neurons, for solving nonlinear discrete dynamic optimization problems, is developed. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. The neural network based algorithm is an advantageous approach for dynamic programming due to the inherent parallelism of the neural networks; further it reduces the severity of computational problems that can occur in methods like conventional methods. Some illustrative application examples are presented to show how this approach works out including the shortest path and fuzzy decision making problems.     

Modelling spatial dynamics of fish

Our ability to model spatial distributions of fish populations is reviewed by describing the available modelling tools. Ultimate models of the individual's motivation for behavioural decisions are derived from evolutionary ecology. Mechanistic models for how fish sense and may respond to their surroundings are presented for vision, olfaction, hearing, the lateral line and other sensory organs. Models for learning and memory are presented, based both upon evolutionary optimization premises and upon neurological information processing and decision making. Functional tools for modelling behaviour and life histories can be categorized as belonging to an optimization or an adaptation approach. Among optimization tools, optimal foraging theory, life history theory, ideal free distribution, game theory and stochastic dynamic programming are presented. Among adaptation tools, genetic algorithms and the combination with artificial neural networks are described. The review advocates the combination of evolutionary and neurological approaches to modelling spatial dynamics of fish.     

Scaling in nests of a social wasp: a property of the social group

The numbers of brood cells in nests built by founding swarms of the Neotropical social wasp Polybia occidentalis closely correlate with the numbers of wasps in the swarms. We analyzed nests of different sizes to determine how they scale with respect to the allocation of brood cells among combs. Three patterns were evident: compared to smaller nests, larger nests have (1) more combs and (2) larger combs; and (3) among nests containing the same number of combs, the last two combs diverge in relative size as nest size increases. Taken together, these results suggest that members of a swarm somehow "know" the size of the swarm they are in. This information feeds back to individual builders, which quantitatively modulate their responses to stigmergic cues in ways that result in the nest-size-scaled allocation of brood cells among combs. The patterns also suggest that swarms fine-tune the final size of their nests by making corrections as they build.     

Quantification and distribution of a Tetragonula carbonaria swarm (Hymenoptera: Apidae)

Manual mark-by-mark image analysis was used to quantify the number of individuals present in a Tetragonula carbonaria swarm. A total of 7328 bees were identified in the swarm. The distribution of individuals within the swarm followed a Gaussian distribution, with the distances to the nearest neighbour strongly positively skewed. The clustering of bees in the centre of the swarm is likely a mechanism for reducing predation risk. In the case of male mating swarms, large aggregations may increase the mating success of the species.     

A cooperative particle swarm optimizer with migration of heterogeneous probabilistic models

Particle Swarm Optimization (PSO) is a stochastic optimization approach that originated from simulations of bird flocking, and that has been successfully used in many applications as an optimization tool. Estimation of distribution algorithms (EDAs) are a class of evolutionary algorithms which perform a two-step process: building a probabilistic model from which good solutions may be generated and then using this model to generate new individuals. Two distinct research trends that emerged in the past few years are the hybridization of PSO and EDA algorithms and the parallelization of EDAs to exploit the idea of exchanging the probabilistic model information. In this work, we propose the use of a cooperative PSO/EDA algorithm based on the exchange of heterogeneous probabilistic models. The model is heterogeneous because the cooperating PSO/EDA algorithms use different methods to sample the search space. Three different exchange approaches are tested and compared in this work. In all these approaches, the amount of information exchanged is adapted based on the performance of the two cooperating swarms. The performance of the cooperative model is compared to the existing state-of-the-art PSO cooperative approaches using a suite of well-known benchmark optimization functions.