Epilogue

After seven chapters of swarm-based approaches, where do we stand? First of all, it is clear that social insects and, more generally, natural systems, can bring much insight into the design of algorithms and artificial problem-solving systems. In particular, artificial swarm-intelligent systems are expected to exhibit the features that may have made social insects so successful in the biosphere: flexibility, robustness, decentralized control, and self-organization. The examples that have been described throughout this book provide illustrations of these features, either explicitly or implicitly. The swarm-based approach, therefore, looks promising, in face of a world that continually becomes more complex, dynamic, and overloaded with information than ever. There remain some issues, however, as to the application of swarm intelligence to solving problems. . . . 1. First, it would be very useful to define methodologies to “program” a swarm or multiagent system so that it performs a given task. There is a similarity here with the problem of training neural networks [167]: how can one tune interaction weights so that the network performs a given task, such as classification, recognition, etc. The fact that (potentially mobile) agents in a swarm can take actions asynchronously and at any spatial location generally makes the problem extremely hard. In order to solve this “inverse” problem and find the appropriate individual algorithm that generates the desired collective pattern, one can either systematically explore the behaviors of billions of different swarms, or search this huge space of possible swarms with some kind of cost function, assuming a reasonable continuity of the mapping from individual algorithms to collective productions. This latter solution can be based, for example, on artificial evolutionary techniques such as genetic algorithms [152, 171] if individual behavior is adequately coded and if a cost function can be defined. 2. Second, and perhaps even more fundamental than the issue of programming the system, is that of defining it: How complex should individual agents be? Should they be all identical? Should they have the ability to learn? Should they be able to make logical inferences? Should they be purely reactive? How local should their knowledge of the environment be?

Cemetery Organization, Brood Sorting, Data Analysis, and Graph Partitioning

In the previous two chapters, foraging and division of labor were shown to be useful metaphors to design optimization and resource allocation algrithms. In this chapter, we will see that the clustering and sorting behavior of ants has stimulated researchers to design new algorithms for data analysis and graph partitioning. Several species of ants cluster corpses to form a “cemetery,” or sort their larvae into several piles. This behavior is still not fully understood, but a simple model, in which agents move randomly in space and pick up and deposit items on the basis of local information, may account for some of the characteristic features of clustering and sorting in ants. The model can also be applied to data analysis and graph partitioning: objects with different attributes or the nodes of a graph can be considered items to be sorted. Objects placed next to each other by the sorting algorithm have similar attributes, and nodes placed next each other by the sorting algorithm are tightly connected in the graph. The sorting algorithm takes place in a two-dimensional space, thereby offering a low-dimensional representation of the objects or of the graph. Distributed clustering, and more recently sorting, by a swarm of robots have served as benchmarks for swarm-based robotics. In all cases, the robots exhibit extremely simple behavior, act on the basis of purely local information, and communicate indirectly except for collision avoidance. In several species of ants, workers have been reported to form piles of corpses— literally cemeteries—to clean up their nests. Chretien [72] has performed experiments with the ant Lasius niger to study the organization of cemeteries. Other experiments on the ant Pheidole pallidula are also reported in Deneubourg et al. [88], and many species actually organize a cemetery. Figure 4.1 shows the dynamics of cemetery organization in another ant, Messor sancta. If corpses, or, more precisely, sufficiently large parts of corposes are randomly distributed in space at the beginning of the experiment, the workers form cemetery clusters within a few hours.

Division of Labor and Task Allocation

Many species of social insects have a division of labor. The resilience of task allocation exhibited at the colony level is connected to the elasticity of individual workers. The behavioral repertoire of workers can be stretched back and forth in response to perturbations. A model based on response thresholds connects individual-level plasticity with colony-level resiliency and can account for some important experimental results. Response thresholds refer to likelihood of reacting to task-associated stimuli. Low-threshold individuals perform tasks at a lower level of stimulus than high-threshold individuals. An extension of this model includes a simple form of learning. Within individual workers, performing a given task induces a decrease of the corresponding threshold, and not performing the task induces an increase of the threshold. This double reinforcement process leads to the emergence of specialized workers, that is, workers that are more responsive to stimuli associated with particular task requirements, from a group of initially identical individuals. The fixed response threshold model can be used to allocate tasks in a multiagent system, in a way that is similar to market-based models, where agents bid to get resources or perform tasks. The response threshold model with learning can be used to generate differentiation in task performance in a multiagent system composed of initially identical entities. Task allocation in this case is emergent and more robust with respect to perturbations of the system than when response thresholds are fixed. An example application to distributed mail retrieval is presented. In social insects, different activities are often performed simultaneously by specialized individuals. This phenomenon is called division of labor [253, 272]. Simultaneous task performance by specialized workers is believed to be more efficient than sequential task performance by unspecialized workers [188, 253]. Parallelism avoids task switching, which costs energy and time. Specialization allows greater efficiency of individuals in task performance because they “know” the task or are better equipped for it. All social insects exhibit reproductive division of labor: only a small fraction of the colony, often limited to a single individual, reproduces.

Cooperative Transport by Insects and Robots

Collective robotics is a booming field, and cooperative transport—particularly cooperative box-pushing—has been an important benchmark in testing new types of robotic architecture. Although this task in itself is not especially exciting, it does provide insight into the design of collective problem-solving robotic systems. One of the swarm-based robotic implementations of cooperative transport that seems to work well is one that is closely inspired by cooperative prey retrieval in social insects. Ants of various species are capable of collectively retrieving large prey that are impossible for a single ant to retrieve. Usually, a single ant finds a prey item and tries to move it alone; when successful, the ant moves the item back to the nest. When unsuccessful, the ant recruits nestmates through direct contact or trail laying. If a group of ants is still unable to move the prey item for a certain time, specialized workers with large mandibles may be recruited in some species to cut the prey into smaller pieces. Although this scenario seems to be fairly well understood in the species where it has been studied, the mechanisms underlying cooperative transport—that is, when and how a group of ants move a large prey item to the nest—remain unclear. No formal description of the biological phenomenon has been developed, and, surprisingly, roboticists went further than biologists in trying to model cooperative transport: perhaps the only convincing model so far is one that has been introduced and studied by roboticists [207] and, although this model was not aimed at describing the behavior of real ants, few adjustments would be required to make it biologically plausible. This chapter first describes empirical research on cooperative transport in ants, and then describes the work of Kube and Zhang [205, 206,207, 209]. A small prey or food item is easily carried by a single ant.

Ant Foraging Behavior, Combinatorial Optimization, and Routing in Communications Networks

This chapter is dedicated to the description of the collective foraging behavior of ants and to the discussion of several computational models inspired by that behavior—ant-based algorithms or ant colony optimization (AGO) algorithms. In the first part of the chapter, several examples of cooperative foraging in ants are described and modeled. In particular, in some species a colony self-organizes to find and exploit the food source that is closest to the nest. A set of conveniently defined artificial ants, the behavior of which is designed after that of their real counterparts, can be used to solve combinatorial optimization problems. A detailed introduction to ant-based algorithms is given by using the traveling salesman problem (TSP) as an application problem. Ant-based algorithms have been applied to other combinatorial optimization problems such as the quadratic assignment problem, graph coloring, job-shop scheduling, sequential ordering, and vehicle routing. Results obtained with ant-based algorithms are often as good as those obtained with other general-purpose heuristics. Application to the quadratic assignment problem is described in detail. Coupling ant-based algorithms with local optimizers obtains, in some cases, world-class results. Parallels are drawn between ant-based optimization algorithms and other nature-inspired optimization techniques, such as neural nets and evolutionary computation. All the combinatorial problems mentioned above are static, that is, their characteristics do not change over time. In the last part of the chapter, the application of ant-based algorithms to a class of stochastic time-varying problems is investigated: routing in telecommunications networks. Given the adaptive capabilities built into the ant-based algorithms, they may be more competitive in stochastic time-varying domains, in which solutions must be adapted online to changing conditions, than in static problems. The performance of AntNet, an ant-based algorithm designed to adaptively build routing tables in packet-switching communications networks, is the best of a number of state-of-the-art algorithms compared on an extensive set of experimental conditions. Many ant species have trail-laying trail-following behavior when foraging: individual ants deposit a chemical substance called pheromone as they move from a food source to their nest, and foragers follow such pheromone trails.

Nest Building and Self-Assembling

Social insect nest architectures can be complex, intricate structures. Stigmergy (see section 1.2.3), that is, the coordination of activities through the environment, is an important mechanism underlying nest construction in social insects. Two types of stigmergy are distinguished: quantitative, or continuous stigmergy, in which the different stimuli that trigger behavior are quantitatively different; and qualitative, or discrete stigmergy, in which stimuli can be classified into different classes that differ qualitatively. If quantitative stigmergy can explain the emergence of pillars in termites, the building behavior of the paper wasps Polistes dominulus seems to be better described by qualitative stigmergy. In this chapter, a simple agent-based model inspired by discrete stigmergy is introduced. In the model, agents move in a three-dimensional grid and drop elementary building blocks depending on the configuration of blocks in their neighborhood. From the viewpoint of bricks, this model is a model of self-assembly. The model generates a large proportion of random or space-filling forms, but some patterns appear to be structured. Some of the patterns even look like wasp nests. The properties of the structured shapes obtained with the model, and of the algorithms that generate them, are reviewed. Based on these properties, a fitness function is constructed so that structured architectures have a large fitness and unstructured patterns a small fitness. A genetic algorithm based on the fitness function is used to explore the space of architectures. Several examples of self-assembling systems in robotics, engineering, and architecture are described. Self-assembling or self-reconfigurable robotic systems, although they are not directly inspired by nest construction in social insects, could benefit from the discrete-stigmergy model of nest building. The method of evolutionary design, that is, the creation of new designs by computers using evolutionary algorithms, is a promising way of exploring the patterns that self-assembling models can produce. Many animals can produce very complex architectures that fulfill numerous functional and adaptive requirements (protection from predators, substrate of social life and reproductive activities, thermal regulation, etc.).

Self-Organization and Templates: Application to Data Analysis and Graph Partitioning

The biological phenomena described in the previous chapter were corpse aggregation and brood sorting by ants. The clusters of items obtained with the models introduced in sections 4.3.1 and 4.3.2 emerged at arbitrary locations. The underlying self-organizing process, whereby large clusters grow even larger because they are more attractive than smaller clusters, does not ensure the formation of clusters at specific locations. In the two biological examples described in this chapter, the self-organizing dynamics of aggregation is constrained by templates. A template is a pattern that is used to construct another pattern. The body of a termite queen or a brood pile in ants are two examples of structures—the second one resulting from the activities of the colony—that serve as templates to build walls. Walls built around the termite queen form the royal chamber; walls built around the brood pile form the ant nest. When a mechanism combines self-organization and templates, it exhibits the characteristic properties of self-organization, such as snowball effect or multistability, and at the same time produces a perfectly predictable pattern that follows the template. The two nonparametric algorithms presented in chapter 4, one for multidimensional scaling and the other for graph partitioning, can be made parametric through the use of templates. The number of clusters of data points or vertices can be predefined by forcing items to be deposited in a prespecified number of regions in the space of representation, so that the number of clusters and their locations are known in advance. In the previous chapter, we saw how the attractivity of corpses or the differential attractivity of items of different types could lead to the formation of clusters of specific items. Self-organization lies in this attractivity, which induces a snowball effect: the larger a cluster, the more likely it is to attract even more items. But selforganization can also be combined with a template mechanism in the process of clustering. A template is a kind of prepattern in the environment, used by insects— or by other animals—to organize their activities.

Introduction

Insects that live in colonies, ants, bees, wasps, and termites, have fascinated naturalists as well as poets for many years. “What is it that governs here? What is it that issues orders, foresees the future, elaborates plans, and preserves equilibrium?,” wrote Maeterlinck [230]. These, indeed, are puzzling questions. Every single insect in a social insect colony seems to have its own agenda, and yet an insect colony looks so organized. The seamless integration of all individual activities does not seem to require any supervisor. For example, Leafcutter ants (Atta) cut leaves from plants and trees to grow fungi. Workers forage for leaves hundreds of meters away from the nest, literally organizing highways to and from their foraging sites [174]. Weaver ant (Oecophylla) workers form chains of their own bodies, allowing them to cross wide gaps and pull stiff leaf edges together to form a nest. Several chains can join to form a bigger one over which workers run back and forth. Such chains create enough force to pull leaf edges together. When the leaves are in place, the ants connect both edges with a continuous thread of silk emitted by a mature larva held by a worker [172, 174]. In their moving phase, army ants (such as Eciton) organize impressive hunting raids, involving up to 200,000 workers, during which they collect thousands of prey (see chapter 2, section 2.2.3) [52, 269, 282]. In a social insect colony, a worker usually does not perform all tasks, but rather specializes in a set of tasks, according to its morphology, age, or chance. This division of labor among nestmates, whereby different activities are performed simultaneously by groups of specialized individuals, is believed to be more efficient than if tasks were performed sequentially by unspecialized individuals [188, 272]. In polymorphic species of ants, two (or more) physically different types of workers coexist. For example, in Pheidole species, minor workers are smaller and morphologically distinct from major workers.