Modelling of Multi-Agent Systems: Experiences with Membrane Computing and Future Challenges

Formal modelling of Multi-Agent Systems (MAS) is a challenging task due to high complexity, interaction, parallelism and continuous change of roles and organisation between agents. In this paper we record our research experience on formal modelling of MAS. We review our research throughout the last decade, by describing the problems we have encountered and the decisions we have made towards resolving them and providing solutions. Much of this work involved membrane computing and classes of P Systems, such as Tissue and Population P Systems, targeted to the modelling of MAS whose dynamic structure is a prominent characteristic. More particularly, social insects (such as colonies of ants, bees, etc.), biology inspired swarms and systems with emergent behaviour are indicative examples for which we developed formal MAS models. Here, we aim to review our work and disseminate our findings to fellow researchers who might face similar challenges and, furthermore, to discuss important issues for advancing research on the application of membrane computing in MAS modelling.Comment: In Proceedings AMCA-POP 2010, arXiv:1008.314

The organization of soil disposal by ants

Colonies of Pheidole ambigua ants excavate soil and drop it outside the nest entrance. The deposition of thousands of loads leads to the formation of regular ring-shaped piles. How is this pattern generated? This study investigated soil pile formation on level and sloping surfaces, both empirically and using an agent-based model. We found that ants drop soil preferentially in the direction in which the slope is least steeply uphill from the nest entrance, both when adding to an existing pile and when starting a new pile. Ants respond to cues from local slope to choose downhill directions. Ants walking on a slope increase the frequency and magnitude of changes in direction, and more of these changes of direction take them downhill than uphill. Also, ants carrying soil on a slope wait longer before dropping their soil compared to ants on a level plane. These mechanisms combine to focus soil dropping in the downhill direction, without the necessity of a direct relationship between slope and probability of dropping soil. These empirically determined rules were used to simulate soil disposal. The slight preference for turning downhill measured empirically was shown in the model to be sufficient to generate biologically realistic patterns of soil dumping when combined with memory of the direction of previous trips. From simple rules governing individual behaviour an overall pattern emerges, which is appropriate to the environment and allows a rapid response to changes

Controlling invasive ant species: a theoretical strategy for efficient monitoring in the early stage of invasion

Invasion by the red imported fire ant, Solenopsis invicta Buren, has destructive effects on native biodiversity, agriculture, and public health. This ant's aggressive foraging behaviour and high reproductive capability have enabled its establishment of wild populations in most regions into which it has been imported. An important aspect of eradication is thorough nest monitoring and destruction during early invasion to prevent range expansion. The question is: How intense must monitoring be on temporal and spatial scales to eradicate the fire ant? Assuming that the ant was introduced into a region and that monitoring was conducted immediately after nest detection in an effort to detect all other potentially established nests, we developed a mathematical model to investigate detection rates. Setting the monitoring limit to three years, the detection rate was maximized when monitoring was conducted shifting bait trap locations and setting them at intervals of 30 m for each monitoring. Monitoring should be conducted in a radius of at least 4 km around the source nest, or wider --depending on how late a nest is found. For ease of application, we also derived equations for finding the minimum bait interval required in an arbitrary ant species for thorough monitoring.Comment: Revised the manuscrip

Individual rules for trail pattern formation in Argentine ants (Linepithema humile)

We studied the formation of trail patterns by Argentine ants exploring an empty arena. Using a novel imaging and analysis technique we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times. Then we derived the response function of individual ants to pheromone concentrations by looking at correlations between concentrations and changes in speed or direction of the ants. Ants were found to turn in response to local pheromone concentrations, while their speed was largely unaffected by these concentrations. Ants did not integrate pheromone concentrations over time, with the concentration of pheromone in a 1 cm radius in front of the ant determining the turning angle. The response to pheromone was found to follow a Weber's Law, such that the difference between quantities of pheromone on the two sides of the ant divided by their sum determines the magnitude of the turning angle. This proportional response is in apparent contradiction with the well-established non-linear choice function used in the literature to model the results of binary bridge experiments in ant colonies (Deneubourg et al. 1990). However, agent based simulations implementing the Weber's Law response function led to the formation of trails and reproduced results reported in the literature. We show analytically that a sigmoidal response, analogous to that in the classical Deneubourg model for collective decision making, can be derived from the individual Weber-type response to pheromone concentrations that we have established in our experiments when directional noise around the preferred direction of movement of the ants is assumed.Comment: final version, 9 figures, submitted to Plos Computational Biology (accepted

A continuous model of ant foraging with pheromones and trail formation

We propose and numerically analyze a PDE model of ant foraging behavior. Ant foraging is a prime example of individuals following simple behavioral rules based on local information producing complex, organized and ``intelligent'' strategies at the population level. One of its main aspects is the widespread use of pheromones, which are chemical compounds laid by the ants used to attract other ants to a food source. In this work, we consider a continuous description of a population of ants and simulate numerically the foraging behavior using a system of PDEs of chemotaxis type. We show that, numerically, this system accurately reproduces observed foraging behavior, such as trail formation and efficient removal of food sources.Comment: Conference proceeding

A Model for Collective Dynamics in Ant Raids

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and the transition from one class of ants to another. Through analysis of an order parameter measuring the orientational order in the system, the model shows self-organization into a collective state consisting of lanes of ants moving in opposite directions as well as the transition back to the individual state once the food source is depleted matching prior experimental results. This indicates that in the absence of direct communication ants naturally form an efficient method for transporting food to the nest/bivouac. The model exhibits a continuous kinetic phase transition in the order parameter as a function of certain system parameters. The associated critical exponents are found, shedding light on the behavior of the system near the transition.Comment: Preprint Version, 30 pgs., 18 figures, complete version with supplementary movies to appear in Journal of Mathematical Biology (Springer