Convergence and Rate of Convergence of a Foraging Ant Model

International audienceWe present an ant model that solves a discrete foraging problem. We describe simulations and provide a complete convergence analysis: we show that the ant population computes the solution of some optimal control problem and converges in some well defined sense. We discuss the rate of convergence with respect to the number of ants: we give experimental and theoretical arguments that suggest that this convergence rate can be superlinear with respect to the number of agents. Furthermore, we explain how this model can be extended in order to solve optimal control problems in general and argue that such an approach can be applied to any problem that involves the computation of the fixed point of a contraction mapping. This allows to design a large class of formally well understood ant like algorithms for problem solving

Ant colony optimisation-based radiation pattern manipulation algorithm for electronically steerable array radiator antennas

A new algorithm for manipulating the radiation pattern of Electronically Steerable Array Radiator Antennas is proposed. A continuous implementation of the Ant Colony Optimisation (ACO) technique calculates the optimal impedance values of reactances loading different parasitic radiators placed in a circle around a centre antenna. By proposing a method to obtain a suitable sampling frequency of the radiation pattern for use in the optimisation algorithm and by transforming the reactance search space into the search space of associated phases, special care was taken to create a fast and reliable implementation, resulting in an approach that is suitable for real-time implementation. The authors compare their approach to analytical techniques and optimisation algorithms for calculating these reactances. Results show that the method is able to calculate near-optimal solutions for gain optimisation and side lobe reduction

The impact of agent density on scalability in collective systems : noise-induced versus majority-based bistability

In this paper, we show that non-uniform distributions in swarms of agents have an impact on the scalability of collective decision-making. In particular, we highlight the relevance of noise-induced bistability in very sparse swarm systems and the failure of these systems to scale. Our work is based on three decision models. In the first model, each agent can change its decision after being recruited by a nearby agent. The second model captures the dynamics of dense swarms controlled by the majority rule (i.e., agents switch their opinion to comply with that of the majority of their neighbors). The third model combines the first two, with the aim of studying the role of non-uniform swarm density in the performance of collective decision-making. Based on the three models, we formulate a set of requirements for convergence and scalability in collective decision-making

An ACO-Inspired, Probabilistic, Greedy Approach to the Drone Traveling Salesman Problem

In recent years, major companies have done research on using drones for parcel delivery. Research has shown that this can result in significant savings, which has led to the formulation of various truck and drone routing and scheduling optimization problems. This paper explains and analyzes a new approach to the Drone Traveling Salesman Problem (DTSP) based on ant colony optimization (ACO). The ACO-based approach has an acceptance policy that maximizes the usage of the drone. The results reveal that the pheromone causes the algorithm to converge quickly to the best solution. The algorithm performs comparably to the MIP model, CP model, and EA of Rich & Ham (2018), especially in instances with a larger number of stops

Convergence results for continuous-time dynamics arising in ant colony optimization

This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding to the shortest path is shown under mild assumptions. A complete study is given for a recently proposed model called EigenAnt: global asymptotic stability is shown, and the speed of convergence is calculated explicitly and shown to be proportional to the difference between the reciprocals of the second shortest and the shortest paths.Comment: A short version of this paper was published in the preprints of the 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, 24-29 August 201

Pooling or sampling: Collective dynamics for electrical flow estimation

The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully decentralized way is implicit in a number of biological systems. Thus, a natural question is whether this task can provably be accomplished in an efficient way by a network of agents executing a simple protocol. We provide a positive answer, proposing two distributed approaches to electrical flow computation on a weighted network: a deterministic process mimicking Jacobi's iterative method for solving linear systems, and a randomized token diffusion process, based on revisiting a classical random walk process on a graph with an absorbing node. We show that both processes converge to a solution of Kirchhoff's node potential equations, derive bounds on their convergence rates in terms of the weights of the network, and analyze their time and message complexity