Novel ant colony optimization approach to optimal control

Reference:
J.M. van Ast, R. Babuska, and B. De Schutter, "Novel ant colony optimization approach to optimal control," International Journal of Intelligent Computing and Cybernetics, vol. 2, no. 3, pp. 414-434, 2009.

Abstract:
Purpose - In this paper, a novel Ant Colony Optimization (ACO) approach to optimal control is proposed. The standard ACO algorithms have proven to be very powerful optimization metaheuristic for combinatorial optimization problems. They have been demonstrated to work well when applied to various NP-complete problems, such as the traveling salesman problem. In this paper, ACO is reformulated as a model-free learning algorithm and its properties are discussed.
Design/methodology/approach - First, it is described how quantizing the state space of a dynamic system introduces stochasticity in the state transitions and transforms the optimal control problem into a stochastic combinatorial optimization problem, motivating the ACO approach. The algorithm is presented and is applied to the time-optimal swing-up and stabilization of an underactuated pendulum. In particular, the effect of different numbers of ants on the performance of the algorithm is studied.
Findings - The simulations show that the algorithm finds good control policies reasonably fast. An increasing number of ants results in increasingly better policies. The simulations also show that although the policy converges, the ants keep on exploring the state space thereby capable of adapting to variations in the system dynamics.
Research limitations/implications - This research introduces a novel ACO approach to optimal control and as such marks the starting point for more research of its properties. In particular, quantization issues must be studied in relation to the performance of the algorithm.
Originality/value - The work presented is original as it presents the first application of ACO to optimal control problems.