Novel ant colony optimization approach to optimal control

Abstract

PurposeThe purpose of this paper is to propose a novel ant colony optimization (ACO) approach to optimal control. 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 nondeterministic polynomial‐complete problems, such as the travelling salesman problem. In this paper, ACO is reformulated as a model‐free learning algorithm and its properties are discussed.Design/methodology/approachFirst, 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.FindingsThe 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/implicationsThis paper 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/valueThe paper presented is original as it presents the first application of ACO to optimal control problems.