Novel ant colony optimization approach to optimal control

Abstract

http://www.dcsc.tudelft.nl/˜bdeschutterPurpose -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.

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

“…They don't really need good initial guesses and deterministic rules. Some of these methods are; Genetic algorithm (GA), see [1,23,24], Genetic programming (GP), see [18], Particle swarm optimization (PSO), see [3,4,21], Ant colony optimization (ACO), see [27] and Differential evolution (DE), see [8,19,28]. Many authors proposed many types of metaheuristics for solving NOCPs.…”

“…Arumugam et al [3] used various optimization algorithms, including PSO, with time varying inertia weight methods, and PSO with globally and locally tuned parameters to solve the NOCPs for steel annealing processes. van Ast et al [27] proposed a novel ACO approach to solve NOCP. Kumar and Balasubramaniam [18], using GA, solved NOCP for a linear system with quadratic performance.…”