Ant Colony Optimization based on Pareto optimality: application to a congested router controlled by PID regulation

Abstract

The subject of this research work is to stabilize the network TCP (transmission control protocol) as well as the queue of the router congestion by designing an Active Queue Management scheme able to ensure this role. The problem is dealt with under the theory of the command by using a tuned PID (proportional–integral–derivative) controller based on an extension of the Hermite–Biehler theorem applied to quasi-polynomials. This tuning approach uses Hurwitz stability concept, that is to say, a sufficient and necessary condition must be given so the roots of the quasi-polynomial lie in the left half plane. Since this stabilization method gives rise to a set of values for parameters ‘P’, ‘I’ and ‘D’, it turns out relevant to optimize the results achieved within this stability region. To achieve this purpose, a multi-criterion Ant Colony Optimization based on Pareto optimality is used, given the conflictual character of the closed-loop system performance parameters. The set of optimal solutions of the problem is given by determining the Pareto front of objective functions. The effectiveness of the proposed control scheme is evaluated via a series of numerical simulations in MATLAB and SIMULINK. The results are compared with those of the genetic algorithm and Ziegler–Nichols methods.

Keywords

• Congestion control
• PID controller
• Hermite–Biehler theorem
• Ant Colony Optimization
• Pareto optimality
• multi-objective optimization