Ian Griffin

Convergence Acceleration Operator for Multiobjective Optimization

A convergence acceleration operator (CAO) is described which enhances the search capability and the speed of convergence of the host multiobjective optimization algorithm. The operator acts directly in the objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). The suggested improved objective vectors are then mapped into the decision variable space and tested. This method improves upon prior work in a number of important respects, such as mapping technique and solution improvement. Further, the paper discusses implications for many-objective problems and studies the impact of the use of the CAO as the number of objectives increases. The CAO is incorporated with two leading MOEAs, the non-dominated sorting genetic algorithm and the strength Pareto evolutionary algorithm and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm while maintaining the desired distribution of solutions. It is shown that the operator is a transferable component that can be hybridized with any MOEA.

Multi-objective optimization approach to the ALSTOM gasifier problem

Abstract A control system design procedure based on the optimization of multiple objectives is used to realize the control design specifications of the linear gasification plant models. A multi-objective genetic algorithm (MOGA) is used in conjunction with an H∞ loop-shaping design procedure (LSDP) in order to satisfy the requirements of this critical system. The H∞ LSDP is used to guarantee the stability and robustness of the controller while its associated weighting matrix parameters are selected using the multi-objective search method in order to achieve performance requirements. A controller emerges which is stable but unable to completely meet some of the control objectives. Despite this shortcoming, the study is an excellent vehicle for introduction to an effective H∞ loop-shaping procedure. Further work, beyond the scope of this challenge has subsequently produced an improved controller design.

Multi-objective optimization approach to the PI tuning problem

This paper presents a simple PI control design approach for first order plus dead time processes. The design method aims to obtain good responses to setpoint and load disturbance signals, good robustness to model errors and small variation of the control signal, simultaneously. The design problem is formulated as a multi-objective optimization problem. Using multi-objective genetic algorithms, the optimization problem is solved and optimal PI tuning formulae are developed. Simulation results demonstrate the effectiveness of the proposed method in coping with conflicting design objectives.

A comparative study of progressive preference articulation techniques for multiobjective optimisation

Multiobjective optimisation has traditionally focused on problems consisting of 2 or 3 objectives. Real-world problems often require the optimisation of a larger number of objectives. Research has shown that conclusions drawn from experimentations carried out on 2 or 3 objectives cannot be generalized for a higher number of objectives. The curse of dimensionality is a problem that faces decision makers when confronted with many objectives. Preference articulation techniques, and especially progressive preference articulation (PPA) techniques are effective methods for supporting the decision maker. In this paper, some of the most recent and most established PPA techniques are examined, and their utility for tackling many-objective optimisation problems is discussed and compared from the viewpoint of the decision maker.

Linear matrix inequalities and evolutionary optimization in multiobjective control

The multiobjective problems of H 2 optimal control (LQG case) and mixed H 2/H ∞ are addressed using two different approaches: Evolutionary Algorithms and Linear Matrix Inequalities (LMIs). This study illustrates with numerical examples how both approaches can be used to find the trade-off between different signal sensitivities to noise and to find the trade-off of the mixed H 2/H ∞ problem. For the mixed H 2/H ∞ example, this paper shows how a Multiobjective Genetic Algorithm (MOGA) could find an improved Pareto-optimal front compared to the LMI approach.

Robust PI Controller for Load Disturbance Rejection and Setpoint Regulation

This paper presents an efficient numerical method to obtain optimal PI tuning formulae for first order plus dead time processes. The design method is based on optimal load disturbance rejection. In order to obtain a robust controller, a constraint on the maximum sensitivity is used. In addition, the design method deals with setpoint response using a two degree of freedom structure. In order to show the performance and effectiveness of the proposed tuning formulae, they are applied to two simulation examples

A hybrid multi-objective evolutionary algorithm using an inverse neural network for aircraft control system design

This study introduces a hybrid multi-objective evolutionary algorithm (MOEA) for the optimization of aircraft control system design. The strategy suggested is composed mainly of two stages. The first stage consists of training an artificial neural network (ANN) with objective values as inputs and decision variables as outputs to model an approximation of the inverse of the objective function used. The second stage consists of a local improvement phase in objective space preserving objectives relationships, and a mapping process to decision variables using the trained ANN. Both the hybrid MOEA and the original MOEA were applied to an aircraft control system design application for assessment

MULTIOBJECTIVE CONTROLLER DESIGN: OPTIMISING CONTROLLER STRUCTURE WITH GENETIC ALGORITHMS

Abstract This paper studies the open problem of reduced- and fixed-order H∞ synthesis. Often, this non-convex constraint is tackled with iterative convex optimisation procedure over LMI constraints. In this paper, an evolutionary approach is proposed such that the trial and error approach involved in LMI techniques might be overcome. The order of the controller is optimised as a multiobjective problem over a set of controller structures, H∞, and time-domain specifications. Numerical results are presented with its counterpart the LMI procedure design, that show the advantage of investigating the Pareto optimal set resulting from the design procedure proposed.

Hybrid multiobjective genetic algorithm with a new adaptive local search process

This paper is concerned with a specific brand of evolutionary algorithms: Memetic algorithms. A new local search technique with an adaptive neighborhood setting process is introduced and assessed against a set of test functions presenting different challenges. Two performance criteria were assessed: the convergence of the achieved results towards the true Pareto fronts and their distribution.

Robust H∞ Controller Design for Aircraft Lateral Dynamics using Multi-objective Optimization and Genetic Algorithms

Two techniques are combined during the design of an optimal controller: Linear Matrix Inequalities (LMIs) and Multi-objective Genetic Algorithms (MOGAs). In this paper the LMI optimization technique is used to obtain a single controller while MOGA is used to convert the controller design into a multi-objective optimization procedure. The combination of these techniques is proposed in this document and is shown to be advantageous against independent application of the aforementioned techniques. It is also presented how the sensitivity and complementary sensitivity functions are shaped with the weighting functions, while restricting the magnitude of the control signals by adding them as a hard objective in the MOGA approach.