Multiobjective Genetic Algorithms

Research Theme: Computational Design

The design of engineering systems involves the simultaneous consideration of multiple criteria or objectives. Often some of these objectives will be in conflict. Thus, a trade-off exists, which can be investigated by using multiobjective optimisation methods.

In such a problem, no single optimal solution exists, rather there is a set of equally valid optimal solutions, known as the Pareto-optimal set. The solutions in this set show the designer what is possible, allowing them to make a fully informed choice.

Motivation

There is widespread interest within the Engineering Design community in applying metaheuristic optimisation techniques, such as Multiobjective Genetic Algorithms (MOGAs), to real-world engineering design problems where other standard optimisation techniques are unsuccessful.

Objectives

  • To develop MOGA to search for robust Pareto-optimal solutions.
  • To develop tools for visualisation and selection among solutions in engineering design.
  • To implement different parallel variants of an existing multiobjective GA in order to reduce the computational time.

Method

Genetic Algorithms (GAs) are a stochastic global search method that mimics natural biological evolution. A GA operates on a population of potential solutions, applying Darwin's principle of survival of the fittest. GAs evolve populations of individuals that are better suited to their environment than the individuals that they were created from, just as in natural adaptation. The basic algorithm has been extended to solve problems with multiple objectives. The design philosophy of MOGAs is to develop a population of (near) Pareto-optimal solutions.

Findings

The use of multiobjective optimisation was motivated by the need to optimise various performance measures when designing a vehicle suspension: a model is depicted in Figure 2 (left-hand side). In Figure 1, the trade-off between ride comfort (J 1), tyre grip in response road disturbances (J 3), and rejection of external loads (J 5) is revealed. The three-dimensional plot shows that the Pareto front is a surface, which can be visualised with the help of the two-dimensional projections of the surface.

Details

The result of a multiobjective optimisation is a Pareto front, which is a set of competing solutions. However, the design implementation for a real-life problem will require a single solution. Assuming that the suspension design requires a solution with the best compromise between the objectives, parallel coordinates can be used to visualise such a solution, as in Figure 2, top-right corner. Each line joining the three objectives represents a solution. The x-axis represents the objectives and the y-axis shows normalized performance in the interval [0,1]. Crossing lines represent conflicting objectives. The best compromise design will be the one closest to a horizontal line across the three objectives and simultaneously with the minimum performance measure for the three objectives. The best choice for this suspension design problem is indicated with a black line, and marked with a " ¬ " in Figure 1. A realisation of this solution is given in Figure 2, bottom-right corner; this is a mechanical network composed of springs, dampers and inerters (a new mechanical element).

Acknowledgements

Support for this project was provided by the EPSRC.

Selected Publications

  • MOLINA-CRISTOBAL, A., PAPAGEORGIOU, C., PARKS, G.T., SMITH, M.C. and CLARKSON, P.J. (2006) 'Multi-objective Controller Design: Evolutionary Algorithms and Bilinear Matrix Inequalities for a Passive Suspension' in Proceedings of the IFAC Workshop on Control Applications of Optimization, Cachan, France, 386-391