Multi-objective optimisation using fuzzy logic

In a design process, it is often necessary to make a compromise decision between different performance requirements when the goal is to minimise or maximise several objectives simultaneously. For multi-objective optimisation there usually exists a group of optimum points known as the Pareto set of solutions. A common method of selecting the ideal solution from the Pareto set would be to assign weights to individual factors so that the overall solution represents a weighted mean of the Pareto set. However, the question remains as to how the weights are to be determined? Manual input requires extensive experience and expertise, and is impractical for on-line design optimisation. This paper presents an approach for solving multi-objective problems by means of fuzzy logic and square-error function. The proposed method seeks to solve multi-objective optimisation problems by combining several objectives into a single cost function. The optimisation technique comprises of two constituent parts. The first part is a fuzzy logic assessment module that serves to combine the user's specified performance objectives with the corresponding analytical predictions from a mathematical model to form a single-cost function. The second part is a hybrid multivariate optimisation algorithm that is capable of searching the global optimum based on a single cost function. Sugeno's fuzzy logic model is used to determine the weighting factors. A square-error function is also added to the cost function to ensure that the iteration process does not terminate prematurely due to slowly varying parameters. The method has been applied to the design and optimisation of single screw extruders as a case study. The results show that the proposed methodology offers potentially a cost-effective means to solve multi-objective design optimisation problems.