A quasi-Monte Carlo method for multicriteria optimization.

Abstract

Multicriteria optimization (MCO) can become difficult when the number of criteria is large and when the design problem lies beyond intuitive comprehension. Solution sets are sparse and difficult to comprehend, and the iterations that often accompany the use of MCO methods become unwieldy. A MCO method is proposed that shifts much of the design effort to the computer. The Quasi-Random Weighted Criteria (QRWC) method is similar to existing methods but is more efficient and is particularly suited to aiding in selection between a finite set of design approaches. The method uses quasi-random sequences to direct a series of optimizations. Quasi-random sequences have been developed to cover a region efficiently and evenly. In the QRWC method they are used to generate a set of candidate solutions that are representative of the range of available solutions for each design approach. The explicit determination of parameter values to represent decision maker preferences, which is an intermediate step in most established methods, is eliminated. Instead, a preferred solution can be selected directly. Further applications of the method can be used to find additional candidate solutions near the selected point. In an anti-lock brake system (ABS) control design demonstration the method is used in the selection between three nonlinear control algorithms. Six performance criteria and four stochastic parameters are considered. After investigation of the theoretical utility of the method to ABS, an investigation of the practical implementation issues in using MCO methods for the design and regulation of ABS is undertaken. The method is demonstrated also on a gearbox design problem which requires selection between two hardware configurations. A weighted criteria MCO method is used with the proposed method. The established weighted criteria method cannot find all potentially desirable solutions. A new weighted criteria method is proposed and its solution is shown to be necessary and sufficient for desirable solutions. The concept of the meta Pareto set is introduced. This set is useful when considering the best solutions available from all strategies. When the strategies are control algorithms, consideration of the meta Pareto set may identify adaptive control opportunities.