Mechanical design, multiple criteria decision making and Pareto optimality gap

Abstract

Purpose We present an approach to multiple criteria mechanical design problems, for cases where problem complexity precludes derivation of the whole Pareto front. For such problems we propose to limit search, and hence also derivation, of the Pareto front exclusively to regions of the direct designer’s interest, thus saving on computing efforts and gaining on tractable problem sizes. Design/methodology/approach To achieve the purpose, we frame the decision making process (design) into a combination of three specific concepts, namely decision maker's preference capture, local Pareto front search and approximate multiobjective optimization with assessments of the Pareto optimality gap. We illustrate the approach with two small design problems, namely Pareto optimal round tube beam and Pareto optimal pneumatic high speed machine drive selection. We solve these problems in a setting which can be regarded as representative for problem solving in real environment. Findings On the decision making side, the proposed approach has turned out to be a versatile tool for selecting designs from the Pareto suboptimal ones, where each such a Pareto suboptimal design has an explicit assessment of the Pareto optimality gap. On the technical (optimization) side, it has been demonstrated that the approach seamlessly works with evolutionary computations, structured to the specific needs of the approach. Research limitations/implications It has been shown that the navigation over the Pareto front can be achieved with limited effort, both on the cognitive and the computing side. Moreover, navigation over the Pareto front can be focused from the very beginning of the design selection process on the regions of the Pareto front which are of the direct designer’s interest. This eliminates the need to derive (or only approximate) the whole Pareto front, a tangible asset as the derivation of that set is the main factor precluding scalability of design selection problems to higher dimensions (to higher problem sizes). Practical implications Because of the general formulation of the Pareto optimal design selection problem considered in the paper, the absence of any assumptions on its form and easiness of implementation of the underlying procedure of the proposed approach, the paper offers a clear option to approaches based on classical optimization computations. Originality/value The approach offers derivation of Pareto suboptimal designs with assessments of the Pareto optimality gap, whereas currently available multiobjective evolutionary optimization algorithms which derive Pareto suboptimal designs as well, offer no such assessments. Thus, the approach provides a firm ground to valuate designs resulting from approximate multiobjective optimization computations.