Multi-objective optimization under uncertainly with real-time integrated decision making applied to structural engineering

One of the major tasks of structural engineering design optimization is the handling of uncertainties (such as variations in material properties, loading conditions, unknown environmental conditions or even uncertainties in modeling assumptions), which affect system performance in terms of robustness and reliability (or, in other words, the ability to respond to input variations with minimal alteration, loss of functionality or damage). This task is usually tackled with Optimization Under Uncertainty (OUU) methods[1], like robust design optimization and reliability-based design optimization. In most cases, the optimization has to deal with multi-objective problems (such as maximizing the performance while minimizing costs, system response variations, etc). These problems do not have a unique solution, but a set of tradeoff optimal solutions (the so-called Pareto front). The action of a decision maker (DM) is necessary for choosing the final optimal design according to some (pre-defined) preferences or criteria. Multi-Criteria Decision Making (MCDM) techniques[2] have been developed over the past years to try to make these choices objective and rational. In most MCDM methods, the preferences are usually taken into account during some a-posteriori analyses of the optimization outcomes. Here we address both OUU and MCDM problems with an approach that integrates directly the action of the DM with the optimization process. The DM is asked to express their preferences (based on their previous experience) to drive the optimization towards the most preferred regions of the Pareto front. This can lead to a more efficient exploration of specific regions of the Pareto front and reduce the computational cost of finding desirable solutions. Interactive MCDM approaches have been recently given more attention in the multi-objective optimization community [3, 4, 5]. A validation of this approach on simple test-cases is shown as well as its application to the design of a simple building structure under uncertainties with seismic hazard and snow loads.