The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame

Risk-informed optimization of the tuned mass-damper-inerter (TMDI) for the seismic protection of multi-storey building structures

The tuned mass-damper-inerter (TMDI) is a recently proposed passive vibration suppression device that couples the classical tuned mass-damper (TMD), comprising a secondary mass attached to the structure via a spring and dashpot, with an inerter. The latter is a two-terminal mechanical device developing a resisting force proportional to the relative acceleration of its terminals by the “inertance” constant. In a number of previous studies, optimally tuned TMDIs have been shown to outperform TMDs in mitigating earthquake-induced vibrations in building structures for the same pre-specified secondary mass. TMDI design in these studies involved simplified modeling assumptions, such as adopting a single performance objective and/or modeling seismic excitation as stationary stochastic process. This paper extends these efforts by examining a risk-informed TMDI optimization, adopting multiple objectives and using response history analysis and probabilistic life-cycle criteria to quantify performance. The first performance criterion, representing overall direct benefits, is the life-cycle cost of the system, composed of the upfront TMDI cost and the anticipated seismic losses over the lifetime of the structure. The second performance criterion, introducing risk-aversion attitudes into the design process, is the repair cost with a specific return period (i.e., probability of exceedance over the lifetime of the structure). The third performance criterion, accounting for practical constraints associated with the size of the inerter and its connection to the structure, is the inerter force with a specific return period. A particular variant of the design problem is also examined by combining the first and third performance criteria/objectives. A case study involving a 21-storey building constructed in Santiago, Chile shows that optimal TMDI configurations can accomplish simultaneous reduction of life-cycle and repair costs. However, these cost reductions come at the expense of increased inerter forces. It is further shown that connecting the inerter to lower floors provides considerable benefits across all examined performance criteria as the inerter is engaged in a more efficient way for the same inerter coefficient and attached mass ratios

Probabilistic Seismic Loss Analysis for Design of Steel Structures - Optimizing for Multiple-Objective Functions

An optimized seismic performance-based design methodology considering structural and non-structural system performance and seismic losses is considered to design steel structures. Multi-objective optimization methodology is implemented considering various sets of optimization objectives which would take into account minimization of the initial construction cost, associated with the weight of the structural system, and the expected annual loss considering direct economic losses, and a social loss parameter defined as expected annual social loss. A non-dominated sorting genetic algorithm method is implemented for the multi-objective optimization. Achieving the desired confidence levels in meeting performance objectives of interest are set as constraints of the optimization problem. Inelastic time history analysis is used to evaluate structural response under different levels of earthquake hazard to obtain engineering demand parameters. Hazus fragility functions are employed for obtaining the damage probabilities for the structural system and non-structural components. The optimized designs and losses are compared for example steel structures, located in two geographic locations: Central United States and Western United States

Mixed-Variable Global Sensitivity Analysis For Knowledge Discovery And Efficient Combinatorial Materials Design

Global Sensitivity Analysis (GSA) is the study of the influence of any given inputs on the outputs of a model. In the context of engineering design, GSA has been widely used to understand both individual and collective contributions of design variables on the design objectives. So far, global sensitivity studies have often been limited to design spaces with only quantitative (numerical) design variables. However, many engineering systems also contain, if not only, qualitative (categorical) design variables in addition to quantitative design variables. In this paper, we integrate Latent Variable Gaussian Process (LVGP) with Sobol' analysis to develop the first metamodel-based mixed-variable GSA method. Through numerical case studies, we validate and demonstrate the effectiveness of our proposed method for mixed-variable problems. Furthermore, while the proposed GSA method is general enough to benefit various engineering design applications, we integrate it with multi-objective Bayesian optimization (BO) to create a sensitivity-aware design framework in accelerating the Pareto front design exploration for metal-organic framework (MOF) materials with many-level combinatorial design spaces. Although MOFs are constructed only from qualitative variables that are notoriously difficult to design, our method can utilize sensitivity analysis to navigate the optimization in the many-level large combinatorial design space, greatly expediting the exploration of novel MOF candidates.Comment: 35 Pages, 10 Figures, 2 Table