Using Stochastic Dominance in Multi-Objective Optimizers for Aerospace Design Under Uncertainty

In optimization under uncertainty for aerospace design, statistical moments of the quan- tity of interest are often treated as separate objectives and are traded off in a multi-objective optimization formulation. However, in many design problems the trade-off between sta- tistical moments can be large and the Pareto front representing this trade-off can include designs with undesirable behavior, such as being robust but being guaranteed to give a worse performance than another design. When a simulation of a system is computation- ally expensive, obtaining the full Pareto front is unfeasible and so spending optimization time obtaining such undesirable designs wastes time that could be spent obtaining more desirable alternatives. As a remedy, we propose an optimization formulation that can use multiple dominance criteria to avoid generating potentially inferior designs. We consider various orders of stochastic dominance as criteria to use alongside statistical moment based Pareto dominance, and illustrate how this gives rise to improved designs using a limited computational budget in an acoustic horn design problem and a transonic airfoil design problem.EPSRC DTA grant, grant number EP/L504920/

Optimization using multiple dominance criteria for aerospace design under uncertainty

In optimization under uncertainty for aerospace design, statistical moments of the quantity of interest are often treated as separate objectives and are traded off in a multi-objective optimization formulation. However, in many design problems the trade-off between statistical moments can be large and the Pareto front representing this trade-off can include designs with undesirable behavior, such as being robust but being guaranteed to give a worse performance than another design. When a simulation of a system is computationally expensive, obtaining the full Pareto front is infeasible and so spending optimization time obtaining such undesirable designs wastes time that could be spent obtaining more desirable alternatives. As a remedy, we propose an optimization formulation that can use multiple dominance criteria to avoid generating potentially inferior designs. We consider various orders of stochastic dominance as criteria to use alongside statistical moment based Pareto dominance, and illustrate how this gives rise to improved designs using a limited computational budget in an acoustic horn design problem and a transonic airfoil design problem.This work is part funded by the Engineering and Physical Sciences Research Council (EPSRC) UK, under grant number EP/L504920/1, with support from the Air Force Office of Scientific Research (AFOSR) MURI on managing multiple information sources of multi-physics systems, Program Manager Jean-Luc Cambier, Award Number FA9550-15-1-003

Horsetail matching: a flexible approach to optimization under uncertainty

It is important to design engineering systems to be robust with respect to uncertainties in the design process. Often, this is done by considering statistical moments, but over-reliance on statistical moments when formulating a robust optimization can produce designs that are stochastically dominated by other feasible designs. This article instead proposes a formulation for optimization under uncertainty that minimizes the difference between a design’s cumulative distribution function and a target. A standard target is proposed that produces stochastically non-dominated designs, but the formulation also offers enough flexibility to recover existing approaches for robust optimization. A numerical implementation is developed that employs kernels to give a differentiable objective function. The method is applied to algebraic test problems and a robust transonic airfoil design problem where it is compared to multi-objective, weighted-sum and density matching approaches to robust optimization; several advantages over these existing methods are demonstrated.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/L504920/1

Extending Horsetail Matching for Optimization Under Probabilistic, Interval and Mixed Uncertainties

This paper presents a new approach for optimization under uncertainty in the presence of probabilistic, interval, and mixed uncertainties, avoiding the need to specify probability distributions on uncertain parameters when such information is not readily available. Existing approaches for optimization under these types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Here, horsetail matching is extended for use with these types of uncertainties to overcome some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems, the design of a wing using a low-fidelity coupled aerostructural code, and the aerodynamic shape optimization of a wing using computational fluid dynamics analysis.This work was funded by the Engineering and Physical Sciences Research Council, grant number EP/L504920/1. The third author acknowledges support of the U.S. Air Force Office of Scientic Research Multidisciplinary Research Program of the University Research Initiative on managing multiple information sources of multiphysics systems, program manager Jean-Luc Cambier, award number FA9550-15-1-0038

Investigations on the Peach 4 Debrite, a Late Pleistocene Mass Movement on the Northwest British Continental Margin

The Peach 4 debrite is the most recent in a series of large scale Pleistocene MTDs within the Barra fan on the northwest British continental margin. Geophysical data indicate that Peach 4 was formed through a combination of blocky and muddy debris flows and affects an area of ~ 700 km2. BGS core sample 56 -10 36, located directly over the Peach 4 debrite, provides a minimum age of 14.68 ka cal BP for the last major failure. An upwards fining turbidite sequence in BGS core sample 56 -10 239 is associ-ated with increased As and S concentrations, indicators of diagenetic pyrite which forms under anoxic conditions. It is proposed that As and S concentrations may pro-vide a method of distinguishing between contourite and turbidite sedimentation, though further research is required

The Relationship Between HR Practices and Firm Performance: Examining Causal Order

Significant research attention has been devoted to examining the relationship between HR practices and firm performance, and the research support has assumed HR as the causal variable. Using data from 45 business units (with 62 data points), this study examines how measures of HR practices correlate with past, concurrent, and future operational performance measures. The results indicate that correlations with performance measures at all three times are both high and invariant, and that controlling for past or concurrent performance virtually eliminates the correlation of HR with future performance. Implications are discussed

How to find an attractive solution to the liar paradox

The general thesis of this paper is that metasemantic theories can play a central role in determining the correct solution to the liar paradox. I argue for the thesis by providing a specific example. I show how Lewis’s reference-magnetic metasemantic theory may decide between two of the most influential solutions to the liar paradox: Kripke’s minimal fixed point theory of truth and Gupta and Belnap’s revision theory of truth. In particular, I suggest that Lewis’s metasemantic theory favours Kripke’s solution to the paradox over Gupta and Belnap’s. I then sketch how other standard criteria for assessing solutions to the liar paradox, such as whether a solution faces a so-called revenge paradox, fit into this picture. While the discussion of the specific example is itself important, the underlying lesson is that we have an unused strategy for resolving one of the hardest problems in philosophy

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Yielding and irreversible deformation below the microscale: Surface effects and non-mean-field plastic avalanches

Nanoindentation techniques recently developed to measure the mechanical response of crystals under external loading conditions reveal new phenomena upon decreasing sample size below the microscale. At small length scales, material resistance to irreversible deformation depends on sample morphology. Here we study the mechanisms of yield and plastic flow in inherently small crystals under uniaxial compression. Discrete structural rearrangements emerge as series of abrupt discontinuities in stress-strain curves. We obtain the theoretical dependence of the yield stress on system size and geometry and elucidate the statistical properties of plastic deformation at such scales. Our results show that the absence of dislocation storage leads to crucial effects on the statistics of plastic events, ultimately affecting the universal scaling behavior observed at larger scales.Comment: Supporting Videos available at http://dx.plos.org/10.1371/journal.pone.002041

Mean-field cooperativity in chemical kinetics

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, the model is able to consistently recover all the various cooperative measures previously introduced, hence obtaining a single unifying framework. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of "susceptibility". We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model $p$-body interactions, whose non-trivial cooperative capability is investigated too.Comment: 25 pages, 4 figure