Robust inverse optimization

Given an observation of a decision-maker’s uncertain behavior, we develop a robust inverse optimization model for imputing an objective function that is robust against mis-specifications of the behavior. We characterize the inversely optimized cost vectors for uncertainty sets that may or may not intersect the feasible region, and propose tractable solution methods for special cases. We demonstrate the proposed model in the context of diet recommendation.     

Robust regression credibility: The influence function approach

In classical credibility theory we assume that the vector of claims conditionally on has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P. (Ed.), Credibility, Theory and Applications. Academic Press, New York) introduced regressors. The presence of large claims can perturb the credibility premium estimation. The lack of robustness of regression credibility estimators, as well as the fairness of tariff evaluation, led to the development of this paper. Our proposal is to apply robust statistics to the regression credibility estimation by using the robust influence function approach of M-estimators.     

Enhancing Built-in Electric Fields for Efficient Photocatalytic Hydrogen Evolution by Encapsulating C60 Fullerene into Zirconium-Based Metal-Organic Frameworks

High-efficiency photocatalysts based on metal-organic frameworks (MOFs) are often limited by poor charge separation and slow charge-transfer kinetics. Herein, a novel MOF photocatalyst is successfully constructed by encapsulating C₆₀ into a nano-sized zirconium-based MOF, NU-901. By virtue of host-guest interactions and uneven charge distribution, a substantial electrostatic potential difference is set-up in C₆₀@NU-901. The direct consequence is a robust built-in electric field, which tends to be 10.7 times higher in C₆₀@NU-901 than that found in NU-901. In the catalyst, photogenerated charge carriers are efficiently separated and transported to the surface. For example, photocatalytic hydrogen evolution reaches 22.3 mmol g⁻¹ h⁻¹ for C₆₀@NU-901, which is among the highest values for MOFs. Our concept of enhancing charge separation by harnessing host-guest interactions constitutes a promising strategy to design photocatalysts for efficient solar-to-chemical energy conversion.     

Improving Low-temperature Performance and Stability of Na2Ti6O13 Anodes by the Ti−O Spring Effect through Nb-doping

Na₂Ti₆O₁₃ (NTO) with high safety has been regarded as a promising anode candidate for sodium-ion batteries. In the present study, integrated modification of migration channels broadening, charge density re-distribution, and oxygen vacancies regulation are realized in case of Nb-doping and have obtained significantly enhanced cycling performance with 92 % reversible capacity retained after 3000 cycles at 3000 mA g⁻¹. Moreover, unexpected low-temperature performance with a high discharge capacity of 143 mAh g⁻¹ at 100 mA g⁻¹ under −15 °C is also achieved in the full cell. Theoretical investigation suggests that Nb preferentially replaces Ti3 sites, which effectively improves structural stability and lowers the diffusion energy barrier. What's more important, both the in situ X-ray diffraction (XRD) and in situ Raman furtherly confirm the robust spring effect of the Ti−O bond, making special charge compensation mechanism and respective regulation strategy to conquer the sluggish transport kinetics and low conductivity, which plays a key role in promoting electrochemical performance.     

Clustering Multivariate Longitudinal Observations: The Contaminated Gaussian Hidden Markov Model

The Gaussian hidden Markov model (HMM) is widely considered for the analysis of heterogenous continuous multivariate longitudinal data. To robustify this approach with respect to possible elliptical heavy-tailed departures from normality, due to the presence of outliers, spurious points, or noise (collectively referred to as bad points herein), the contaminated Gaussian HMM is here introduced. The contaminated Gaussian distribution represents an elliptical generalization of the Gaussian distribution and allows for automatic detection of bad points in the same natural way as observations are typically assigned to the latent states in the HMM context. Once the model is fitted, each observation has a posterior probability of belonging to a particular state and, inside each state, of being a bad point or not. In addition to the parameters of the classical Gaussian HMM, for each state we have two more parameters, both with a specific and useful interpretation: one controls the proportion of bad points and one specifies their degree of atypicality. A sufficient condition for the identifiability of the model is given, an expectation-conditional maximization algorithm is outlined for parameter estimation and various operational issues are discussed. Using a large-scale simulation study, but also an illustrative artificial dataset, we demonstrate the effectiveness of the proposed model in comparison with HMMs of different elliptical distributions, and we also evaluate the performance of some well-known information criteria in selecting the true number of latent states. The model is finally used to fit data on criminal activities in Italian provinces. Supplementary materials for this article are available online     

A discussion on the conservatism of robust linear optimization problems

In 2004, Bertsimas and Sim proposed a robust approach that can control the degree of conservatism by applying a limitation Γ to the maximum number of parameters that are allowed to change. However, the robust approach can become extremely conservative even when Γ is relatively small. In this paper, we provide a theoretical analysis to explain why this extreme conservatism occurs. We further point out that the robust approach does not reach an extremely conservative state when Γ is less than k, where k is the number of nonzero components of the optimal solution of the extremely conservative robust approach. This research also shows that care must be taken when adjusting the value of Γ to control the degree of conservatism because the approach may result in greater conservatism than was intended. We subsequently apply our analysis to additive combinatorial optimization problems. Finally, we illustrate our results on numerical simulations.     

Robust Stability and Performance Analysis of Uncertain Systems Using Linear Matrix Inequalities

A wide variety of problems in system and control theory can be formulated or reformulated as convex optimization problems involving linear matrix inequalities (LMIs), that is, constraints requiring an affine combination of symmetric matrices to be positive semidefinite. For a few very special cases, there are analytical solutions to these problems, but in general LMI problems can be solved numerically in a very efficient way. Thus, the reduction of a control problem to an optimization problem based on LMIs constitutes, in a sense, a solution to the original problem. The objective of this article is to provide a tutorial on the application of optimization based on LMIs to robust control problems. In the first part of the article, we provide a brief introduction to optimization based on LMIs. In the second part, we describe a specific example, that of the robust stability and performance analysis of uncertain systems, using LMI optimization.     

US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.     

A minmax regret approach to the critical path method with task interval times

The execution of a given project, with a number of interrelated tasks due to precedence constraints, represents a challenge when one must to control the available resources and the compromised due dates. In this paper, we analyse this problem under uncertain individual task completing times, specifically, we will assume that a given range, for the admissible values of each individual completing time, is available. Taking into account that the precedence relations between tasks must be preserved, each realization of the admissible execution times for the set of tasks will define a new scenario determining the ending time for the project and the subset of critical tasks.