Inverse optimal transport

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted by noise. In this paper we propose a systematic approach to infer unknown costs from noisy observations of optimal transportation plans. The algorithm requires only the ability to solve the forward optimal transport problem, which is a linear program, and to generate random numbers. It has a Bayesian interpretation, and may also be viewed as a form of stochastic optimization. We illustrate the developed methodologies using the example of international migration flows. Reported migration flow data captures (noisily) the number of individuals moving from one country to another in a given period of time. It can be interpreted as a noisy observation of an optimal transportation map, with costs related to the geographical position of countries. We use a graph-based formulation of the problem, with countries at the nodes of graphs and non-zero weighted adjacencies only on edges between countries which share a border. We use the proposed algorithm to estimate the weights, which represent cost of transition, and to quantify uncertainty in these weights

Genomic selection in rubber tree breeding: A comparison of models and methods for managing G×E interactions

Several genomic prediction models combining genotype × environment (G×E) interactions have recently been developed and used for genomic selection (GS) in plant breeding programs. G×E interactions reduce selection accuracy and limit genetic gains in plant breeding. Two data sets were used to compare the prediction abilities of multienvironment G×E genomic models and two kernel methods. Specifically, a linear kernel, or GB (genomic best linear unbiased predictor [GBLUP]), and a nonlinear kernel, or Gaussian kernel (GK), were used to compare the prediction accuracies (PAs) of four genomic prediction models: 1) a single-environment, main genotypic effect model (SM); 2) a multienvironment, main genotypic effect model (MM); 3) a multienvironment, single-variance G×E deviation model (MDs); and 4) a multienvironment, environment-specific variance G×E deviation model (MDe). We evaluated the utility of genomic selection (GS) for 435 individual rubber trees at two sites and genotyped the individuals via genotyping-by-sequencing (GBS) of single-nucleotide polymorphisms (SNPs). Prediction models were used to estimate stem circumference (SC) during the first 4 years of tree development in conjunction with a broad-sense heritability (H2) of 0.60. Applying the model (SM, MM, MDs, and MDe) and kernel method (GB and GK) combinations to the rubber tree data revealed that the multienvironment models were superior to the single-environment genomic models, regardless of the kernel (GB or GK) used, suggesting that introducing interactions between markers and environmental conditions increases the proportion of variance explained by the model and, more importantly, the PA. Compared with the classic breeding method (CBM), methods in which GS is incorporated resulted in a 5-fold increase in response to selection for SC with multienvironment GS (MM, MDe, or MDs). Furthermore, GS resulted in a more balanced selection response for SC and contributed to a reduction in selection time when used in conjunction with traditional genetic breeding programs. Given the rapid advances in genotyping methods and their declining costs and given the overall costs of large-scale progeny testing and shortened breeding cycles, we expect GS to be implemented in rubber tree breeding programs

Harnessing Flexible and Reliable Demand Response Under Customer Uncertainties

Demand response (DR) is a cost-effective and environmentally friendly approach for mitigating the uncertainties in renewable energy integration by taking advantage of the flexibility of customers' demands. However, existing DR programs suffer from either low participation due to strict commitment requirements or not being reliable in voluntary programs. In addition, the capacity planning for energy storage/reserves is traditionally done separately from the demand response program design, which incurs inefficiencies. Moreover, customers often face high uncertainties in their costs in providing demand response, which is not well studied in literature. This paper first models the problem of joint capacity planning and demand response program design by a stochastic optimization problem, which incorporates the uncertainties from renewable energy generation, customer power demands, as well as the customers' costs in providing DR. We propose online DR control policies based on the optimal structures of the offline solution. A distributed algorithm is then developed for implementing the control policies without efficiency loss. We further offer enhanced policy design by allowing flexibilities into the commitment level. We perform real world trace based numerical simulations. Results demonstrate that the proposed algorithms can achieve near optimal social costs, and significant social cost savings compared to baseline methods