This article proposes a probabilistic method that infers the transport modes and the physical paths of trips from smartphone data that were recorded during travels. This method synthesizes multiple kinds of data from smartphone sensors, which provide relevant location or transport mode information: global positioning system (GPS), Bluetooth, and accelerometer. The method is based on a smartphone measurement model that calculates the likelihood of observing the smartphone data in the multimodal transport network. The output of this probabilistic method is a set of candidate true paths and the probability of each path being the true one. The transport mode used on each arc is also inferred. Numerical experiments include map visualizations of some example trips and an analysis on the performance of the transport mode inference.

Derivative-free optimization (DFO) involves the methods used to minimize an expensive objective function when its derivatives are not available. We present here a trust-region algorithm based on Radial Basis Functions (RBFs). The main originality of our approach is the use of RBFs to build the trust-region models and our management of the interpolation points based on Newton fundamental polynomials. Moreover the complexity of our method is very attractive. We have tested the algorithm against the best state-of-the-art methods (UOBYQA, NEWUOA, DFO). The tests on the problems from the CUTEr collection show that BOOSTERS is performing very well on medium-size problems. Moreover, it is able to solve problems of dimension 200, which is considered very large in DFO.