Diffusion equations for adaptive affine distributions

In this paper, we propose an extension of the adaptive diffusion technique for time-frequency representations proposed by Payot and Gonçalvès in 1998. Instead of processing time-frequency representations and keeping the covariance with respect to time and frequency shifts untouched, our adaptive filtering technique processes time-scale representations of the affine class while preserving the covariance properties of such representations. In order to obtain representations with improved readability, we aim at removing cumbersome interference terms while not blurring the signal terms. We show that the association of a conductance function to our diffusion scheme can make significant improvement toward reaching this goal. Indeed a conductance function provides a way to adapt locally the amount of smoothing to the representation. Note that the adaptivity of this affine technique is not based on any waveform dictionary as matching pursuit algorithms. 1

Multiobjective Capacitated Arc Routing Problem

Abstract. The Capacitated Arc Routing Problem (CARP) is a very hard vehicle routing problem raised for instance by urban waste collection. In addition to the total route length (the only criterion minimized in the academic problem), waste management companies seek to minimize also the length of the longest trip. In this paper, a bi-objective genetic algorithm is presented for this more realistic CARP, never studied before in literature. Based on the NSGA-II template, it includes two-key features: use of good constructive heuristics to seed the initial population and hybridization with a powerful local search procedure. This genetic algorithm is appraised on 23 classical CARP instances, with excellent results. For instance, for a majority of instances, its efficient solutions include an optimal solution to the academic CARP (minimization of the total route length). 1 Introduction: the CARP and its Applications The Capacitated Arc Routing Problem (CARP) is defined in the literature o