The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole. In this paper, such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique. The method is general and can be easily adapted to other linear PDEs and other types of boundary conditions.

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The aim of the topological sensitivity analysis is to derive an asymptotic expansion of a design functional with respect to a topological perturbation of the domain. In this paper, such an expansion is obtained for the 3D Maxwell equations when we introduce a small dielectric object in the domain and when we insert a small metallic obstacle. Some numerical results are presented in the context of buried object detection and shape inversion of 3D objects in free space from time-domain scattered field data.

The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a functional with respect to the creation of a small hole in the domain. In this paper such an expansion is obtained for the Helmholtz equation with a Dirichlet condition on the boundary of a circular hole. Some applications of this work to waveguide optimization are presented.

This paper investigates the Heterogeneous Dial-A-Ride Problem (H-DARP) that consists of determining a vehicle route planning for heterogeneous users' transportation with a heterogeneous fleet of vehicles. A hybrid Genetic Algorithm (GA) is proposed to solve the problem. Efficient construction heuristics, crossover operators and local search techniques, specifically tailored to the characteristics of the H-DARP, are provided. The proposed algorithm is tested on 92 benchmarks instances and 40 newly introduced larger instances. Computational experiments show the effectiveness of our approach compared to the current state-of-the-art algorithms for the DARP and H-DARP. When tested on the existing instances, we achieved average gaps of only 0.47% to the bestknown solutions for the DARP, and 0.05% to the optimal solutions for the H-DARP, compared to 0.85% and 0.10%, respectively, obtained by the current state-of-the-art algorithms. For the 40 newly generated instances, average gaps of the hybrid GA are 0.35% smaller compared to the current stateof-the-art method. Besides, our method provides best results for 31 of these instances and ties with the existing method on 8 other instances.

Abstract.In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations.It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized lake.Mathematics Subject Classification. 49Q10, 49Q12, 74P05, 74P10, 74P15.

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