A Hybrid Optimization Approach For the Steiner k -Connected Network Design Problem Ibrahima Diarrassouba 1 Le Havre University, LMAH, FR-CNRS-3335, Le Havre, France Mohamed Khalil Labidi 2 University of Tunis el Manar - Faculty of Science of Tunis, URAPOP, UR13ZS38, Tunis, Tunisia & Paris Dauphine University - PSL Research University, CNRS UMR 7243, LAMSADE, 75016 Paris, France Ali Ridha Mahjoub 3 Paris Dauphine University - PSL Research University, CNRS UMR 7243, LAMSADE, 75016 Paris, France Abstract In this paper, we consider the Steiner k-Edge-Connected Network Design Prob- lem (SkESNDP). The problem finds its applications in the design of survivable telecommunications networks. We propose a parallel hybrid algorithm which aims to produce good solutions for large scale instances of the problem. Our approach is based on a Lagrangian relaxation of a flow-based integer programming formulation of the problem, a greedy and a genetic algorithms. Keywords: Lagrangian relaxation, large scale, genetic algorithm, hybridization, parallel computing, SkESNDP. Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 64 (2018) 305–314 1571-0653/© 2018 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm https://doi.org/10.1016/j.endm.2018.02.005