The paper deals with the design of resilient networks that are fault tolerant against link failures. Usually, fault tolerance is achieved by providing backup paths, which are used in case of an edge failure on a primary path. We consider this task as a multiobjective optimization problem: to provide resilience in networks while minimizing the cost subject to capacity constraint. We propose a stochastic approach, which can generate multiple Pareto solutions in a single run. The feasibility of the proposed method is illustrated by considering several network design problems using a single weighted average of objectives and a direct multiobjective optimization approach using the Pareto dominance concept.

This paper proposes a modified line search method which makes use of partial derivatives and re-starts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high dimensional benchmark functions, we illustrate that the proposed Line Search Re-Start (LSRS) approach is very suitable for high dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 10,000 dimensions clearly illustrate that the proposed approach performs very well for the tested high dimensional functions.