Shifted robust multi-objective test problems

In 2013 Gaspar-Cunha et al. proposed a set of novel robust multi-objective benchmark functions to increase the difficulty of the current test problems and effectively mimic the characteristics of real search spaces. Despite the merits of the proposed benchmark problems, it is observed that the robust Pareto optimal fronts are located on the boundaries of the search space, which may result in the infeasibility of solutions obtained in case of perturbations along the negative side of the second parameter. This paper modifies the proposed test functions by Gaspar-Cunha et al. to mimic real problems better and allow the parameters to be fluctuated by any degree of perturbations. In fact, the robust fronts are shifted to the centre of the search space, so that any degree of uncertainties can be considered. The paper considers theoretical and experimental analysis of both set of test functions as well.