If an optimal solution is very sensitive to perturbations, then it may not be the most appropriate solution to use. In situations where natural variation is inevitable, it is therefore necessary to find a robust optimal solution. This paper examines emerging techniques for finding robust solutions to multiobjective optimisation problems. One of the major concerns in robust optimisation is that ...

The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large...

The uncertainty of transportation duration between nodes is an inherent characteristic and should be concerned in the routing optimization multimodal network to guarantee reliability delivery time. interval number used deal with duration, multi-objective robust model established which covers cost. To solve combinatorial problem this study, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) de...

The numerical results from a finite element (FE) model often differ from the experimental results of real structures. FE model updating is often required to identify and correct the uncertain parameters of FE model and is usually posed as an optimisation problem. Setting up of an objective function, selecting updating parameters and using robust optimisation algorithm are three crucial steps in...

Based on the definition of approximate solution (also known as $ \varepsilon $-solution), we propose idea generalized convexity semi-infinite optimization in this research. The nonsmooth sufficient and necessary criteria resilient solutions are then provided. Additionally, it is demonstrated that approximative assumption holds for both strong weak robust dual theorems. efficient cardinality/mea...

W propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and incorporate constraints that need to be feasible under perturbations. The proposed method iteratively moves along descent directions for the robust problem with nonconvex constraints and terminates at a robust local minimum. We generalize the algorithm further to m...

In this paper, we consider adjustable robust versions of convex optimization problems with uncertain constraints and objectives and show that under fairly general assumptions, a static robust solution provides a good approximation for these adjustable robust problems. An adjustable robust optimization problem is usually intractable since it requires to compute a solution for all possible realiz...