We investigate the complexity of bilevel combinatorial optimization with uncertainty in follower's objective, a robust approach. show that counterpart problem under interval can be Σ2P-hard, even when certain is NP-equivalent and tractable. On contrary, discrete case, at most one level harder than problem.

This study has been inspired by the paper "An efficient 3D topology optimization code written in MATLAB” written by Liu and Tovar (2014) demonstrating that SIMP-based three-dimensional (3D) topology optimization of continuum structures can be implemented in 169 lines of MATLAB code. Based on the above paper, we show here that, by simple and easy-to-understand modificati...

An evaluated method based on Data envelopmentanalysis (DEA) to a second order conic robustcounterpart was developed and used to protect theperturbation of the output within an uncertaintyenvironment. This robust DEA was then evaluatedby studying the effect of the wood hardeningtreatment on the hybrid poplar clones. Thenumerical results indicated that the performa...

We propose a framework for robust modeling of linear programming problems using uncertainty sets described by an arbitrary norm. We explicitly characterize the robust counterpart as a convex optimization problem that involves the dual norm of the given norm. Under a Euclidean norm we recover the second order cone formulation in BenTal and Nemirovski [1, 2], El Ghaoui et al. [8, 9], while under ...

optimization of reservoir parameters is an important issue in petroleum exploration and production. the ant colony optimization(aco) is a recent approach to solve discrete and continuous optimization problems. in this paper, the ant colony optimization is usedas an intelligent tool to estimate reservoir rock properties. the methodology is illustrated by using a case study on shear wave velocity...

The problem of scheduling under bounded uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to mixed-integer linear programming (MILP) problems produces “robust” solutions which are in a sense immune against bounded uncertainty. Both the coefficients in the objective function, the left-hand-side parameters and the right-hand-side parameters of the in...

index tracking is the process of developing a portfolio that reproduces the performance of an index. the tracker portfolio has relatively good diversity and low turnover and low transaction costs. in this paper we applied a binary programming model for index tracking problem. in this model the number of assets for portfolio construction is defined by portfolio manager. the robust optimization f...

We consider combinatorial optimization problems with uncertain objective functions. In the min-max-min robust optimization approach, a fixed number k of feasible solutions is computed such that the respective best of them is optimal in the worst case. The idea is to calculate a set of candidate solutions in a potentially expensive preprocessing and then select the best solution out of this set ...

In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the duality theory for nonconvex quadratic programs (QPs), we reformulate the robust counterpart as a sem...

abstractaccidents and natural disasters and crises coming out of them indicate the importance of an integrated planning to reduce their effected. therefore, disaster relief logistics is one of the main activities in disaster management. in this paper, we study the response phase of the disaster management cycle and a bi-objective model has been developed for relief chain logistic in uncertainty...