In this paper, we study the solution quality of robust optimization problems when they are used to approximate probabilistic constraints and propose a novel method to improve the quality. Two solution frameworks are first compared: (1) the traditional robust optimization framework which only uses the a priori probability bounds and (3) the approximation framework which uses the a posteriori pro...

The design of closed-loop logistics (forward and reverse logistics) has attracted growing attention with the stringent pressures of customer expectations, environmental concerns and economic factors. This paper considers a multi-product, multi-period and multi-objective closed-loop logistics network model with regard to facility expansion as a facility location–allocation problem, which more cl...

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior know...

In this paper we study Support Vector Machine(SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowled...

A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generat...

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization problems with expected value objectives and constraints where the underlying probability distributions are observed via limited data. This approach relies o...

An extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated studied theoretically We also design a computational procedure to solve numerically. The desired data that appeared the are considered be uncertain quantities, which treated according concept optimization. A discretization counterpart and solved obtain...