Set functions are widely used in many domains of Operations Research (cooperative game theory, decision under risk and uncertainty, combinatorial optimization) under different names (TU-game, capacity, nonadditive measure, pseudo-Boolean function, etc.). Remarkable families of set functions form polyhedra, e.g., the polytope of capacities, the polytope of p-additive capacities, the cone of supe...

This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (`, S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (`, S) inequalities to a general class of valid inequalities, called the (Q, SQ) inequalities, an...

Abstract: This paper deals with the robust lateral control to improve vehicle dynamic behavior. Bounded variations on longitudinal speed, front and rear tire stiffnesses are considered allowing the vehicle model to form a polytope of linear systems. In fact, the vehicle model depends affinely on the longitudinal speed and its inverse. Taking this dependence into account, the polytope is associa...

Data coming from real-world applications are very often affected by uncertainty. On the other hand, it is difficult to translate uncertainty in terms of combinatorial optimization. In this paper we study a combinatorial optimization model to deal with uncertainty in arc costs in shortest path problems. We consider a model where feasible arc cost scenarios are described via a convex polytope. We...

This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞ guaranteed cost of time-delay continuous-time linear time-invariant systems subjected to polytopic uncertainties. The proposed analysis approach is based on a branch-and-bound algorithm that incorporates a recent LMI-based analysis formulation and a new polytope partition strategy. In the branch-an...

A suucient LMI condition is proposed for checking robust stability of a polytope of polynomial matrices. It hinges upon two recent results: a new approach to polynomial matrix stability analysis and a new robust stability condition for convex polytopic uncertainty. Numerical experiments illustrate that the condition narrows signiicantly the unavoidable gap between conservative tractable quadrat...

here‎, ‎we aim to develop a new algorithm for solving a multiobjective linear programming problem‎. ‎the algorithm is to obtain a solution which approximately meets the decision maker's preferences‎. ‎it is proved that the proposed algorithm always converges to a weak efficient solution and at times converges to an efficient solution‎. ‎numerical examples and a simulation study are used to...

we consider the semigroup $s$ of highest weights appearing in tensor powers $v^{otimes k}$ of a finite dimensional representation $v$ of a connected reductive group. we describe the cone generated by $s$ as the cone over the weight polytope of $v$ intersected with the positive weyl chamber. from this we get a description for the asymptotic of the number of highest weights appearing in $v^{otime...

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formula...

objective: animal studies show that vaccination with epitope-based peptides results in protective immunity. however, immunodominance should be regarded as a major challenge in this area. considering the advantages of epitopic-vaccines against hepatitis c virus (hcv) infection, herein, we compared the occurrence of immunodominance following mice immunization with three different hcv epitopic-pep...