A Clustering-based uncertainty set for Robust Optimization

Robust Optimization (RO) is an approach to tackle uncertainties in the parameters of an optimization problem. Constructing an uncertainty set is crucial for RO, as it determines the quality and the conservativeness of the solutions. In this paper, we introduce an approach for constructing a data-driven uncertainty set through volume-based clustering, which we call Minimum-Volume … Read more

Quadratic Optimization Through the Lens of Adjustable Robust Optimization

Quadratic optimization (QO) has been studied extensively in the literature due to its applicability in many practical problems. While practical, it is known that QO problems are generally NP-hard. So, researchers developed many approximation methods to find good solutions. In this paper, we go beyond the norm and analyze QO problems using robust optimization techniques. … Read more

A New Dual-Based Cutting Plane Algorithm for Nonlinear Adjustable Robust Optimization

This paper explores a class of nonlinear Adjustable Robust Optimization (ARO) problems, containing here-and-now and wait-and-see variables, with uncertainty in the objective function and constraints. By applying Fenchel’s duality on the wait-and-see variables, we obtain an equivalent dual reformulation, which is a nonlinear static robust optimization problem. Using the dual formulation, we provide conditions under … Read more

Robust planning of production routing problem in closed-loop supply chain of beverage glass bottles

Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be … Read more

Robust location-transportation problems with integer-valued demand

A Location-Transportation (LT) problem concerns designing a company’s distribution network consisting of one central warehouse with ample stock and multiple local warehouses for a long but finite time horizon. The network is designed to satisfy the demands of geographically dispersed customers for multiple items within given delivery time targets. The company needs to decide on … Read more

Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective

In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this … Read more

Extending the Scope of Robust Quadratic Optimization

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In particular, we show how to reformulate the support functions of uncertainty sets represented in terms of matrix norms and cones. Our … Read more

Solving sparse polynomial optimization problems with chordal structure using the sparse, bounded-degree sum-of-squares hierarchy

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality … Read more

A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem

The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre, Toh, and Yang [EURO J. Comput. Optim., 2015] constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. Lasserre, Toh, and Yang prove that these lower bounds converge to the optimal value of the original … Read more

When are static and adjustable robust optimization with constraint-wise uncertainty equivalent?

Adjustable Robust Optimization (ARO) yields, in general, better worst-case solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we derive conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that if the uncertainty is constraint-wise and the adjustable variables lie … Read more