Multi-Stage Robust Mixed-Integer Programming

Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more

Machine Learning for K-adaptability in Two-stage Robust Optimization

Two-stage robust optimization problems constitute one of the hardest optimization problem classes.One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizesdecisions corresponding to each of these subsets. In general case, it is solved using the … Read more

An adaptive robust optimization model for parallel machine scheduling

Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is completed and a machine becomes idle. Robust optimization is the natural methodology to cope with the first characteristic of duration … Read more

First-order algorithms for robust optimization problems via convex-concave saddle-point Lagrangian reformulation

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first order approaches, based on online-convex-optimization, have been proposed (Ben-Tal et al. (2015), Kilinc-Karzan and Ho-Nguyen … Read more

Piecewise constant decision rules via branch-and-bound based scenario detection for integer adjustable robust optimization

Multi-stage problems with uncertain parameters and integer decisions variables are among the most difficult applications of robust optimization (RO). The challenge in these problems is to find optimal here-and-now decisions, taking into account that the wait-and-see decisions have to adapt to the revealed values of the uncertain parameters. Postek and den Hertog (2016) and Bertsimas … Read more

Distributionally robust optimization with polynomial densities: theory, models and algorithms

In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much … Read more

Computing the channel capacity of a communication system affected by uncertain transition probabilities

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min … Read more

Bridging the gap between predictive and prescriptive analytics – new optimization methodology needed

Business analytics is becoming more and more important nowadays. Up to now predictive analytics appears to be much more applied in practice than prescriptive analytics. We argue that although optimization is used to obtain predictive models, and predictive tools are used to forecast parameters in optimization models, still the deep relation between the predictive and … Read more

Efficient methods for several classes of ambiguous stochastic programming problems under mean-MAD information

We consider decision making problems under uncertainty, assuming that only partial distributional information is available – as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be … Read more

Adjustable robust strategies for flood protection

Flood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management requires often to determine a cost-efficient protection strategy, i.e., one with lowest possible long run cost and satisfying flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges … Read more