Csaba I. Fabian. Institute of Informatics, Kecskemét College, Kecskemét, Hungary.

Functions involving expectations, probabilities and risk measures typically occur in stochastic programming problems. This means large amounts of data to be organized, and inaccuracy in function evaluations. In this talk we discuss computational issues of decomposing two-stage problems, and of handling probabilistic constraints in static problems. We overview different solution approaches with a focus on convex problems. Specifically, enhanced cutting-plane methods will be described in primal and dual forms. To compare methods, we present several computational studies that were carried through in collaboration with different research teams. The importance of efficiency will be demonstrated in a case study.

Daniel Kuhn. École Polytechnique de Lausanne, Lausanne, Switzerland.

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this ball. We show that the resulting optimization problems can be solved efficiently and that their solutions enjoy powerful out-of-sample performance guarantees on test data. The wide applicability of this approach is illustrated with examples in portfolio selection, uncertainty quantification, statistical learning and inverse optimization.

Nenad Mladenovic. University of Valenciennes, Valenciennes, France.

(joint work with Brimberg J, Todosijevic R and Urosevic D)

The hub location problems consists of choosing hub locations from a set of nodes with pairwise traffic demands in order to route the traffic between the origin-destination pairs at minimum cost. The transportation between non-hub nodes is possible only via hub nodes to whom non-hub nodes are assigned. In this talk I will give possible classification of hub location problems and show how some of them could be solved by recent new variants of Variable neighborhood search metaheuristics.

Asgeir Tomasgard. Norwegian University of Science and Technology, Trondheim, Norway.

Mathematical programming is frequently used to analyse the effect of implementing various climate and energy policies. A common feature of these problems is that the best long-term strategies, consider co-optimization of investments and short-term system operation. To construct solutions robust to the uncertainty, stochastic programming is often the method of choice. In these models there are uncertainties present at different time-scales. In a power system, for instance, investments in generation capacity are done under uncertainty, about short-term operating conditions (load, prices, intermittent production), but also about long-term developments (fuel prices, demand growth, policy regulation). Representing all the uncertainty in a single multi-stage tree will quickly produce an intractable problem, but there is a way to cast the problem such that it does not immediately explode in size. By making the assumption that observing realizations of short-term operational uncertainty does not provide updated information about future uncertainty (both short-term and long-term) the operational decisions in one stage of the tree, can be decoupled from decisions in the following stages. The resulting tree then have two types of nodes, strategic nodes (representing investment stages) which are affected by future uncertainty, and operational nodes which are only affected by short-term uncertainty. This greatly reduces the size of the problem and is the essence of multi-horizon tree formulation in stochastic programming. We present the EMPIRE model (European Model for Power system Investment with Renewable Energy ). Further give examples on use of the model, illustrated by several studies performed in cooperation with the “European Technology Platform for Zero Emission Fossil Fuel Power Plants” in order to inform EC policy makers.