Application-Driven Learning via Joint Prediction and Optimization of Demand and Reserves Requirement

Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In power systems, operators first forecast loads trying to minimize errors with respect to historical data. They also size reserve requirements based on error estimates. Next, energy and reserves are scheduled and the system is operated following the … Read more

A Bilevel Optimization Approach to Decide the Feasibility of Bookings in the European Gas Market

The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a … Read more

A Robust Approach for Modeling Limited Observability in Bilevel Optimization

In bilevel optimization, hierarchical optimization problems are considered in which two players – the leader and the follower – act and react in a non-cooperative and sequential manner. In many real-world applications, the leader may face a follower whose reaction deviates from the one expected by the leader due to some kind of bounded rationality. … Read more

A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and … Read more

The follower optimality cuts for mixed-integer linear bilevel programming problems

We address mixed-integer linear bilevel programming. A discussion ofthe relationships between the optimistic and the pessimistic setting ispresented, providing necessary and sufficient conditions for them to beequivalent. A new class of inequalities, the follower optimality cuts, isintroduced and a related single-level non-compact reformulation of theproblem is derived. The same is done for a revision of … Read more

Twenty years of continuous multiobjective optimization in the twenty-first century

The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some … Read more

An Exact Projection-Based Algorithm for Bilevel Mixed-Integer Problems with Nonlinearities

We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, \eg, products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level reformulation suitable for off-the-shelf solvers is not available in general. In order to solve these problems … Read more

Optimization under rare chance constraints

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe sampling and computational requirements on classical solution methods that render them impractical. This work proposes a novel sampling-free method for solving … Read more

Valid Inequalities for Mixed Integer Bilevel Linear Optimization Problems

Despite the success of branch-and-cut methods for solving mixed integer bilevel linear optimization problems (MIBLPs) in practice, there have remained some gaps in the theory surrounding these methods. In this paper, we take a first step towards laying out a theory of valid inequalities and cutting-plane methods for MIBLPs that parallels the existing theory for … Read more

On Linear Bilevel Optimization Problems with Complementarity-Constrained Lower Levels

We consider a novel class of linear bilevel optimization models with a lower level that is a linear program with complementarity constraints (LPCC). We present different single-level reformulations depending on whether the linear complementarity problem (LCP) as part of the lower-level constraint set depends on the upper-level decisions or not as well as on whether … Read more