Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

We present a solution framework for general alternating current optimal power flow (AC OPF) problems that include discrete decisions. The latter occur, for instance, in the context of the curtailment of renewables or the switching of power generation units and transmission lines. Our approach delivers globally optimal solutions and is provably convergent. We model AC … Read more

Global Optimization for the Multilevel European Gas Market System with Nonlinear Flow Models on Trees

The European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is … Read more

On Refinement Strategies for Solving MINLPs by Piecewise Linear Relaxations: A Generalized Red Refinement

We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal in a mixed-integer nonlinear program (MINLP) context. We show that the red refinement meets sufficient convergence conditions for a known MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure … Read more

The confined primal integral

It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more

Improved optimization models for potential-driven network flow problems via ASTS orientations

The class of potential-driven network flow problems provides important models for a range of infrastructure networks that lead to hard-to-solve MINLPs in real-world applications. On large-scale meshed networks the relaxations usually employed are rather weak due to cycles in the network. To address this situation, we introduce the concept of ASTS orientations, a generalization of … Read more

Improving relaxations for potential-driven network flow problems via acyclic flow orientations

The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the usually employed relaxations are rather weak due to cycles … Read more

Γ-counterparts for robust nonlinear combinatorial and discrete optimization

Γ-uncertainty sets have been introduced for adjusting the degree of conservatism of robust counterparts of (discrete) linear programs. The contribution of this paper is a generalization of this approach to (mixed–integer) nonlinear optimization programs. We focus on the cases in which the uncertainty is linear or concave but also derive formulations for the general case. … Read more

Mixed-Integer Nonlinear Optimization for District Heating Network Expansion

We present a mixed-integer nonlinear optimization model for computing the optimal expansion of an existing tree-shaped district heating network given a number of potential new consumers. To this end, we state a stationary and nonlinear model of all hydraulic and thermal effects in the pipeline network as well as nonlinear models for consumers and the … Read more

The SCIP Optimization Suite 7.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies … Read more

Solving Mixed-Integer Nonlinear Optimization Problems using Simultaneous Convexification – a Case Study for Gas Networks

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each … Read more