mixed-integer nonlinear programming – Page 2

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

Published: 2020/12/11, Updated: 2022/07/04

(Mixed) Integer Nonlinear Programming, Game Theory, Global Optimization bilevel optimization, global optimization, mixed-integer nonlinear programming, projection, strong duality

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

Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

Published: 2020/08/24, Updated: 2022/11/15

(Mixed) Integer Nonlinear Programming, Second-Order Cone Programming ac optimal power flow, curtailment of renewables, discrete decisions, generator switching, mixed-integer nonlinear programming, piecewise linear relaxation, second-order cone programming, transmission line switching

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

Published: 2020/08/21, Updated: 2021/09/20

Lars Schewe

Martin Schmidt

Johannes Thürauf

Applications - OR and Management Sciences, Global Optimization, Robust Optimization european entry-exit gas market, mixed-integer nonlinear programming, multiobjective optimization, nonlinear flows, robust optimization

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

Published: 2020/07/27, Updated: 2021/02/18

Robert Burlacu

(Mixed) Integer Nonlinear Programming incremental method, mixed-integer nonlinear programming, piecewise linear relaxation, 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

Published: 2020/07/20

Timo Berthold

Zsolt Csizmadia

(Mixed) Integer Nonlinear Programming, Optimization Software Benchmark mixed-integer nonlinear programming, optimization software, performance measure

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

Published: 2020/07/09

Kai Helge Becker

Benjamin Hiller

(Mixed) Integer Nonlinear Programming, Network Optimization asts orientations, bipolar orientations, combinatorial acyclicity models, mixed-integer nonlinear programming, potential-driven network flows

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

Published: 2020/06/20

Kai Helge Becker

Benjamin Hiller

(Mixed) Integer Nonlinear Programming, Network Optimization acyclic orientations, combinatorial acyclicity models, flow orientations, mixed-integer nonlinear programming, potential-driven network flows

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

Published: 2020/05/25, Updated: 2021/12/06

Dennis Adelhütte

Frauke Liers

Robust Optimization budget uncertainty, combinatorial optimization, discrete optimization, flexible gamma-approach, gamma-uncertainty, mixed-integer nonlinear programming, robust 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

Published: 2020/04/16, Updated: 2020/09/15

Marius Roland

Martin Schmidt

(Mixed) Integer Nonlinear Programming, Applications - Science and Engineering district heating networks, mixed-integer nonlinear programming, 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

Published: 2020/03/30

Matthias Miltenberger

(Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming benders decomposition, branch-and-cut, branch-and-price, column generation, constraint integer programming, linear programming, mixed-integer linear programming, mixed-integer nonlinear programming, mixed-integer semidefinite programming, optimization solver, parallelization, presolving, steiner tree optimization, tree size estimation

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