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 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 (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
We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with \emph{non-Lipschitz-continuous} value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient … Read more
Stochastic mixed-integer nonlinear programming (MINLP) is a very challenging type of problem. Although there have been recent advances in developing decomposition algorithms to solve stochastic MINLPs, none of the existing algorithms can address stochastic MINLPs with continuous distributions. We propose a sample average approximation-based outer approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs … Read more
The design of water networks consists of selecting pipe connections and pumps to ensure a given water demand to minimize investment and operating costs. Of particular importance is the modeling of variable speed pumps, which are usually represented by degree two and three polynomials approximating the characteristic diagrams. In total, this yields complex mixed-integer (non-convex) … Read more
The application of mathematical optimization methods provides the capacity to increase the energy efficiency and to lower the investment costs of technical systems, considerably. We present a system approach for the optimization of the design and operation of pumping systems and exemplify it by applying it to the water supply of high-rise buildings. The underlying … Read more
Recently, Guan, Pan, and Zohu presented a MIP model for the thermal single- unit commitment claiming that provides an integer feasible solution for any convex cost function. In this note we provide a counterexample to this statement and we produce evidence that the perspective function is needed for this aim. Citation Research Report 19-03, Istituto … Read more
This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear Model Predictive Control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as … Read more