scholarly journals Global optimization for the multilevel European gas market system with nonlinear flow models on trees

2022 ◽  
Author(s):  
Lars Schewe ◽  
Martin Schmidt ◽  
Johannes Thürauf
Keyword(s):  
Real World ◽  
Flow Model ◽  
Solution Process ◽  
Nonlinear Flow ◽  
Mixed Integer ◽  
Global Optimality ◽  
Convex Constraints ◽  
Gas Network ◽  
Flow Models ◽  
Gas Market

AbstractThe 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 another major challenge. These lead to nonlinear adjustable robust constraints that are computationally intractable in general. We provide techniques to equivalently reformulate these nonlinear adjustable constraints as finitely many convex constraints including integer variables in the case that the underlying network is tree-shaped. We further derive additional combinatorial constraints that significantly speed up the solution process. Using our results, we can recast the multilevel model as a single-level nonconvex mixed-integer nonlinear problem, which we then solve on a real-world network, namely the Greek gas network, to global optimality. Overall, this is the first time that the considered multilevel entry-exit system can be solved for a real-world sized network and a nonlinear flow model.

scholarly journals Optimization and validation of pumping system design and operation for water supply in high-rise buildings

2020 ◽  
Author(s):  
Tim M. Müller ◽  
Philipp Leise ◽  
Imke-Sophie Lorenz ◽  
Lena C. Altherr ◽  
Peter F. Pelz
Keyword(s):  
Water Supply ◽  
System Design ◽  
Real World ◽  
Solution Process ◽  
Solution Space ◽  
Computation Time ◽  
Mixed Integer ◽  
Linear Modeling ◽  
Piecewise Linearization ◽  
High Rise

Abstract The application of mathematical optimization methods for water supply system design and operation provides the capacity to increase the energy efficiency and to lower the investment costs considerably. We present a system approach for the optimal design and operation of pumping systems in real-world high-rise buildings that is based on the usage of mixed-integer nonlinear and mixed-integer linear modeling approaches. In addition, we consider different booster station topologies, i.e. parallel and series-parallel central booster stations as well as decentral booster stations. To confirm the validity of the underlying optimization models with real-world system behavior, we additionally present validation results based on experiments conducted on a modularly constructed pumping test rig. Within the models we consider layout and control decisions for different load scenarios, leading to a Deterministic Equivalent of a two-stage stochastic optimization program. We use a piecewise linearization as well as a piecewise relaxation of the pumps’ characteristics to derive mixed-integer linear models. Besides the solution with off-the-shelf solvers, we present a problem specific exact solving algorithm to improve the computation time. Focusing on the efficient exploration of the solution space, we divide the problem into smaller subproblems, which partly can be cut off in the solution process. Furthermore, we discuss the performance and applicability of the solution approaches for real buildings and analyze the technical aspects of the solutions from an engineer’s point of view, keeping in mind the economically important trade-off between investment and operation costs.

Mathematical modelling of salt purification by recrystallization. A cross-current flow model and its comparison with the countercurrent arrangement

1986 ◽  
Vol 51 (11) ◽  
pp. 2489-2501
Author(s):  
Benitto Mayrhofer ◽  
Jana Mayrhoferová ◽  
Lubomír Neužil ◽  
Jaroslav Nývlt
Keyword(s):  
Flow Model ◽  
Current Flow ◽  
Countercurrent Flow ◽  
Flow Models ◽  
Multi Stage ◽  
Stage Crystallization ◽  
The Cross ◽  
Current Flows ◽  
Set Up ◽  
Cross Current

A model is derived for a multi-stage crystallization with cross-current flows of the solution and the crystals being purified. The purity of the product is compared with that achieved in the countercurrent arrangement. A suitable function has been set up which allows the cross-current and countercurrent flow models to be compared and reduces substantially the labour of computation for the countercurrent arrangement. Using the recrystallization of KAl(SO4)2.12 H2O as an example, it is shown that, when the cross-current and countercurrent processes are operated at the same output, the countercurrent arrangement is more advantageous because its solvent consumption is lower.

scholarly journals Bi-objective design-for-control of water distribution networks with global bounds

2021 ◽  
Author(s):  
Aly-Joy Ulusoy ◽  
Filippo Pecci ◽  
Ivan Stoianov
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Mixed Integer ◽  
Global Optimality ◽  
Linear Programs ◽  
Design For Control ◽  
Non Linear ◽  
Feasible Solutions

AbstractThis manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

scholarly journals A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jianxun Cui ◽  
Shi An ◽  
Meng Zhao
Keyword(s):  
Flow Model ◽  
Time Window ◽  
Programming Model ◽  
Real Life ◽  
Minimum Cost ◽  
Emergency Evacuation ◽  
Mixed Integer ◽  
Fixed Cost ◽  
Minimum Cost Flow ◽  
Cost Flow

During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR) function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed-integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

A flexible mixed integer programming-based system for real-world nurse rostering

2021 ◽  
Author(s):  
Elín Björk Böðvarsdóttir ◽  
Niels-Christian Fink Bagger ◽  
Laura Elise Høffner ◽  
Thomas J. R. Stidsen
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Real World ◽  
Mixed Integer ◽  
Nurse Rostering

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

TAP Project

2004 ◽  
Author(s):  
Carlo Maria Spinelli ◽  
Furio Marchersani
Keyword(s):  
High Pressure ◽  
High Strength Steel ◽  
High Strength ◽  
Innovation Activity ◽  
Long Distance ◽  
Gas Network ◽  
Research And Innovation ◽  
Gas Market ◽  
High Pressure Pipeline ◽  
Very High

International gas market development is towards very long transportation distances (3000–6000 km); the only suitable onshore technology to conjugate economics, large amount of gas conveyed and possibility to exploit remote gas fields appears to be the Very High Pressure (P > 14 MPa), Very High Strength Steel (Steel grade X100 API 5L [1] equivalent) option. Eni Group is going to sponsor a 3 years long project, called TAP (Trasporto gas Alta Pressione) [High Pressure gas Transportation] aimed to demonstrate: • economic evaluation; • technology reliability; • real possibility to build Very High Pressure Pipeline. The project itself is framed into five logical areas: • Evaluation of the applicability of alternative technological solution in extreme enterprise; • Technological innovation, mainly within Eni Group; • FEED (Front End Engineering Development) for strategic route gas pipeline and comparison with LNG option; • Demonstrative construction of a High Strength Steel (X80) pipeline section on Snam Rete Gas Network in Italy; • Demonstrative construction of a Very High Strength Steel (X100 API equivalent) provisioning pilot section pipeline. To achieve this object Eni has involved: • Eni Gas & Power Division as Business Developer; • Snamprogetti as Technology Developer; • Aquater, Enidata, Enitecnologie, Saipem, Snam Rete Gas as specific item expertises; • CSM and Universita` di Bergamo as high qualified partners for lab and full scale testing; • Pipe steel makers and coating producers as fundamental partners to develop new solutions. TAP, within Eni Group, is the final step of a long development research and innovation activity started 8 years ago with two explorative “Long distance pipeline High Grade Steel” projects on Very High Strength Steel performances (strength, toughness, weldability) carried out mainly with the support of Snam, Snamprogetti and Saipem. TAP final goal is to collect, transfer, develop all the possible technological solutions to be ready for building “The pipeline network for Very High Pressure Transportation”.

scholarly journals A system of conservative regridding for ice/atmosphere coupling in a GCM

2013 ◽  
Vol 6 (4) ◽  
pp. 6493-6568 ◽  
Author(s):  
R. Fischer ◽  
S. Nowicki ◽  
M. Kelley ◽  
G. A. Schmidt
Keyword(s):  
Finite Element ◽  
General Circulation ◽  
Flow Model ◽  
Source Code ◽  
Circulation Model ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Flow Models ◽  
Ice Model

Abstract. The method of elevation classes has proven to be a useful way for a low-resolution general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields, for use in one-way studies coupling GCMs and ice flow models. Past uses of elevation classes have been a cause of non-conservation of mass and energy, caused by inconsistency in regridding schemes chosen to regrid to the atmosphere vs. downscaling to the ice model. This causes problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded, and five transformations between those grids required by a typical coupled GCM–ice flow model. This paper shows how each of those transformations may be achieved in a consistent, conservative manner. These transformations are implemented in GLINT2, a library used to couple GCMs with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.

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