Showing papers by "Marc E. Pfetsch published in 2017"

The SCIP Optimization Suite 5.0

Abstract: This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG.

GasLib—A Library of Gas Network Instances

Abstract: The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML (extensible markup language) format. In this paper, we explain this format and present the instances that are available in the library.

The SCIP Optimization Suite 4.0

Abstract: The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences.

A compact formulation for the l21 mixed-norm minimization problem

Abstract: We present an equivalent, compact reformulation of the l 2,1 mixed-norm minimization problem for joint sparse signal reconstruction from multiple measurement vectors (MMVs). The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the joint sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the l 2,1 mixed-norm minimization and the atomic-norm minimization.

Joint active device identification and symbol detection using sparse constraints in massive MIMO systems

Abstract: In this paper, we consider a wireless system with a central station equipped with a large number of antennas surveilling a multitude of single antenna devices. The devices become active and transmit blocks of symbols sporadically. Our objective is to blindly identify the active devices and detect the transmit symbols. To this end, we exploit the sporadic nature of the device to station communication and formulate a sparse optimization problem as an integer program. Furthermore, we employ the convex relaxation of the discrete optimization variables in the problem in order reduce its computational complexity. A procedure to further lower the symbol detection errors is also discussed. Finally, the influence of system parameters on the performance of the proposed techniques is analysed using simulation results.

Geometry and topology optimization of sheet metal profiles by using a branch‐and‐bound framework

Abstract: In this paper well established procedures from partial differential equation (PDE)-constrained and discrete optimization are combined in a new way to find an optimal design of a multi-chambered profile. Given a starting profile design, a load case and corresponding design constraints (e.g. sheet thickness, chamber sizes), the aim is to find an optimal subdivision into a predefined number of chambers with optimal shape subject to structural stiffness. In the presented optimization scheme a branch-and-bound tree is generated with one additional chamber in each level. Before adding the next chamber, the geometry of the profile is optimized. Then a relaxation of a topology optimization problem is solved. Based on this relaxation, a best fitting feasible topology subject to manufacturability conditions is determined using a new mixed integer method employing shortest paths. To improve the running time, the finite element simulations for the geometry optimization and topology relaxation are performed with different levels of accuracy. Finally, numerical experiments are presented including different starting geometries, load scenarios and mesh sizes.

On the Complexity of Instationary Gas Flows

Abstract: We study a simplistic model of instationary gas flows consisting of a sequence of k stationary gas flows. We present efficiently solvable cases and NP-hardness results, establishing complexity gaps between stationary and instationary gas flows (already for k=2) as well as between instationary gas s-t-flows and instationary gas b-flows.

The Result: A New Design Paradigm

Abstract: One of the key challenges faced by engineers is finding, concretizing, and optimizing solutions for a specific technical problem in the context of requirements and constraints (Pahl et al. 2007). Depending on the technical problem’s nature, specifically designed products and processes can be its solution with product and processes depending on each other. Although products are usually modeled within the context of their function, consideration of the product’s life cycle processes is also essential for design. Processes of the product’s life cycle concern realization of the product (e.g., manufacturing processes), processes that are realized with the help of the product itself (e.g., use processes) and processes at the end of the product’s life cycle (recycling or disposal). Yet, not just product requirements have to be considered during product development, as requirements regarding product life cycle processes need to be taken into account, too. Provision for manufacturing process requirements plays an important role in realizing the product’s manufacturability, quality, costs, and availability (Chap. 3). Further life cycle demands, such as reliability, durability, robustness, and safety, result in additional product and life cycle process requirements. Consequently, the engineer’s task of finding optimal product and process solutions to solve a technical problem or to fulfill a customer need is characterized by high complexity, which has to be handled appropriately (Chaps. 5 and 6).

Finding the Best: Mathematical Optimization Based on Product and Process Requirements

Abstract: The challenge of finding the best solution for a given problem plays a central role in many fields and disciplines. In mathematics, best solutions can be found by formulating and solving optimization problems. An optimization problem consists of an objective function, optimization variables, and optimization constraints, all of which define the solution space. Finding the optimal solution within this space means minimizing or maximizing the objective function by finding the optimal variables of the solution. Problems, such as geometry optimization of profiles (Hess and Ulbrich 2012), process control for stringer sheet forming (Backer et al. 2015) and optimization of the production sequence for branched sheet metal products (Gunther and Martin 2006) are solved using mathematical optimization methods (Sects. 5.2 and 5.3). A variety of mathematical optimization methods is comprised within the field of engineering design optimization (EDO) (Roy et al. 2008).