The SCIP Optimization Suite 4.0 (original) (raw)

2017

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 softwar...

The SCIP Optimization Suite 6.0

2018

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 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders' decomposition in a generic framework. GCG's detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders' framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver So-Plex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.

The SCIP Optimization Suite 8.0

2021

Enabling Research through the SCIP Optimization Suite 8.0

ACM Transactions on Mathematical Software

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP . The focus of this paper is on the role of the SCIP Optimization Suite in supporting research. SCIP ’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP ’s application as a research tool and as a platform for further developments. Further, the paper gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP .

A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space

We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in R n and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP problems to solve the ESTP. Our main emphasis is on isomorphism pruning, in order to prevent solving several equivalent subproblems corresponding to isomorphic Steiner trees. We introduce the concept of representative Steiner trees, which allows the pruning of these subproblems, as well as the implementation of procedures to fix variables and add valid inequalities. We also propose more general procedures to improve the efficiency of the b&b algorithm, which may be extended to the solution of other MINLP problems. Computational results demonstrate substantial gains compared to the standard b&b for convex MINLP.

Modular Optimizer for Mixed Integer Programming MOMIP Version 2.3

1996

The research described in this Working Paper was performed at the Institute of Informatics, Warsaw University (IIUW) as a part of IIASA CSA project activities on \Methodology and Techniques of Decision Analysis". While earlier work within this project resulted in the elaboration of prototype decision support systems (DSS) for various models, like the DINAS system for multiobjective transshipment problems with facility location developed in IIUW, these systems were closed in their architecture. In order to spread the scope of potential applications and to increase the ability to meet specic needs of users, in particular in various IIASA projects, there is a need to modularize the architecture of such DSS. A modular DSS consists of a collection of tools rather than one closed system, thus allowing the user to carry out various and problem-specic analyses.

Modular Optimizer for Mixed Integer Programming MOMIP Version 2.1

1994

The research described in this Working Paper was performed at the Institute of Informatics, Warsaw University (IIUW) as a part of IIASA CSA project activities on \Methodology and Techniques of Decision Analysis". While earlier work within this project resulted in the elaboration of prototype decision support systems (DSS) for various models, like the DINAS system for multiobjective transshipment problems with facility location developed in IIUW, these systems were closed in their architecture. In order to spread the scope of potential applications and to increase the ability to meet speci c needs of users, in particular in various IIASA projects, there is a need to modularize the architecture of such DSS. A modular DSS consists of a collection of tools rather than one closed system, thus allowing the user to carry out various and problem-speci c analyses.

A Computational Study for the Steiner Tree Problem with Revenue, Budget and Hop Constraints

HAL (Le Centre pour la Communication Scientifique Directe), 2013

We address the Steiner tree problem with revenues, budget and hop constraints (STPRBH), which is a generalization of the well-known Steiner tree problem. Given a connected undirected graph, a root node, edge costs and delays, nodes revenues, as well as a preset budget and hop, the STPRBH seeks to …nd a subtree that includes the root node, satis…es bound constraints on the total edge cost as well as the number of edges between any node and the root node, while maximizing the sum of the total node revenues. We focus on investigating polynomial-sized formulations. First, we propose an enhanced formulation based on the Miller-Tucker-Zemlin subtour constraints. Next, we investigate a nonlinear MIP formulation that is linearized using the Reformulation-Linearization Technique (RLT). We present the results of a comprehensive computational study of the proposed formulations. These result provide evidence that benchmark instances with up to 500 nodes can be e¤ectively solved using the proposed RLT-based formulation.

Solving the Steiner Tree Problem with Revenues,Budget and Hop Constraints to optimality

In : 2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO). IEEE conference, 2013

We investigate the Steiner tree problem with revenues , budget and hop constraints (STPRBH) on graph, which is a generalization of the well-known Steiner tree problem. Given a root node, edge costs, nodes revenues, as well as a preset budget and hop, the STPRBH seeks to find a subtree that includes the root node and maximizes the sum of the total edge revenues respecting the budget and hop constraints. These constraints impose limits on the total cost of the network and the number of edges between any vertex and the root. Not surprisingly, the STPRBH is NP-hard. For this challenging network design problem that arises in telecommunication settings and multicast routing, we present several polynomial size formulations. We propose an enhanced formulation based on the classical work of Miller, Tucker, and Zemlin by using additional set of variables representing the rank-order of visiting the nodes. Also, we investigate a new formulation for the STPRBH by tailoring a partial rank-1 of the Reformulation-Linearization Technique. Extensive results are exhibited using a set of benchmark instances to compare the proposed formulations by using a general purpose MIP solver.

Solving the bi-objective prize-collecting Steiner tree problem with the ϵ-constraint method

Electronic Notes in Discrete Mathematics, 2013

In this paper, we study the bi-objective prize-collecting Steiner tree problem, whose goal is to find a subtree that minimizes the edge costs for building that tree, and, at the same time, to maximize the collected node revenues. We propose to solve the problem using an ǫ-constraint algorithm. This is an iterative mixed-integerprogramming framework that identifies one solution for every point on the Pareto front. In this framework, a branch-and-cut approach for the single-objective variant of the problem is enhanced with warm-start procedures that are used to (i) generate feasible solutions, (ii) generate violated cutting planes, and (iii) guide the branching process. Standard benchmark instances from the literature are used to assess the efficacy of our method.

The SCIP Optimization Suite 4.0 (original) (raw)

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