The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problemspecific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-ofthe-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances.

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 .

Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, various solution approaches have been employed, including decomposition methods and approximation techniques. There has been increasing interest in the development of efficient and accurate solution techniques to solve an integrated airline recovery problem. In this paper, an integrated airline recovery problem is developed, integrating the schedule, crew and aircraft recovery stages, and is solved using column-and-row generation. A general framework for column-and-row generation is presented as an extension of current generic methods. This extension considers multiple secondary variables and linking constraints and is proposed as an alternative solution approach to Benders' decomposition. The application of column-and-row generation to the integrated recovery problem demonstrates the improvement in the solution runtimes and quality compared to a standard column generation approach. Columnand-row generation improves solution runtimes by reducing the problem size and thereby achieving faster execution of each LP solve. As a result of this evaluation, a number of general enhancement techniques are identified to further reduce the runtimes of column-and-row generation. This paper also details the integration of the row generation procedure with branch-and-price, which is used to identify integral optimal solutions.

The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this article we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90% of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-JACK.Proof. First, note that both of the minima attained in (7) and (8) correspond to a path. Next, let t (1)min ) is minimal. The corresponding path between t i and t (1) min contains an edge {v j , v k }∈ (N(t i )) and since the