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Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature.
Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature.
SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively parallel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best-known solutions to instances from the benchmark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been considerably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB.
SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively par- allel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best known solutions to instances from the bench- mark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been con- siderably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB.
This paper introduces an implementation for solving the single-source shortest path problem on distributed-memory machines. It is tailored to power-law graphs and scales to trillions of edges.
The new implementation reached 2nd and 10th place in the latest Graph500 benchmark in June 2022 and handled the largest and second-largest graphs among all participants.
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 article 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. Furthermore, this article 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.
The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years. This article aims to advance the state of the art in the exact solution of both problems—by using mathematical programming techniques. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse maximum-cut and quadratic unconstrained binary optimization instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.
On the state of QUBO solving
(2023)
It is regularly claimed that quantum computers will bring breakthrough progress in solving challenging combinatorial
optimization problems relevant in practice. In particular, Quadratic Unconstrained Binary Optimization
(QUBO) problems are said to be the model of choice for use in (adiabatic) quantum systems during the noisy intermediate-
scale quantum (NISQ) era. Even the first commercial quantum-based systems are advertised to solve
such problems. Theoretically, any Integer Program can be converted into a QUBO. In practice, however, there are
some caveats, as even for problems that can be nicely modeled as a QUBO, this might not be the most effective
way to solve them. We review the state of QUBO solving on digital and quantum computers and provide insights
regarding current benchmark instances and modeling.