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In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures.
This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.
In designing energy supply systems, designers are requested to rationally determine equipment types, capacities, and numbers in consideration of equipment operational strategies corresponding to seasonal and hourly variations in energy demands. However, energy demands have some uncertainty at the design stage, and the energy demands which become certain at the operation stage may differ from those estimated at the design stage. Therefore, designers should consider that energy demands have some uncertainty, evaluate the performance robustness against the uncertainty, and design the systems to heighten the robustness. Especially, this issue is important for cogeneration plants, because their performances depend significantly on both heat and power demands. Although robust optimal design methods of energy supply systems under uncertain energy demands were developed, all of them are based on linear models for energy supply systems. However, it is still a hard challenge to develop a robust optimal design method even based on a mixed-integer linear model. At the first step for this challenge, in this paper, a method of evaluating the performance robustness of energy supply systems under uncertain energy demands is proposed based on a mixed-integer linear model. This problem is formulated as a bilevel mixed-integer linear programming one, and a sequential solution method is applied to solve it approximately by discretizing uncertain energy demands within their intervals. In addition, a hierarchical optimization method in consideration of the hierarchical relationship between design and operation variables is applied to solve large scale problems efficiently. Through a case study on a gas turbine cogeneration plant for district energy supply, the validity and effectiveness of the proposed method and features of the performance robustness of the plant are clarified.
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 problem-specific. 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-of-the-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.
Portfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite it's simplicity portfolio parallelization has been shown to perform well for modern mixed-integer programming (MIP) and boolean satisfiability problem (SAT) solvers. Domain propagation has also been shown to be a simple technique in modern MIP and SAT solvers that effectively finds additional domain reductions after a variables domain has been reduced. This paper investigates the impact of distributed domain propagation in modern MIP solvers that employ portfolio parallelization. Computational experiments were conducted for two implementations of this parallelization approach. While both share global variable bounds and solutions they communicate differently. In one implementation the communication is performed only at designated points in the solving process and in the other it is performed completely asynchronously. Computational experiments show a positive performance impact of communicating global variable bounds and provide valuable insights in communication strategies for parallel solvers.
The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers.
This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.