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26-04
26-03
In this paper, we develop distributed and parallel general-purpose solvers for combinatorial optimization through the framework of domain-independent dynamic programming (DIDP), a model-based paradigm based on dynamic programming. In particular, we parallelize heuristic state space search algorithms to develop such solvers. Benefiting from the general-purpose nature of DIDP, we apply our solvers to four problem classes: the traveling salesperson problem with time windows (TSPTW), the type1 simple assembly line balancing problem (SALBP-1), the one-to-one multi-commodity pickup and delivery traveling salesperson problem (m-PDTSP), and the type2 assembly line balancing problem with sequence-dependent setup times (SUALBP-2). We demonstrate the scalability of our solvers using up to 192 TB of RAM and 49,152 CPU cores. Using the developed solvers, we close 14 open instances of TSPTW, 49 of m-PDTSP, and 152 of SUALBP-2.
26-01
We present a structure-aware parallel presolve framework specialized to arrowhead linear programs (AHLPs) and designed for high-performance computing (HPC) environments, integrated into the parallel interior point solver PIPS-IPM++. Large-scale LPs arising from automated model generation frequently contain redundancies and numerical pathologies that necessitate effective presolve, yet existing presolve techniques are primarily serial or structure-agnostic and can become time-consuming in parallel solution workflows.
Within PIPS-IPM++, AHLPs are stored in distributed memory, and our presolve builds on this to apply a highly parallel, distributed presolve across compute nodes while keeping communication overhead low and preserving the underlying arrowhead structure. We demonstrate the scalability and effectiveness of our approach on a diverse set of AHLPs and compare it against state-of-the-art presolve implementations, including PaPILO and the presolve implemented within Gurobi. Even on a single machine, our presolve significantly outperforms PaPILO by a factor of 18 and Gurobi’s presolve by a factor of 6 in terms of shifted geometric mean runtime, while reducing the problems by a similar amount to PaPILO. Using a distributed compute environment, we outperform Gurobi's presolve by a factor of 13.
25-19
Designing efficient energy systems is indispensable for shaping a more sustainable society. This involves making infrastructure investment decisions that must be valid for a long-term time horizon. While energy system optimization models constitute a powerful technique to support planning decisions, they need to cope with inherent uncertainty. For example, predicting future demand on a scale of decades is not only an intricate challenge in itself, but small fluctuations in such a forecast might also largely impact the layout of a complex energy system.
In this paper, we compare two methodologies of capturing demand uncertainty for linear-programming based energy system optimization models. On one hand, we generate and analyze catalogs of varying demand scenarios, where each individual scenario is considered independently, so that the optimization produces scenario-specific investment pathways. On the other hand, we make use of robust linear programming to meet the demand of all scenarios at once. Since including a multitude of scenarios increases the size and complexity of the optimization model, we will show how to use warm-starting approaches to accelerate the computation process, by exploiting the similar structure of the linear program across different demand inputs. This allows to integrate a meaningful number of demand scenarios with fully-fledged energy system models.
We demonstrate the practical use of our methods in a case study of the Berlin-Brandenburg area in Germany, a region that contains both a metropolitan area and its rural surroundings. As a backbone, we use the open-source framework oemof to create a sector-coupled optimization model for planning an energy system with up to 100% reduction of greenhouse gas emissions. This model features a fine-grained temporal resolution of one hour for the full year 2050. We consider uncertainty in demand for electricity, hydrogen, natural gas, central, and decentral heat.
Based on our computations, we analyze the trade-offs in terms of quality and computation time for scenario catalogs and the robust optimization approach. We further demonstrate that our procedure provides a valuable strategy for decision makers to gain insight on the robustness and sensitivity of solutions regarding demand variability.
25-13
For the yearly over 500,000 vehicle inspections of the German Federal Logistics and Mobility Office (BALM), crew rosters must be scheduled to efficiently achieve Germany's road inspection control targets. For that, we present a model to solve the respective duty scheduling and crew rostering problem in order to obtain duty rosters that comply with numerous legal regulations while maximizing the 'control success' to achieve the control targets. We formulate the Template Assignment Problem, which can be modelled as a large scale mixed-integer linear program. Here, feasible combinations of control topics are assigned to the duties using a hypergraph approach. The model is used in production by BALM, and we prove its effectiveness on a number of real-world instances.
25-17
Large-scale functional network time series model solved with mathematical programming approach
(2025)
A functional network autoregressive model is proposed for studying large-scale network time series observed at high temporal resolution. The model incorporates high-dimensional curves to capture both serial and cross-sectional dependence in large-scale network functional time series. Estimation of the model is approached using a Mixed Integer Optimization method. Simulation studies confirm the consistency of parameter and adjacency matrix estimation. The method is applied to data from a real-life natural gas supply network. Compared to alternative prediction models, the proposed model delivers more accurate day-ahead hourly out-of-sample forecasts of the gas inflows and outflows at most gas nodes.
25-18
Mixed-Integer Linear Programming (MIP) is applicable to such a wide range of real-world decision problems that the competition for the best code to solve such problems has lead to tremendous progress over the last decades. While current solvers can solve some of the problems that seemed completely out-of-reach just 10 years ago, there are always relevant MIP problems that currently cannot be solved. With the Smoothie solver we intend to solve extremely hard MIP problems by building on the many years that went into the development of several state-of-the-art MIP solvers and by utilizing some of the largest computing resources available. The high-level task parallelization framework UG (Ubiquity Generator) is used and extended by Smoothie to build a solver that uses large-scale parallelization to distribute the solution of a single MIP on a shared- or distributed-memory computing infrastructure, thereby employing several established MIP solvers simultaneously. For the first development phase, which is the topic of this report, both FICO Xpress and Gurobi are used in concurrent mode on a single machine, while information on incumbent solutions and explored branch-and-bound subtrees is exchanged. A dynamic restarting mechanism ensures that solver configurations are selected that promise most suitable for the MIP to be solved. We report on initial findings using this early version of Smoothie on unsolved problems from MIPLIB 2017.
25-16
Branching decisions play a crucial role in branch-and-bound algorithms for solving combinatorial optimization problems. In this paper, we investigate several branching rules applied to the Quota Steiner Tree Problem with Interference (QSTPI). The Quota Steiner Tree Problem (QSTP) generalizes the classical Steiner Tree Problem (STP) in graphs by seeking a minimum-cost tree that connects a subset of profit-associated vertices to meet a given quota. The extended version, QSTPI, introduces interference among vertices: Selecting certain vertices simultaneously reduces their individual contributions to the overall profit. This problem arises, for example, in positioning and connecting wind turbines, where turbines possibly shadow other turbines, reducing their energy yield. While exact solvers for standard STP-related problems often rely heavily on reduction techniques and cutting-plane methods – rarely generating large branch-and-bound trees – experiments reveal that large instances of QSTPI require significantly more branching to compute provably optimal solutions. In contrast to branching on variables, we utilize the combinatorial structure of the QSTPI by branching on the graph’s vertices. We adapt classical and problem-specific branching rules and present a comprehensive computational study comparing the effectiveness of these branching strategies.
25-15
The expressiveness of energy system optimization models (ESOMs) depends on a multitude of exogenous parameters. For example, sound estimates of the future energy demand are essential to enable qualified decisions on long-term investments. However, the enormous demand fluctuations even on a fine-grained scale diminish the computational performance of large-scale ESOMs. We therefore propose a clustering-and-decomposition method for linear programming based ESOMs that first identifies and solves prototypical demand scenarios with the dual simplex algorithm, and then composes dual optimal prototype bases to a warm-start basis for the full model. We evaluate the feasibility and computational efficiency our approach on a real-world case study, using a sector-coupled ESOM with hourly resolution for the Berlin-Brandenburg area in Germany, based on the oemof framework.
25-14
The timetable is a central pillar of any public transportation system. Constructing and optimizing periodic timetables in terms of passenger comfort and operational efficiency leads to NP-hard optimization problems that are also computationally challenging in applications. The Periodic Event Scheduling Problem (PESP) as standard mathematical tool benefits from its succinct formulation and rich combinatorial structure, but suffers from poor linear programming relaxations and weak dual bounds. These difficulties persist in a reduced version, where driving and dwelling activities of the lines are assumed to be fixed. In this case, fixing the initial departure time of each line fully determines the timetable, and for each pair of lines, the resulting (weighted) transfer durations can be expressed in terms of a piecewise linear non-convex function in terms of the difference of the initial times. When the number of activities between two lines is bounded, this function can be computed in polynomial time. By inserting precomputed piecewise linear functions into a mixed-integer program with the initial departure times as variables, we introduce an equivalent formulation for reduced PESP instances. The model bears analogies with quadratic semi-assignment approaches and offers alternative ways to compute primal and dual bounds. We evaluate the computational behavior of our approach on realistic benchmarking instances.