TY - CHAP A1 - Sofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - An Algorithm-Independent Measure of Progress for Linear Constraint Propagation T2 - 27th International Conference on Principles and Practice of Constraint Programming (CP 2021) N2 - Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure -- independently of the algorithmic design -- the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported. Y1 - 2021 U6 - https://doi.org/10.4230/LIPIcs.CP.2021.52 VL - 210 SP - 52:1 EP - 52:17 ER - TY - JOUR A1 - Hoppmann-Baum, Kai T1 - On the Complexity of Computing Maximum and Minimum Min‐Cost‐Flows JF - Networks N2 - Consider a flow network, i.e., a directed graph where each arc has a nonnegative capacity value and an associated length, together with nonempty supply intervals for the sources and nonempty demand intervals for the sinks. The Maximum Min-Cost-Flow Problem (MaxMCF) is to find fixed supply and demand values within these intervals such that the optimal objective value of the induced Min-Cost-Flow Problem (MCF) is maximized. In this paper, we show that MaxMCF as well as its uncapacitated variant, the Maximum Transportation Problem (MaxTP), are NP-hard. Further, we prove that MaxMCF is APX-hard if a connectedness-condition regarding the sources and the sinks of the flow network is dropped. Finally, we show how the Minimum Min-Cost-Flow Problem (MinMCF) can be solved in polynomial time. Y1 - 2021 U6 - https://doi.org/10.1002/net.22060 ER - TY - CHAP A1 - Sofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices T2 - 2020 IEEE/ACM 10th Workshop on Irregular Applications: Architectures and Algorithms (IA3) N2 - Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, more generally, on parallel architectures challenging. This is one of the main reasons why domain propagation in state-of-the-art solvers is single thread only. In this paper, we present a new algorithm for domain propagation which (a) avoids these problems and allows for an efficient implementation on GPUs, and is (b) capable of running propagation rounds entirely on the GPU, without any need for synchronization or communication with the CPU. We present extensive computational results which demonstrate the effectiveness of our approach and show that ample speedups are possible on practically relevant problems: on state-of-the-art GPUs, our geometric mean speed-up for reasonably-large instances is around 10x to 20x and can be as high as 195x on favorably-large instances. Y1 - 2020 U6 - https://doi.org/10.1109/IA351965.2020.00007 N1 - URL of the Slides: https://app.box.com/s/qy0pjmhtbm7shk2ypxjxlh2sj4nudvyu N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2020/09/20/gpu-prob.html SP - 1 EP - 11 ER - TY - JOUR A1 - Šofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - Accelerating domain propagation: An efficient GPU-parallel algorithm over sparse matrices JF - Parallel Computing N2 - • Currently, domain propagation in state-of-the-art MIP solvers is single thread only. • The paper presents a novel, efficient GPU algorithm to perform domain propagation. • Challenges are dynamic algorithmic behavior, dependency structures, sparsity patterns. • The algorithm is capable of running entirely on the GPU with no CPU involvement. • We achieve speed-ups of around 10x to 20x, up to 180x on favorably-large instances. Y1 - 2022 U6 - https://doi.org/10.1016/j.parco.2021.102874 VL - 109 SP - 102874 ER - TY - JOUR A1 - Ramin, Elham A1 - Bestuzheva, Ksenia A1 - Gargalo, Carina A1 - Ramin, Danial A1 - Schneider, Carina A1 - Ramin, Pedram A1 - Flores-Alsina, Xavier A1 - Andersen, Maj M. A1 - Gernaey, Krist V. T1 - Incremental design of water symbiosis networks with prior knowledge: The case of an industrial park in Kenya JF - Science of the Total Environment N2 - Industrial parks have a high potential for recycling and reusing resources such as water across companies by creating symbiosis networks. In this study, we introduce a mathematical optimization framework for the design of water network integration in industrial parks formulated as a large-scale standard mixed-integer non-linear programming (MINLP) problem. The novelty of our approach relies on i) developing a multi-level incremental optimization framework for water network synthesis, ii) including prior knowledge of demand growth and projected water scarcity to evaluate the significance of water-saving solutions, iii) incorporating a comprehensive formulation of water network synthesis problem including multiple pollutants and different treatment units and iv) performing a multi-objective optimization of the network including freshwater savings and relative cost of the network. The significance of the proposed optimization framework is illustrated by applying it to an existing industrial park in a water-scarce region in Kenya. Firstly, we illustrated the benefits of including prior knowledge to prevent an over-design of the network at the early stages. In the case study, we achieved a more flexible and expandable water network with 36% lower unit cost at the early stage and 15% lower unit cost at later stages for the overall maximum freshwater savings of 25%. Secondly, multi-objective analysis suggests an optimum freshwater savings of 14% to reduce the unit cost of network by half. Moreover, the significance of symbiosis networks is highlighted by showing that intra-company connections can only achieve a maximum freshwater savings of 17% with significantly higher unit cost (+45%). Finally, we showed that the values of symbiosis connectivity index in the Pareto front correspond to higher freshwater savings, indicating the significant role of the symbiosis network in the industrial park under study. This is the first study, where all the above elements have been taken into account simultaneously for the design of a water reuse network. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1016/j.scitotenv.2020.141706 VL - 751 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning JF - Algorithms N2 - We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach. KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - https://doi.org/10.3390/a14010004 SN - 1438-0064 VL - 14 IS - 1 SP - 4 PB - MDPI ER -