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CYCLIC m-DCI-GROUPS AND m-CI-GROUPS

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arXiv 2025年

作者： Kovács, István Šinkovec, Luka UP IAM University of Primorska Muzejski trg 2 KoperSI-6000 Slovenia UP FAMNIT University of Primorska Glagolǰaska ulica 8 KoperSI-6000 Slovenia

Based on the earlier work of Li (European J. Combin. 1997) and Dobson (Discrete Math. 2008), in this paper we complete the classification of cyclic m-DCI-groups and m-CI-groups. For a positive integer m such that m ≥ 3, we show that the group Zn is an m-DCI-group if and only if n is not divisible by 8 nor by p2 for any odd prime p n is an m-CI-group if and only if either n ∈ {8, 9, 18}, or n ∈/ {8, 9, 18} and n is not divisible by 8 nor by p2 for any odd prime p m-12MSC Codes 05C25, 20B25 © 2025, CC BY.

关键词： mixed-integer linear programming

The SCIP Optimization Suite 9.0

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arXiv 2024年

作者： Bolusani, Suresh Besançon, Mathieu Bestuzheva, Ksenia Chmiela, Antonia Dionísio, João Donkiewicz, Tim van Doornmalen, Jasper Eifler, Leon Ghannam, Mohammed Gleixner, Ambros Graczyk, Christoph Halbig, Katrin Hedtke, Ivo Hoen, Alexander Hojny, Christopher van der Hulst, Rolf Kamp, Dominik Koch, Thorsten Kofler, Kevin Lentz, Jurgen Manns, Julian Mexi, Gioni Mühmer, Erik Pfetsch, Marc E. Schlösser, Franziska Serrano, Felipe Shinano, Yuji Turner, Mark Vigerske, Stefan Weninger, Dieter Xu, Liding Gaul, Oliver Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany Université Grenoble Alpes Inria LIG Grenoble38000 France CMUP Department of Computer Science Faculty of Sciences University of Porto R Campo Alegre Porto4169-007 Portugal RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Eindhoven University of Technology Department of Mathematics and Computer Science P.O. Box 513 Eindhoven5600 MB Netherlands Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany Schenker AG Global Data & AI Kruppstr. 4 Essen45128 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands University of Bayreuth Universitaetsstr. 30 Bayreuth95440 Germany Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany Zuse Institute Berlin Department A2IM Takustr. 7 Berlin14195 Germany DAGOPT Optimization Technologies GmbH Austria Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany Fair Isaac Germany GmbH Takustr. 7 Berlin14195 Germany COPT GmbH Berlin Germany GAMS Software GmbH c/o Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Mathematics Cauerstr. 11 Erlangen91058 Germany École polytechnique LIX CNRR Rue Honoré d’Estienne d’Orves. 1 Palaiseau9120 France

MSC Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bugfixes. SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Hybrid optimal control with mixed-integer Lagrangian methods

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arXiv 2024年

作者： Nikitina, Viktoriya De Marchi, Alberto Gerdts, Matthias University of the Bundeswehr Munich Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing Neubiberg85577 Germany

Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to decomposition techniques, does not require relaxing the integrality constraints. Based on the discretize-then-optimize approach, our scheme addresses mixed-integer nonlinear problems under mild assumptions. The proposed numerical algorithm builds upon the augmented Lagrangian framework, whose subproblems are handled using successive mixed-integer linearizations with trust regions. We validate the performance of the numerical routine with extensive investigations using hybrid optimal control problems from different fields of application. Promising preliminary results are presented for a motion planning task with hysteresis and a Lotka-Volterra fishing problem with total *** Codes 65K05, 90C06, 90C11, 90C30 © 2024, CC BY.

关键词： mixed-integer linear programming

Assortment Optimization Under History-Dependent Effects

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arXiv 2024年

作者： He, Taotao Zhang, Yating Zheng, Huan Antai College of Economics and Management Shanghai Jiao Tong University Shanghai200030 China

This paper examines how to plan multi-period assortments when customer utility depends on historical assortments. We formulate this problem as a nonlinear integer programming problem and propose solution methodologies for different regimes of this problem. First, we present a sequential revenue-ordered policy and show that it is optimal when historical assortments positively affect customer utility. Second, we show that the problem is NP-hard under the presence of a negative history-dependent effect (such as a satiation effect). In this case, we propose using a lifting-based framework to reformulate the problem as a mixed-integer exponential cone program that state-of-the-art solvers can solve. Additionally, we identify an optimal cyclic policy for an asymptotic regime, and we also relate its length to the customer's memory length. Finally, we present a case study using a catering service dataset that shows that our model demonstrates good fitness and can effectively balance variety and revenue. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

All In: Give me your money!

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arXiv 2024年

作者： He, Angel Y. Holmes, Mark Department of Computer Science The University of Oxford United Kingdom School of Mathematics and Statistics The University of Melbourne Australia

We present a computer assisted proof for a result concerning a three player betting game, introduced by Angel and Holmes. The three players start with initial capital x, y, z > 0 respectively. At each step of this game two players are selected at random to bet on the outcome of a fair coin toss, with the size of the bet being the largest possible, namely the total capital held by the poorer of the two players at that time. The main quantity of interest is the probability of player 1 being eliminated (reaching 0 capital) first. Angel and Holmes have shown that this probability is not monotone decreasing as a function of the initial capital x of player 1. They conjecture that if x MSC Codes 60 © 2024, CC BY.

关键词： mixed-integer linear programming

Early Versus Late Traffic Management For Autonomous Agents

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arXiv 2024年

作者： Ghori, Salman Adil, Ania Feron, Eric KAUST Saudi Arabia

Intersections pose critical challenges in traffic management, where maintaining operational constraints and ensuring safety are essential for efficient flow. This paper investigates the effect of intervention timing in management strategies on maintaining operational constraints at intersections while ensuring safe separation distance, avoiding collisions, and minimizing delay. We introduce control regions, represented as circles around the intersection, which refers to the timing of interventions by a centralized control system when agents approach the intersection. We use a mixed-integer linear programming (MILP) approach to optimize the system’s performance. To analyze the effectiveness of early and late control measures, a simulation study is conducted, focusing on the safe, efficient, and robust management of agent movement within the control regions. © 2024, CC BY.

关键词： mixed-integer linear programming

A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic mixed-integer Problems

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arXiv 2024年

作者： Markhorst, Berend Leitner, Markus Berkhout, Joost Zocca, Alessandro van der Mei, Rob CWI stochastics department Science Park 123 Amsterdam1098 XG Netherlands VU mathematics department De Boelelaan 1105 Amsterdam1081 HV Netherlands Department of Operations Analytics Vrije Universiteit Amsterdam De Boelelaan 1105 Amsterdam1081 HV Netherlands

Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm ("Two-step warm start method Used for solving Large-scale stochastic mixed-integer Problems"), a two-step approach for solving two-stage stochastic (mixed) integer linear programs with an exponential number of constraints. In this approach, we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of TULIP on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. The results of our extensive numerical experiments show that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Enhancing the MILP/MIQCP-based Automatic Search for Differential-linear Distinguishers of Simon-Like Ciphers

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arXiv 2024年

作者： Chen, Siwei Xiang, Zejun Zeng, Xiangyong Qin, Guangxue School of Cyber Science and Technology Key Laboratory of Intelligent Sensing System and Security Hubei University Wuhan China Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University Wuhan China

In this paper, we propose an improved method based on mixed-integer linear programming/mixed-integer Quadratic Constraint programming (MILP/MIQCP) to automatically find better differential-linear (DL) distinguishers for the all members of Simon and Simeck block cipher families. To be specific, we first give the completely precise MILP model to describe the linear part, and explain how to utilize the general expressions of Gurobi solver to model the propagation of continuous difference for the middle part in a quite easy way. Secondly, in order to solve the MILP/MIQCP model in a reasonable time, we propose two heuristic strategies based on the divide-and-conquer idea to speed up the search process. Thirdly, we introduce the transforming technique, which exploits the clustering effect on DL trails, to improve the estimated correlation of the DL approximation. We apply our method to Simon and Simeck block cipher families. Consequently, we find the 14/17/21/26-round theoretical DL distinguishers of Simon 32/48/64/96, which extend the previous longest ones of Simon 32/48/96 by one round and Simon 64 by two rounds, respectively. For Simeck, we do not explore longer distinguishers compared to the currently best results, but refresh all the results of Zhou et al. (the first work to automate finding DL distinguishers for Simon-like ciphers using MILP/MIQCP). Besides, in order to validate the correctness of these distinguishers, the experimental verifications are conducted on Simon 32/Simeck 32 and Simon 48/Simeck 48. The results show that our theoretical estimations on correlations are very close to the experimental ones, which can be regarded as a concrete support for the effectiveness of our method. © 2024, CC BY.

关键词： mixed-integer linear programming

Risk-averse decision strategies for influence diagrams using rooted junction trees

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arXiv 2024年

作者： Herrala, Olli Terho, Topias Oliveira, Fabricio Department of Mathematics and Systems Analysis Aalto University School of Science FI-00076 Aalto Finland

This paper presents how a mixed-integer programming (MIP) formulation for influence diagrams, based on a gradual rooted junction tree representation of the diagram, can be generalized to incorporate risk considerations such as conditional value-at-risk and chance constraints. We present two algorithms on how targeted modifications can be made to the underlying influence diagram or to the gradual rooted junction tree representation to enable our reformulations. We present computational results comparing our reformulation with another MIP formulation for influence diagrams. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming