TY - THES A1 - Mexi, Gioni T1 - Node Partitioning and Subtours Creation Problem (NPSC) Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77094 ER - TY - CHAP A1 - Hoppmann-Baum, Kai A1 - Mexi, Gioni A1 - Burdakov, Oleg A1 - Casselgren, Carl Johan A1 - Koch, Thorsten ED - Hebrard, Emmanuel ED - Musliu, Nysret T1 - Minimum Cycle Partition with Length Requirements T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research N2 - In this article we introduce a Minimum Cycle Partition Problem with Length Requirements (CPLR). This generalization of the Travelling Salesman Problem (TSP) originates from routing Unmanned Aerial Vehicles (UAVs). Apart from nonnegative edge weights, CPLR has an individual critical weight value associated with each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is regarded as a feasible solution if the length of each cycle, which is the sum of the weights of its edges, is not greater than the critical weight of each of its vertices. The goal is to find a feasible partition, which minimizes the number of cycles. In this article, a heuristic algorithm is presented together with a Mixed Integer Programming (MIP) formulation of CPLR. We furthermore introduce a conflict graph, whose cliques yield valid constraints for the MIP model. Finally, we report on computational experiments conducted on TSPLIB-based test instances. Y1 - 2020 SN - 978-3-030-58941-7 U6 - https://doi.org/10.1007/978-3-030-58942-4_18 VL - 12296 SP - 273 EP - 282 PB - Springer International Publishing CY - Cham ER - TY - GEN A1 - Hoppmann-Baum, Kai A1 - Mexi, Gioni A1 - Burdakov, Oleg A1 - Casselgren, Carl Johan A1 - Koch, Thorsten T1 - Length-Constrained Cycle Partition with an Application to UAV Routing N2 - In this article, we discuss the Length-Constrained Cycle Partition Problem (LCCP). Besides edge weights, the undirected graph in LCCP features an individual critical weight value for each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is a feasible solution if the length of each cycle is not greater than the critical weight of each of the vertices in the cycle. The goal is to find a feasible partition with the minimum number of cycles. In this article, we discuss theoretical properties, preprocessing techniques, and two mixed-integer programming models (MIP) for LCCP both inspired by formulations for the closely related Travelling Salesperson Problem (TSP). Further, we introduce conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a report on computational experiments conducted on (A)TSPLIB-based instances. As an example, we use a routing problem in which a fleet of uncrewed aerial vehicles (UAVs) patrols a set of areas. T3 - ZIB-Report - 20-30 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-80489 SN - 1438-0064 ER - TY - THES A1 - Mexi, Gioni T1 - New Ideas for the Feasibility Pump: Using Multiple Reference Vectors Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83724 ER - TY - JOUR A1 - Hoppmann-Baum, Kai A1 - Burdakov, Oleg A1 - Mexi, Gioni A1 - Casselgren, Carl Johan A1 - Koch, Thorsten T1 - Length-Constrained Cycle Partition with an Application to UAV Routing JF - Optimization Methods and Software N2 - This article discusses the Length-Constrained Cycle Partition Problem (LCCP), which constitutes a new generalization of the Travelling Salesperson Problem (TSP). Apart from nonnegative edge weights, the undirected graph in LCCP features a nonnegative critical length parameter for each vertex. A cycle partition, i.e., a vertex-disjoint cycle cover, is a feasible solution for LCCP if the length of each cycle is not greater than the critical length of each vertex contained in it. The goal is to find a feasible partition having a minimum number of cycles. Besides analyzing theoretical properties and developing preprocessing techniques, we propose an elaborate heuristic algorithm that produces solutions of good quality even for large-size instances. Moreover, we present two exact mixed-integer programming formulations (MIPs) for LCCP, which are inspired by well-known modeling approaches for TSP. Further, we introduce the concept of conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a discussion on computational experiments that we conducted using (A)TSPLIB-based problem instances. As a motivating example application, we describe a routing problem where a fleet of uncrewed aerial vehicles (UAVs) must patrol a given set of areas. Y1 - 2022 U6 - https://doi.org/10.1080/10556788.2022.2053972 ER - TY - GEN A1 - Berthold, Timo A1 - Mexi, Gioni A1 - Salvagnin, Domenico T1 - Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump N2 - The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate the usage of multiple reference vectors in all stages of the FP algorithm. In particular, we use LP-feasible vectors obtained during the main loop to tighten the variable domains before entering the computationally expensive enumeration stage. Moreover, we consider multiple integer reference vectors to explore further optimizing directions and introduce alternative objective scaling terms to balance the contributions of the distance functions and the original MIP objective. Our computational experiments demonstrate that the new method can improve performance on general MIP test sets. In detail, our modifications provide a 29.3% solution quality improvement and 4.0% running time improvement in an embedded setting, needing 16.0% fewer iterations over a large test set of MIP instances. In addition, the method’s success rate increases considerably within the first few iterations. In a standalone setting, we also observe a moderate performance improvement, which makes our version of FP suitable for the two main use-cases of the algorithm. T3 - ZIB-Report - 22-14 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88513 SN - 1438-0064 ER - TY - JOUR A1 - Berthold, Timo A1 - Mexi, Gioni A1 - Salvagnin, Domenico T1 - Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump JF - EURO Journal on Computational Optimization N2 - The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate the usage of multiple reference vectors in all stages of the FP algorithm. In particular, we use LP-feasible vectors obtained during the main loop to tighten the variable domains before entering the computationally expensive enumeration stage. Moreover, we consider multiple integer reference vectors to explore further optimizing directions and introduce alternative objective scaling terms to balance the contributions of the distance functions and the original MIP objective. Our computational experiments demonstrate that the new method can improve performance on general MIP test sets. In detail, our modifications provide a 29.3% solution quality improvement and 4.0% running time improvement in an embedded setting, needing 16.0% fewer iterations over a large test set of MIP instances. In addition, the method’s success rate increases considerably within the first few iterations. In a standalone setting, we also observe a moderate performance improvement, which makes our version of FP suitable for the two main use-cases of the algorithm. Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87392 VL - 11 ER - TY - CHAP A1 - Mexi, Gioni A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Nordström, Jakob T1 - Improving Conflict Analysis in MIP Solvers by Pseudo-Boolean Reasoning T2 - 29th International Conference on Principles and Practice of Constraint Programming (CP 2023) N2 - Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in so-called pseudo-Boolean solving, where solvers can reason directly with 0-1 integer linear inequalities rather than with clausal constraints extracted from such inequalities. In this work, we investigate how pseudo-Boolean conflict analysis can be integrated in MIP solving, focusing on 0-1 integer linear programs (0-1 ILPs). Phrased in MIP terminology, conflict analysis can be understood as a sequence of linear combinations and cuts. We leverage this perspective to design a new conflict analysis algorithm based on mixed integer rounding (MIR) cuts, which theoretically dominates the state-of-the-art division-based method in pseudo-Boolean solving. We also report results from a first proof-of-concept implementation of different pseudo-Boolean conflict analysis methods in the open-source MIP solver SCIP. When evaluated on a large and diverse set of 0-1 ILP instances from MIPLIB2017, our new MIR-based conflict analysis outperforms both previous pseudo-Boolean methods and the clause-based method used in MIP. Our conclusion is that pseudo-Boolean conflict analysis in MIP is a promising research direction that merits further study, and that it might also make sense to investigate the use of such conflict analysis to generate stronger no-goods in constraint programming. Y1 - 2023 U6 - https://doi.org/10.4230/LIPIcs.CP.2023.27 VL - 280 SP - 27:1 EP - 27:19 PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik ER - TY - CHAP A1 - Mexi, Gioni A1 - Besançon, Mathieu A1 - Bolusani, Suresh A1 - Chmiela, Antonia A1 - Hoen, Alexander A1 - Gleixner, Ambros T1 - Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization T2 - Proceedings of Conference of the Society for Operations Research in Germany Y1 - 2023 ER - TY - GEN A1 - Bolusani, Suresh A1 - Besançon, Mathieu A1 - Bestuzheva, Ksenia A1 - Chmiela, Antonia A1 - Dionísio, João A1 - Donkiewicz, Tim A1 - van Doornmalen, Jasper A1 - Eifler, Leon A1 - Ghannam, Mohammed A1 - Gleixner, Ambros A1 - Graczyk, Christoph A1 - Halbig, Katrin A1 - Hedtke, Ivo A1 - Hoen, Alexander A1 - Hojny, Christopher A1 - van der Hulst, Rolf A1 - Kamp, Dominik A1 - Koch, Thorsten A1 - Kofler, Kevin A1 - Lentz, Jurgen A1 - Manns, Julian A1 - Mexi, Gioni A1 - Mühmer, Erik A1 - E. Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Turner, Mark A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Xu, Liding T1 - The SCIP Optimization Suite 9.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming framework SCIP. This report discusses the enhancements and extensions included in the 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 bug fixes. The 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. The 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. T3 - ZIB-Report - 24-02-29 KW - Constraint integer programming KW - Linear programming KW - Mixed-integer linear programming KW - Mixed-integer nonlinear programming KW - Optimization solver KW - Branch-and-cut KW - Branch-and-price KW - Column generation KW - Parallelization KW - Mixed-integer semidefinite programming Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-95528 SN - 1438-0064 ER - TY - CHAP A1 - Mexi, Gioni A1 - Shamsi, Somayeh A1 - Besançon, Mathieu A1 - Bodic, Pierre T1 - Probabilistic Lookahead Strong Branching via a Stochastic Abstract Branching Model T2 - Proceedings of International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research Y1 - 2024 ER -