Article
Mathematics, Applied
Bo Zhang, Yuelin Gao, Xia Liu, Xiaoli Huang
Summary: This paper proposes a new global optimization algorithm for solving the mixed-integer quadratically constrained quadratic fractional programming problem. By converting the problem into an equivalent generalized bilinear fractional programming problem and using linear fractional relaxation technique and rectangular adjustment-segmentation technique, combined with the branch-and-bound procedure, an efficient algorithm is proposed.
JOURNAL OF COMPUTATIONAL MATHEMATICS
(2023)
Article
Thermodynamics
Dominik Hering, Andre Xhonneux, Dirk Muller
Summary: District heating is an efficient heat supply technology that integrates waste heat sources. Optimization models are used to design heating networks by considering factors such as temperature. Design decisions, such as the positioning of heat pumps, influence the optimal operation and result in a trade-off between economic and ecological solutions.
Article
Mathematics
Loay Alkhalifa, Hans Mittelmann
Summary: This paper introduces the method of piecewise linear approximation (PLA) and its application on mixed integer nonlinear programming (MINLP) problems. By using nonuniform domain partitioning, the PLA models are improved to obtain more accurate solutions and reduce computation time.
Article
Computer Science, Software Engineering
Benjamin Mueller, Gonzalo Munoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
Summary: This work explores the use of a nonconvex relaxation obtained through constraint aggregation for solving MINLPs, highlighting the computational advantages and challenges.
MATHEMATICAL PROGRAMMING
(2022)
Article
Computer Science, Artificial Intelligence
Daniel Molina-Perez, Efren Mezura-Montes, Edgar Alfredo Portilla-Flores, Eduardo Vega-Alvarado, Barbara Calva-Yanez
Summary: This paper presents a new proposal based on two fundamental strategies to improve the performance of the differential evolution algorithm when solving MINLP problems. The proposal considers a set of good fitness-infeasible solutions to explore promising regions and introduces a composite trial vector generation method to enhance combinatorial exploration and convergence capacity.
SWARM AND EVOLUTIONARY COMPUTATION
(2024)
Article
Automation & Control Systems
Iosif Pappas, Nikolaos A. Diangelakis, Efstratios N. Pistikopoulos
Summary: This paper presents an algorithm for solving explicit nonlinear model predictive control problems with convex quadratic constraints, based on the theoretical developments of second-order Taylor approximation and active set strategy. By comparing with approximate solutions, the benefits of this approach are demonstrated, and a practical application in the optimal operation of a chemostat in the presence of disturbances is exhibited.
JOURNAL OF PROCESS CONTROL
(2021)
Article
Thermodynamics
Dominik Hering, Mehmet Ege Cansev, Eugenio Tamassia, Andre Xhonneux, Dirk Mueller
Summary: Lowering the operating temperatures of district heating networks is crucial to reduce energy losses and utilize low-temperature heat sources, such as waste heat. This paper focuses on modeling, control, and optimization of a low-temperature district heating network, with a case study on waste heat from high-performance computers. The optimization model presented in the study demonstrates energy savings of 1.55%-5.49% by controlling the operation temperatures of heat pumps and thermal energy storages.
Article
Operations Research & Management Science
Andrew Allman, Qi Zhang
Summary: This work aims to combine the strengths of global mixed-integer nonlinear optimization and branch-and-price, solving a class of nonconvex mixed-integer nonlinear programs effectively. The study shows that using discretization of integer linking variables can lead to the application of Dantzig-Wolfe reformulation and branch-and-price method for solution, which has been underutilized in literature.
JOURNAL OF GLOBAL OPTIMIZATION
(2021)
Article
Operations Research & Management Science
Moritz Link, Stefan Volkwein
Summary: In this paper, a new method is proposed for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements. The method uses piecewise linear relaxations to bypass the nonconvexity of the original problem. It adaptsively chooses the level of relaxation needed in different parts of the image space. After finitely many iterations, an enclosure of the nondominated set of prescribed quality is guaranteed. The advantages of this approach are demonstrated through its application to multiobjective energy supply network problems.
JOURNAL OF GLOBAL OPTIMIZATION
(2023)
Article
Energy & Fuels
Roymel R. Carpio, Thiago C. dAvila, Daniel P. Taira, Leonardo D. Ribeiro, Bruno F. Viera, Alex F. Teixeira, Mario M. Campos, Argimiro R. Secchi
Summary: The study evaluates the performance of two approaches for oil production optimization on offshore platforms, highlighting the limitations of each strategy and proposing a hybrid two-stage optimization strategy to achieve global optimal operating conditions.
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
David Bergman, Leonardo Lozano
Summary: The study proposes a method using decision diagrams to solve binary optimization problems with quadratic constraints, decomposing the quadratic matrix with multiple diagrams linked through channeling constraints and optimized by a cutting-plane algorithm, leading to significant improvements in solver efficiency for quadratic constraints.
INFORMS JOURNAL ON COMPUTING
(2021)
Article
Computer Science, Software Engineering
Shixuan Zhang, Xu Andy Sun
Summary: This paper studies multistage stochastic mixed-integer nonlinear programs (MS-MINLP) and proposes a new type of cuts based on generalized conjugacy. The developed algorithms are shown to achieve global optimality under certain conditions, and the iteration complexity is analyzed to reveal its dependence on the number of stages.
MATHEMATICAL PROGRAMMING
(2022)
Article
Management
Pengfei Yu, Ruotian Gao, Wenxun Xing
Summary: This study examines the maximization of perturbation radius of an ellipsoidal set under perturbed uncertain coefficients for each constraint, in the context of robust convex quadratically constrained quadratic programming problems. By formulating a fractional programming problem and reformulating it into linear conic programs solvable in polynomial time, the proposed sensitivity analysis concept is demonstrated through numerical experiments related to robust Markowitz's portfolio selection. Comparative numerical results show the efficiency of direct solutions of linear conic programs versus a bisection method for the corresponding fractional programming problem.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2021)
Article
Operations Research & Management Science
Hatim Djelassi, Alexander Mitsos
Summary: The paper discusses existence-constrained semi-infinite programs, a generalization of regular semi-infinite programs with three levels. It proposes an algorithm for the global solution without convexity or concavity assumptions, ensuring termination with a globally optimal solution under certain conditions. Numerical results for a robust design problem in chemical engineering literature are provided.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Pavel Dvorak, Eduard Eiben, Robert Ganian, Dusan Knop, Sebastian Ordyniak
Summary: This study introduces the concept of fracture backdoors in ILP instances and provides exact and approximation algorithms for computing them. These backdoors are then utilized to develop parameterized algorithms for ILP, with the performance scaling based on the number of global variables or constraints in the instance, accompanied by matching lower bounds.
ARTIFICIAL INTELLIGENCE
(2021)
Article
Operations Research & Management Science
Ambros Gleixner, Stephen J. Maher, Benjamin Mueller, Joao Pedro Pedroso
ANNALS OF OPERATIONS RESEARCH
(2020)
Article
Computer Science, Software Engineering
Ambros Gleixner, Daniel E. Steffy
MATHEMATICAL PROGRAMMING
(2020)
Article
Operations Research & Management Science
Felipe Serrano, Robert Schwarz, Ambros Gleixner
JOURNAL OF GLOBAL OPTIMIZATION
(2020)
Article
Computer Science, Artificial Intelligence
Jo Devriendt, Ambros Gleixner, Jakob Nordstrom
Summary: Inspired by mixed integer programming, a hybrid approach is proposed in this research that combines incremental LP solving with cut generation within the conflict-driven pseudo-Boolean search, significantly improving performance on a wide range of benchmarks. This approach marks the first time that MIP techniques are combined with full-blown conflict analysis operating directly on linear inequalities using the cutting planes method.
Article
Computer Science, Software Engineering
Benjamin Mueller, Gonzalo Munoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
Summary: This work explores the use of a nonconvex relaxation obtained through constraint aggregation for solving MINLPs, highlighting the computational advantages and challenges.
MATHEMATICAL PROGRAMMING
(2022)
Article
Management
Daniel Rehfeldt, Hannes Hobbie, David Schonheit, Thorsten Koch, Dominik Most, Ambros Gleixner
Summary: This article introduces an interior-point solver designed for linear energy system models, which efficiently runs in parallel on distributed memory systems. The solver utilizes new techniques and methods to handle large-scale linear programming problems, making it applicable to various energy system models.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2022)
Article
Computer Science, Software Engineering
Leon Eifler, Ambros Gleixner
Summary: A new algorithmic framework for general mixed integer programming problems is proposed, which integrates symbolic presolving, exact repair steps, and a faster LP solver. This framework shows significantly improved performance on benchmark instances, with an average speedup of 10.7x and 2.9 times as many instances solved within a time limit of two hours compared to the original framework.
MATHEMATICAL PROGRAMMING
(2023)
Article
Computer Science, Theory & Methods
Boro Sofranac, Ambros Gleixner, Sebastian Pokutta
Summary: The paper presents a novel, efficient GPU algorithm for domain propagation in state-of-the-art MIP solvers, achieving speed-ups of around 10x to 20x, up to 180x on favorably-large instances. Challenges include dynamic algorithmic behavior, dependency structures, and sparsity patterns. The algorithm can run entirely on the GPU with no CPU involvement.
PARALLEL COMPUTING
(2022)
Article
Computer Science, Software Engineering
Leon Eifler, Ambros Gleixner, Jonad Pulaj
Summary: This paper presents a general and safe computational framework for machine-assisted proofs of mathematical theorems using integer programming. The framework relies on a rational branch-and-bound certificate to avoid floating-point round-off errors and provides checker software to independently verify the correctness of the certificate.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2022)
Proceedings Paper
Computer Science, Theory & Methods
Leon Eifler, Ambros Gleixner
Summary: This study presents a significant advancement in solving general mixed integer programs over the rational numbers, achieving a substantial performance improvement. The new framework outperforms the original framework on the MIPLIB 2017 benchmark set, solving instances faster and more efficiently.
INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, IPCO 2021
(2021)
Article
Computer Science, Interdisciplinary Applications
Jakob Witzig, Ambros Gleixner
Summary: This article investigates the integration of conflict analysis and diving heuristics to improve the performance of solvers, combining the goals of producing valid conflict constraints and generating improving solutions. Through a detailed computational study in SCIP, two methods are evaluated for their potential in advancing MIP solvers.
INFORMS JOURNAL ON COMPUTING
(2021)
Article
Computer Science, Software Engineering
Ambros Gleixner, Gregor Hendel, Gerald Gamrath, Tobias Achterberg, Michael Bastubbe, Timo Berthold, Philipp Christophel, Kati Jarck, Thorsten Koch, Jeff Linderoth, Marco Lubbecke, Hans D. Mittelmann, Derya Ozyurt, Ted K. Ralphs, Domenico Salvagnin, Yuji Shinano
Summary: The sixth version of the MIPLIB, known as MIPLIB 2017, was compiled from an initial pool of 5721 instances, resulting in a collection of 1065 instances with a subset of 240 instances selected for solver performance benchmarking. This selection process utilized a data-driven approach supported by solving a series of mixed integer optimization problems to ensure diversity and balancedness in instance features and performance data.
MATHEMATICAL PROGRAMMING COMPUTATION
(2021)
Proceedings Paper
Computer Science, Hardware & Architecture
Boro Sofranac, Ambros Gleixner, Sebastian Pokutta
PROCEEDINGS OF IA3 2020: 2020 IEEE/ACM 10TH WORKSHOP ON IRREGULAR APPLICATIONS: ARCHITECTURES AND ALGORITHMS (IA3)
(2020)
Article
Mathematics, Applied
Benjamin Mueller, Felipe Serrano, Ambros Gleixner
SIAM JOURNAL ON OPTIMIZATION
(2020)
Proceedings Paper
Computer Science, Theory & Methods
Ambros Gleixner, Daniel E. Steffy
INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, IPCO 2019
(2019)