Article
Operations Research & Management Science
Matthew E. Wilhelm, Matthew D. Stuber
Summary: Deterministic nonconvex optimization solvers generate convex relaxations of nonconvex functions by transforming the problem into a higher-dimensional decision space. In contrast, the generalized McCormick relaxation approach constructs relaxations in the lower dimensionality space of the original problem without introducing auxiliary variables. This research presents a method that combines McCormick relaxations with factorable programming to formulate tighter relaxations in the original decision space, leading to improved CPU time for solving optimization problems.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Operations Research & Management Science
Matthew E. Wilhelm, Chenyu Wang, Matthew D. Stuber
Summary: This study introduces general methods to construct convex/concave relaxations of commonly used activation functions for artificial neural networks (ANNs) to improve optimization performance. The developed library of activation function envelopes leads to tighter relaxations of ANNs, resulting in a significant reduction in computational time required for solving optimization problems.
JOURNAL OF GLOBAL OPTIMIZATION
(2022)
Article
Operations Research & Management Science
Jaromil Najman, Dominik Bongartz, Alexander Mitsos
Summary: This paper discusses the computation of lower bounds through solving convex lower bounding problems, and proposes algorithms for calculating linearization points for convex relaxations constructed via McCormick theorems. Alternative approaches based on Kelley's algorithm, computation of all vertices of an n-simplex, a combination of the two, and random selection are also introduced. It is noted that all algorithms provide substantial speed ups compared to the single point strategy used previously.
JOURNAL OF GLOBAL OPTIMIZATION
(2021)
Article
Operations Research & Management Science
Gabriele Eichfelder, Kathrin Klamroth, Julia Niebling
Summary: The difficulty in dealing with optimization problems with nonconvex constraints lies in finding feasible solutions. Introducing a filtering approach inspired by a multiobjective reformulation, the trade-off between constraint satisfaction and objective value can be identified, leading to the discovery of feasible and often optimal solutions where traditional methods fail.
JOURNAL OF GLOBAL OPTIMIZATION
(2021)
Article
Operations Research & Management Science
Gabriele Eichfelder, Peter Kirst, Laura Meng, Oliver Stein
Summary: This paper introduces a new framework for multi-objective branch-and-bound, including constructions for partial lower bounds, overall upper bounds, and overall lower bounds along with node selection steps. Additionally, it proposes a new enclosure of non-dominated points by a union of boxes and suggests a discarding test based on linearization technique. The convergence proof for the general branch-and-bound framework is provided along with numerical examples to illustrate the results.
JOURNAL OF GLOBAL OPTIMIZATION
(2021)
Article
Management
Nicolas Forget, Sune Lauth Gadegaard, Lars Relund
Summary: In this paper, a generic branch-and-bound algorithm for solving multi-objective integer linear programming problems is proposed. The algorithm speeds up the computations and significantly reduces CPU time, effectively addressing the difficulties that arise when non-binary integer variables are introduced.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2022)
Article
Engineering, Chemical
Zaid Ashraf Rana, Cheng Seong Khor, Haslinda Zabiri
Summary: This study investigated the performance of several representative piecewise linear and piecewise affine relaxation schemes in refinery planning optimization, finding that uniform partition sizes typically perform better and that there is not always a direct relationship between relaxation size and tightness for non-uniform partition sizes.
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
Engineering, Electrical & Electronic
Pengxiang Liu, Zhi Wu, Wei Gu, Yuping Lu
Summary: In this paper, an improved spatial branch-and-bound algorithm is proposed to solve the non-convex problem in optimal electricity-gas flow models. The algorithm divides the problem into convex and small sub-models and uses a novel spatial branching strategy to improve effectiveness and efficiency. The experimental results demonstrate the superiority of the proposed algorithm in terms of feasibility, optimality, and efficiency.
IEEE TRANSACTIONS ON POWER SYSTEMS
(2022)
Article
Operations Research & Management Science
Bo Zhang, YueLin Gao, Xia Liu, XiaoLi Huang
Summary: This paper investigates linear fractional programming (LFP) problem and provides an equivalence problem using a new two-stage transformation method. The characteristics of the branch-and-bound algorithm are considered to discuss the operations and complexity of the algorithm. The effectiveness, feasibility, and other performance of the proposed algorithm are verified through experiments.
Article
Automation & Control Systems
Loris Cannelli, Francisco Facchinei, Gesualdo Scutari, Vyacheslav Kungurtsev
Summary: This study introduces a distributed, asynchronous algorithm for convex and nonconvex constrained optimization with a partially separable objective function. The algorithm is proven to converge at a sublinear rate in nonconvex cases and at a linear rate under specific error bound conditions. Numerical results show the effectiveness of the method in matrix completion and LASSO problems.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Article
Management
Shaonan Liu, Mingzheng Wang, Nan Kong, Xiangpei Hu
Summary: In this paper, an enhanced branch-and-bound algorithm is proposed for a class of BILP problems, which can significantly reduce computation time while maintaining solution quality. Computational studies show that the enhanced branching rule achieves significant speedup and superior performance on large-sized BILP instances with complex lower-level problems.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2021)
Article
Mathematics
Hongming Li, Xintao Li
Summary: This study considers the practical aspects of efficiency and energy consumption in quay crane scheduling, motivated by the emission targets set by the International Maritime Organization for 2030. By formulating a bi-objective mixed-integer programming model and using a branch-and-bound algorithm, the study efficiently finds the full set of Pareto-optimal solutions for small- and medium-sized problems.
Article
Computer Science, Software Engineering
Christina Buesing, Timo Gersing, Arie M. C. A. Koster
Summary: Since its introduction in the early 2000s, robust optimization with budget uncertainty has gained attention. However, the existing compact robust reformulation performs poorly for robust integer problems. To address this, a bilinear formulation is proposed for robust binary programming, resulting in strong linear formulations and structural properties. Computational testing on real-world instances shows that the proposed algorithm outperforms existing approaches significantly. The fundamental properties proven in this paper also have potential to improve other approaches.
MATHEMATICAL PROGRAMMING COMPUTATION
(2023)
Article
Operations Research & Management Science
Sven de Vries, Bernd Perscheid
Summary: This paper investigates the use of cutting planes from the Boolean Quadric Polytope to reduce the optimality gap of the NP-hard nonconvex quadratic program with box constraints (BoxQP). By obtaining a compact extended relaxation of all A-odd cycle inequalities, optimization over the Chvatal-Gomory closure can be achieved without repeated calls to separation algorithms and with fewer inequalities. Computational studies confirm the strength of this relaxation and demonstrate that strong bounds can be obtained for the BoxQP, even with a plain linear program, which are significantly stronger than those obtained using heuristic separation of A-odd cycle inequalities by Bonami et al. (Math Program Comput 10(3):333-382, 2018).
JOURNAL OF GLOBAL OPTIMIZATION
(2022)
Article
Chemistry, Multidisciplinary
John D. Martin, Myrofora Panagi, Chenyu Wang, Thahomina T. Khan, Margaret R. Martin, Chrysovalantis Voutouri, Kazuko Toh, Panagiotis Papageorgis, Fotios Mpekris, Christiana Polydorou, Genichiro Ishii, Shinichiro Takahashi, Naoto Gotohda, Toshiyuki Suzuki, Matthew E. Wilhelm, Vinicio Alejandro Melo, Sabina Quader, Jumpei Norimatsu, Ryan M. Lanning, Motohiro Kojima, Matthew David Stuber, Triantafyllos Stylianopoulos, Kazunori Kataoka, Horacio Cabral
Article
Computer Science, Interdisciplinary Applications
William T. Hale, Matthew E. Wilhelm, Kyle A. Palmer, Matthew D. Stuber, George M. Bollas
COMPUTERS & CHEMICAL ENGINEERING
(2019)
Article
Engineering, Chemical
Matthew E. Wilhelm, Anne Le, Matthew Stuber
Article
Engineering, Environmental
Zhiheng Xu, Farzaneh MahmoodPoor Dehkordy, Yan Li, Yingzheng Fan, Tianbao Wang, Yuankai Huang, Wangchi Zhou, Qiuchen Dong, Yu Lei, Matthew D. Stuber, Amvrossios Bagtzoglou, Baikun Li
Article
Computer Science, Interdisciplinary Applications
Shaylin A. Cetegen, Matthew D. Stuber
Summary: The novel methodology proposed in this study offers a robust design and scheduling approach for controlled environment agricultural systems, addressing multi-period risks and uncertainties. It enhances the system's robustness to market uncertainty, improves long-term economic benefits, and validates the economic viability of producing various crop portfolios.
COMPUTERS & CHEMICAL ENGINEERING
(2021)
Article
Engineering, Environmental
Tianbao Wang, Chenyu Wang, Zhiheng Xu, Can Cui, Xingyu Wang, Zoe Demitrack, Zheqin Dai, Amvrossios Bagtzoglou, Matthew D. Stuber, Baikun Li
Summary: Non-ideal heterogeneous mixing models are developed and incorporated into advanced closed-loop control strategies utilizing high-resolution sensing to maximize resiliency and minimize energy consumption in water treatment processes. The models are simple with few parameters, allowing for fast online prediction and regular recalibration. They outperform CFD and data-driven models, offering superior performance in water and wastewater treatment processes.
CHEMICAL ENGINEERING JOURNAL
(2022)
Article
Engineering, Chemical
Chenyu Wang, Samuel Degnan-Morgenstern, John D. Martin, Matthew D. Stuber
Summary: Tumor microenvironment (TME) normalization enhances the delivery of anticancer nanocarriers by restoring transvascular pressure gradients and inducing convection. The effectiveness of this normalization depends on TME biophysics, normalization dose, and nanocarrier size. By using computation, we can personalize the dose and size of normalization. Experimental results show that normalization with dexamethasone significantly increases the convection rate of nanocarriers, tumor volume fraction with convection, and total amount of convection. However, a portion of the tumor still lacks convection. Artificial neural network surrogate modeling can be used to rapidly determine the optimal dose and size of nanocarriers for maximum accumulation. This digital testbed provides a quantitative evaluation of transport and allows for therapy design.
Article
Engineering, Chemical
Chenyu Wang, Matthew E. Wilhelm, Matthew D. Stuber
Summary: The robust design of performance/safety-critical process systems from a model-based perspective remains a challenge. Hybrid first-principles data-driven models can improve model prediction accuracy, moving closer to the concept of a digital twin. This study addresses worst-case engineering design feasibility and reliability problems using a class of semi-infinite program formulations with hybrid models as equality constraints. The reduced-space deterministic global optimization methods used in this approach demonstrate their effectiveness in solving the problems with a finite number of iterations. Two case studies are presented to showcase the application of this approach in addressing worst-case feasibility verification of dynamical systems and overcoming numerical domain violations in a three-phase separation system.
INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH
(2022)
Article
Operations Research & Management Science
Matthew E. Wilhelm, Chenyu Wang, Matthew D. Stuber
Summary: This study introduces general methods to construct convex/concave relaxations of commonly used activation functions for artificial neural networks (ANNs) to improve optimization performance. The developed library of activation function envelopes leads to tighter relaxations of ANNs, resulting in a significant reduction in computational time required for solving optimization problems.
JOURNAL OF GLOBAL OPTIMIZATION
(2022)
Article
Operations Research & Management Science
Matthew E. Wilhelm, Matthew D. Stuber
Summary: Deterministic nonconvex optimization solvers generate convex relaxations of nonconvex functions by transforming the problem into a higher-dimensional decision space. In contrast, the generalized McCormick relaxation approach constructs relaxations in the lower dimensionality space of the original problem without introducing auxiliary variables. This research presents a method that combines McCormick relaxations with factorable programming to formulate tighter relaxations in the original decision space, leading to improved CPU time for solving optimization problems.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Green & Sustainable Science & Technology
Justin Rastinejad, Sloane Putnam, Matthew D. Stuber
Summary: The industrial process heat sector has the potential to replace fossil fuel energy with solar alternatives, such as parabolic trough collectors (PTC) or photovoltaics (PV). PV technology has seen significant improvements in cost and efficiency, and the energy generated can be stored in batteries. However, current optimization-based approaches lack global optimality guarantees. PTC with thermal energy storage (ES) is currently the most economically favorable option for low-to-medium temperature IPH, regardless of location or process scale.
