Article
Computer Science, Software Engineering
Navid Ansari, Hans-Peter Seidel, Vahid Babaei
Summary: In the field of computational design and fabrication, neural networks have become important alternatives to bulky forward simulations. The question of inverse design, i.e., how to compute a design that meets a desired target performance, has been long-standing. In this study, we demonstrate that the commonly occurring piecewise linear property in neural networks enables an inverse design formulation based on mixed-integer linear programming. Our method uncovers globally optimal or near optimal solutions in a principled manner and greatly facilitates combinatorial inverse design tasks. Additionally, we propose an efficient yet near-optimal hybrid approach for problems where finding the optimal solution is intractable.
ACM TRANSACTIONS ON GRAPHICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Hamza Bouzekri, Gulgun Alpan, Vincent Giard
Summary: In this paper, the integrated Laycan and Berth Allocation Problem (LBAP) is studied in the context of bulk ports. The LBAP considers both the tactical Laycan Allocation Problem and the dynamic hybrid case of the operational Berth Allocation Problem. Various constraints and considerations are incorporated to make the LBAP more realistic. An integer programming model is proposed to define an efficient schedule for berthing chartered vessels and new vessels to charter, which is formulated with predicates to improve computational performance. The model is tested and validated using relevant case studies inspired by the operations of OCP Group at the bulk port of Jorf Lasfar in Morocco.
COMPUTERS & INDUSTRIAL ENGINEERING
(2023)
Article
Physics, Fluids & Plasmas
V Graber, E. Schuster
Summary: ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. Careful regulation of the plasma's temperature and density, or burn control, is required to prevent potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. The controller manages uncertainties in the plasma confinement properties and the particle recycling conditions. It regulates the plasma density and controls the electron and ion temperatures separately.
Article
Computer Science, Software Engineering
Felix Bestehorn, Christoph Hansknecht, Christian Kirches, Paul Manns
Summary: We explored an extension of Mixed-Integer Optimal Control Problems by introducing switching costs, allowing for penalization of chattering and expanding modeling capabilities. By reformulating the rounding problem as a shortest path problem, we achieved minimization of switching costs while maintaining approximability. The effectiveness of our approach was demonstrated through comparison with an integer programming method on a benchmark problem.
MATHEMATICAL PROGRAMMING
(2021)
Article
Computer Science, Artificial Intelligence
Bahriye Akay, Dervis Karaboga, Beyza Gorkemli, Ebubekir Kaya
Summary: This paper reviews the use of Artificial Bee Colony algorithm for solving discrete numeric optimization problems, discussing various encoding types, search operators and selection operators integrated into ABC. It is the first comprehensive survey study on this topic and aims to benefit readers interested in utilizing ABC for binary, integer and mixed integer discrete optimization problems.
APPLIED SOFT COMPUTING
(2021)
Article
Robotics
Abhishek Cauligi, Preston Culbertson, Edward Schmerling, Mac Schwager, Bartolomeo Stellato, Marco Pavone
Summary: This study proposes a data-driven algorithm CoCo for quickly finding high quality solutions to MICPs through training a neural network classifier and applying logical strategies.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2022)
Article
Engineering, Civil
Nadire Ucler, Hale Gonce Kocken
Summary: Rapid population growth, industrialization, and lifestyle modernization have led to an increased demand for water. However, water supplies are decreasing due to declining precipitation, excessive use, and resource deterioration. This study proposes a multi-objective mixed-integer programming approach to create a feasible strategic plan for selecting alternative water supply projects. The proposed model considers various criteria and integrates the analytical hierarchical process technique. Simulation results demonstrate the applicability of the proposed model compared to a classic optimization model.
WATER RESOURCES MANAGEMENT
(2023)
Article
Management
Martina Fischetti, Matteo Fischetti
Summary: This article addresses the important problem of combined optimization of the turbine location and connection cables in offshore wind farm design. The authors propose a mixed-integer linear programming model and improve it with additional inequalities, including new classes of Benders-like cuts. Computational tests show significant improvement in the dual bound provided by the standard model. The authors also present an exact branch-and-cut solver that separates the new cuts at run time, confirming their effectiveness.
MANAGEMENT SCIENCE
(2023)
Article
Computer Science, Software Engineering
Ilias Zadik, Miles Lubin, Juan Pablo Vielma
Summary: We investigate the structural geometric properties of mixed-integer convex representable (MICP-R) sets and compare them with the class of mixed-integer linear representable (MILP-R) sets. We provide examples of MICP-R sets that are countably infinite unions of convex sets with countably infinitely many different recession cones, and countably infinite unions of polytopes with different shapes. These examples highlight the differences between MICP-R sets and MILP-R sets.
MATHEMATICAL PROGRAMMING
(2023)
Article
Computer Science, Interdisciplinary Applications
Vicky Mak-Hau, Brendan Hill, David Kirszenblat, Bill Moran, Vivian Nguyen, Ana Novak
Summary: This paper addresses a unique combinatorial optimization problem derived from helicopter aircrew training for the Royal Australian Navy. The main objective is to find optimal course scheduling solutions and minimize the total time required to complete the syllabus.
COMPUTERS & INDUSTRIAL ENGINEERING
(2021)
Article
Computer Science, Information Systems
Minh Dat Nguyen, Long Bao Le, Andre Girard
Summary: This article examines trajectory control, subchannel assignment, and user association design for UAV-based wireless networks, proposing optimization methods and algorithms to address these challenges. Extensive numerical studies demonstrate the effectiveness of the proposed design compared to simple heuristics.
IEEE INTERNET OF THINGS JOURNAL
(2021)
Article
Mechanics
G. Ntourmas, F. Glock, F. Daoud, G. Schuhmacher, D. Chronopoulos, E. Oezcan
Summary: This manuscript presents two novel formulations for manufacturable stacking sequence retrieval, achieving solutions that meet both design and manufacturing requirements through a two-stage optimization approach. Using mathematical programming algorithms, high-quality solutions can be consistently obtained, with increased design freedom concerning blending formulation.
COMPOSITE STRUCTURES
(2021)
Article
Multidisciplinary Sciences
Tomas Thorbjarnarson, Neil Yorke-Smith
Summary: Recent research has shown potential in optimizing certain aspects of neural networks (NNs) using Mixed Integer Programming (MIP) solvers. However, the approach of training NNs with MIP solvers has not been explored thoroughly. This article introduces new MIP models for training integer-valued neural networks (INNs) and provides two methods to improve the efficiency and data handling capabilities of MIP solvers. Experimental results demonstrate the superiority of our approach in terms of accuracy, training time, and data usage compared to previous state-of-the-art methods. Our methodology is particularly proficient at training NNs with minimal data and memory requirements, making it valuable for deployment on low-memory devices.
Article
Operations Research & Management Science
Dominic Yang, Prasanna Balaprakash, Sven Leyffer
Summary: In this study, we investigate nonlinear optimization problems involving surrogate models represented by neural networks. We first demonstrate the direct embedding of neural network evaluation into optimization models and highlight a potential convergence issue. Next, we analyze the stationarity of these models. Additionally, we propose two alternative formulations for feedforward neural networks with ReLU activation: a mixed-integer optimization problem and a mathematical program with complementarity constraints. We prove that the stationarity of the latter formulation corresponds to the stationarity of the embedded formulation. These formulations can be solved using state-of-the-art optimization methods, and we provide techniques for obtaining good initial feasible solutions. We compare the different formulations through three practical applications related to combustion engine design and control, generation of adversarial attacks on classifier networks, and optimization of flows in an oil well network.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2022)
Article
Thermodynamics
Ryohei Yokoyama, Hiroki Kamada, Yuji Shinano, Tetsuya Wakui
Summary: A robust optimal design method using a hierarchical MILP approach is proposed in this paper, aiming to enhance the tolerance of energy supply systems to uncertainties by evaluating the robustness of performance criteria based on the minimax regret criterion.
