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Cutting Planes from the Branch-and-Bound Tree: Challenges and Opportunities

INFORMS JOURNAL ON COMPUTING 2023年第1期35卷 2-4页

作者： Contardo, Claudio Lodi, Andrea Tramontani, Andrea IBM Canada Lab Toronto ON L6G 1C7 Canada Cornell Tech Jacobs Technion Cornell Inst New York NY 10044 USA Israel Inst Technol Technion New York NY 10044 USA FICO Italy FICO Xpress Optimizat I-20123 Milan Italy

In this short paper, we argue that the standard approach adopted by modern mixed-integer linear programming solvers of using very little cutting plane generation in the branch-and-bound tree can be too conservative and lead to the loss of significant opportunities. Our observation is motivated by some relatively simple computational investigation on a couple of instances in the MIPlib 2010 collection for which the benefit of generating globally valid cuts in the tree is significant.

关键词： cutting planes branching tree mixed-integer programming

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A sustainable decision-making framework and a mixed-integer formulation for the project portfolio selection problem

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JOURNAL OF SUPERCOMPUTING 2024年第14期80卷 20743-20792页

作者： Hosseinian, Amir Hossein Esmaeeli, Hamid Islamic Azad Univ Fac Engn Dept Ind Engn North Tehran Branch Tehran Iran

This research has concentrated on the project portfolio selection (PPS) in the petroleum industry. In this study, the PPS has been treated as a multi-attribute decision-making (MADM) problem;therefore, a hybrid framework comprising five MADM techniques has been proposed to tackle this problem. Several MADM techniques have been integrated to acquire more reliable decisions and consequently to decrease the risk of failure in the decision-making process. Since the proposed methodology is an MADM-based framework, there was a need to discover the influential attributes on selection of petroleum projects. In this respect, the literature of the PPS has been comprehensively reviewed and the most influential attributes have been detected. Sustainable development has been a concern for the researchers;hence, the sustainability-related attributes have been embraced in the decision-making process as well. To strengthen the practicality of the developed framework, the Delphi method has been employed to gather and converge the viewpoints of experts on the identified attributes. The Kruskal-Wallis statistical test has been implemented to compute the weights of the attributes. Having determined the influential attributes and their weights, the embedded MADM techniques in the proposed framework have been implemented to prioritize the potential petroleum projects of a real case study. To obtain the ultimate ranking of alternatives, the proposed framework consolidates the outputs of the aforementioned techniques through using the Copeland method. This paper has also proposed a mixed-integer mathematical formulation for the PPS problem to assess the precision and validity of the results delivered by the decision-making framework. Comparing the outputs of the proposed framework and the model revealed that the developed framework is capable of providing credible outcomes. Furthermore, several sensitivity analyses have been performed to demonstrate the robustness of the framework.

关键词： Project portfolio selection Sustainable development MADM mixed-integer programming Petroleum industries

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Two-Layer MPC Architecture for Efficient mixed-integer-Informed Obstacle Avoidance in Real-Time

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2024年第10期25卷 13767-13784页

作者： Gratzer, Alexander L. Broger, Maximilian M. Schirrer, Alexander Jakubek, Stefan TU Wien Inst Mech & Mechatron A-1060 Vienna Austria

Safe and efficient obstacle avoidance in complex traffic situations is a major challenge for real-time motion control of connected and automated vehicles (CAVs). Limited processing power leads to a trade-off between real-time capability and maneuver efficiency, especially for trajectory planning in highly dynamic traffic environments like urban intersections. Addressing this problem, we propose a novel two-layer model predictive control (MPC) architecture utilizing a differentially flat representation of the kinematic single-track vehicle model for optimal control. While a real-time capable quadratic programming-based MPC ensures local obstacle avoidance at every time step, its problem formulation is asynchronously updated by the globally optimal solution of a computationally more expensive mixed-integer MPC formulation. Both optimization problems are computed in parallel and incorporate position predictions of surrounding traffic participants available via vehicle-to-everything (V2X) communication. Collision-free and efficient obstacle avoidance in real time under realistic model errors is validated via high-fidelity co-simulations of typical urban intersection and highway scenarios with the traffic simulator CARLA.

关键词： Collision avoidance Real-time systems Predictive models Computer architecture Computational modeling Vehicle dynamics Trajectory Obstacle avoidance model predictive control flatness-based control mixed-integer programming motion planning trajectory planning nonlinear control single-track model

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Exact Obstacle Avoidance for Autonomous Vehicles in Polygonal Domains

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2024年第10期54卷 5964-5976页

作者： Fan, Jiayu Murgovski, Nikolce Liang, Jun Elawad, Amal Zhejiang Univ Coll Control Sci & Engn Hangzhou 310027 Peoples R China Chalmers Univ Technol Dept Elect Engn Gothenburg 41296 Sweden

This research investigates optimization-based schemes aimed at achieving effective collision avoidance in autonomous vehicles. The study introduces three explicit formulations of collision constraints that can be applied universally to both general vehicles and obstacles regardless of whether they are represented by convex or nonconvex polygons. These formulations are devised by reformulating implicit vertex-edge constraints, exclusively designed to prevent collisions between any vertex and any edge, as explicit constraints through analytically characterizing modified signed distance functions (MSDFs), equilibrium functions, and binary variables, respectively. The proposed schemes can formulate the optimization-based planning problem involving collision avoidance as a nonlinear program (NLP), a mathematical program with equilibrium constraints, and a mixed-integer NLP, which are readily addressed using off-the-shelf solvers. Furthermore, the research examines the sensitivity of the MSDFs, indicating that the formulation can exhibit numerical sensitivity to the sign. Finally, the efficacy of the proposed schemes is demonstrated in the context of an autonomous bus parallel parking in a confined bus stop with multiple corridors. The results illustrate that all the three schemes perform equally well in terms of identifying feasible solutions, while the scheme using MSDFs avoids adding dual variables to be optimized, exhibiting the added benefit of requiring lower computational resources compared to the state of the art.

关键词： Collision avoidance Autonomous vehicles Trajectory planning Planning Shape Trajectory Vectors equilibrium constraints exact collision formulations mixed-integer programming modified signed distance functions (MSDFs) nonconvex vehicles and obstacles

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A multi-objective site selection model for evacuation centers in Taguig City, Philippines

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NATURAL HAZARDS 2024年第9期120卷 8303-8321页

作者： Rico, Emerson Rabajante, Jomar Tubay, Jerrold Lapitan, Aileen Madrid, Val Randolf Univ Philippines Los Banos Inst Math Sci & Phys Los Banos 4031 Laguna Philippines Univ Philippines Los Banos Ctr Strateg Planning & Policy Studies Los Banos 4031 Laguna Philippines Univ Philippines Los Banos Inst Comp Sci Los Banos 4031 Laguna Philippines

The exposure of Taguig City, Philippines to multiple natural hazards underscores the importance of the proper location of evacuation centers. Although there are multiple guidelines that provide the criteria for the site selection of evacuation centers, none of these guidelines specified a model that determines the optimal location of the facilities. Moreover, none of the existing models completely conform to the criteria provided by the guidelines. This study proposes a multi-objective optimization model for city-wide site selection of evacuation centers. The model was designed to conform to the criteria, data, and methodologies provided by the official authorities of the Philippines and make it applicable to all cities and municipalities of the country. The model was tested to find the optimal location of evacuation centers in Taguig City. The result shows that the evacuation centers of the model solution have better coverage, a safer location, greater accessibility, and are closer to critical facilities when compared to existing evacuation centers in the city.

关键词： Disaster risk reduction Multi-hazard risk assessment Optimal site selection Evacuation centers mixed-integer programming Mathematical modeling

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Planning an airport shuttle network with air taxis using choice-based optimization

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OR SPECTRUM 2025年 1-35页

作者： Hagspihl, Thomas Kolisch, Rainer Schiffels, Sebastian Tech Univ Munich TUM Sch Management Arcisstr 21 D-80333 Munich Germany Univ Augsburg Inst Business Adm Univ Str 16 D-86159 Augsburg Germany

Airports and airlines share a common interest in providing passengers with fast and convenient access to airports. With the introduction of air taxis as a new means of transport, the opportunity will soon emerge to introduce air taxi shuttle services to airports. In this context, for each individual airport the question arises where the facilities for landing, ground handling and take-off, also called vertiports, should be located in the area surrounding the airport. We formulate the problem as a hub location problem with multiple allocation, with the objective to maximize the number of passengers who choose to reach the airport by air taxi. In our model, we explicitly incorporate passengers' choice behavior with respect to available means of transport using a multinomial logit model. We linearize the problem and provide guidance on the steps needed to use the model in practice. In an extensive case study, we apply the model to real data for Munich Airport, perform a stated preference study to parameterize the multinomial logit model, suggest locations for vertiports throughout Bavaria as a result, and investigate to what extent the introduction of air taxi shuttle flights can reduce travel times to Munich Airport.

关键词： Transportation Advanced air mobility eVTOL Airport operations mixed-integer programming Discrete choice modeling

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Optimizing Incentive Plans for Renewable Energy Growth in the Electricity Market

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IEEE ACCESS 2024年 12卷 38830-38848页

作者： Pac, A. Burak Seker, Ezgi Z. Gebze Tech Univ Dept Ind Engn TR-41400 Kocaeli Turkiye Yildiz Tech Univ Dept Ind Engn TR-34349 Istanbul Turkiye

The competitive edge of renewable energy depends on financial support from central planners. An effective intervention with reasonable burden on taxpayers requires anticipating the choice of profit maximizing investors regarding capacity installation and electricity generation from certain locations for solar, wind and fossil-based power plants in response to technology, cost, price and incentive parameters. A 10-year generation expansion planning horizon is favored, during which capacity factors, cost projections, and electricity prices remain reasonably predictable. Investment costs within the horizon are accounted for using a depreciation model. Scenarios are considered for technology, costs, demand, wholesale prices and depreciation rates for investigating outcomes of intervention by investment subsidies and generation incentives. A mixed-integer model is devised for optimal investor decisions. Pareto analysis is conducted for each scenario setting over the optimal solutions at different incentive and subsidy rates for wind and solar plants considering three criteria: cost of intervention, renewable shares in installed capacity and overall energy generation. Under a moderate scenario, sharing 20% of the commissioning and operation costs, the central planner elicits nearly 30% increase in the shares of renewable plants in installed capacity to 72%, and electricity generation to 80%. An overall optimistic scenario achieves 75% renewables with similar interventions, while an overall pessimistic scenario attains 60%. Most of this variability is accountable to the depreciation scheme, scenarios on renewable technology and cost are partially effective, while fluctuations in demand, wholesale prices, technology and cost of the natural gas alternative are shown to have negligible impact on outcomes of the intervention.

关键词： Renewable energy sources Costs Electricity Production Investment Planning Finance Wind power generation Wind forecasting Wind energy generation Pareto analysis Natural gas Financial management Predictive models Energy management Power generation Pricing Power system economics Generation expansion planning incentive policies mixed-integer programming multicriteria Pareto optimal renewable energy

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Cardinality Minimization, Constraints, and Regularization: A Survey

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SIAM REVIEW 2024年第3期66卷 403-477页

作者： Tillmann, Andreas M. Bienstock, Daniel Lodi, Andrea Schwartz, Alexandra Tech Univ Carolo Wilhelmina Braunschweig Inst Math Optimizat D-38106 Braunschweig Germany Columbia Univ Dept Ind Engn & Operat Res New York NY 10027 USA Cornell Tech & Technion IIT Jacobs Technion Cornell Inst New York NY 10044 USA Tech Univ Dresden Fac Math D-64293 Dresden Germany

We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and we give concrete examples from diverse application fields such as signal and image processing, portfolio selection, and machine learning. The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches. While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered. In particular, we highlight that modern mixed-integer programming, which is often regarded as impractical due to the commonly unsatisfactory behavior of black-box solvers applied to generic problem formulations, can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings. Achieving such performance typically involves drawing on the merits of problem-specific knowledge that may stem from different fields of application and, e.g., can shed light on structural properties of a model or its solutions, or can lead to the development of efficient heuristics. We also provide some illustrative examples.

关键词： sparsity cardinality constraints regularization mixed-integer programming signal pro- cessing portfolio optimization regression machine learning

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Berth and quay cranes allocation problem with on-shore power supply assignment in container terminals

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 188卷

作者： Wang, Zhu Hu, Hongtao Zhen, Lu Shanghai Maritime Univ Logist Engn Coll Shanghai 201306 Peoples R China Shanghai Maritime Univ Container Supply Chain Technol Engn Res Ctr Minist Educ Shanghai 201306 Peoples R China Shanghai Univ Sch Management Shanghai 200444 Peoples R China

On -shore power supply (OPS) is a promising carbon emission -reduction technology for vessels and ports. Optimizing its allocation for berthing vessels is a new operational challenge due to different deployments on shore and on board. This article proposes an innovative solution to enhance the effectiveness of berths and on -shore power utilization in container terminals. The proposed solution integrates continuous berth allocation, quay crane assignment, and OPS allocation to address optimization challenges. First, a mixed -integer programming model is formulated based on the in-depth analysis of the OPS service coverage and carbon emissions of vessels, aiming to increase service efficiency, reduce energy consumption, and minimize carbon taxation. Then, an adaptive immune clone selection algorithm is developed to solve this problem. Adaptive and elite strategies are adopted to enrich population diversity. To improve convergence speed, a heuristic algorithm is designed based on the established model. Numerical experiments based on practical instances confirm the model's validity and the proposed algorithm's superiority over benchmark methods. The proposed integrated optimization strategy yields an average cost reduction of 2.14% and reduces carbon emissions by 2.90% by combining carbon taxation and OPS implementation. The study also highlights that OPS utilization is determined by fuel price and vessel retrofit ratio. Managerial insights suggest that raising the OPS service coverage to 50% and the vessel retrofit ratio to 70% would greatly benefit the port both economically and environmentally. To increase OPS utilization, coordination between port and shipping companies is necessary.

关键词： Continuous berth and quay crane allocation Carbon taxation On-shore power supply mixed-integer programming Immune clone algorithm

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Trajectory optimization for arbitrary layered geometries in wire-arc additive manufacturing

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OPTIMIZATION AND ENGINEERING 2024年第1期25卷 529-553页

作者： Schmidt, Johannes Fuegenschuh, Armin Brandenburg Univ Technol Cottbus Senftenberg Pl Deutsch Einheit 1 D-03046 Cottbus Germany

In wire-arc additive manufacturing, a wire is molten by an electrical or laser arc and deposited droplet-by-droplet to construct the desired workpiece, given as a set of two-dimensional layers. The weld source can move freely over a substrate plate, processing each layer, but there is also the possibility of moving without welding. A primary reason for stress inside the material is the large thermal gradient caused by the weld source, resulting in lower product quality. Thus, it is desirable to control the temperature of the workpiece during the process. One way of its optimization is the trajectory of the weld source. We consider the problem of finding a trajectory of the moving weld source for a single layer of an arbitrary workpiece that maximizes the quality of the part and derive a novel mixed-integer PDE-constrained model, including the calculation of a detailed temperature distribution measuring the overall quality. The resulting optimization problem is linearized and solved using the state-of-the-art numerical solver IBM CPLEX. Its performance is examined by several computational studies.

关键词： mixed-integer programming Wire are additive manufacturing Trajectory planning Partial differential equations Finite element method Heat conduction

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