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Globally Solving Nonconvex Quadratic Programs via linear integer programming Techniques

INFORMS JOURNAL ON COMPUTING 2020年第1期32卷 40-56页

作者： Xia, Wei Vera, Juan Zuluaga, Luis F. Lehigh Univ Ind & Syst Engn Dept Bethlehem PA 18015 USA Tilburg Univ Tilburg Sch Econ & Management Econometr & Operat NL-5037 AB Tilburg Netherlands

We reformulate a (indefinite) quadratic program (QP) as a mixed-integer linear programming (MILP) problem by first reformulating a QP as a linear complementary problem, and then using binary variables and big-M constraints to model its complementary constraints. To obtain such reformulation, we use fundamental results on the solution of perturbed linear systems to impose bounds on the QP's dual variables without eliminating any of its (globally) optimal primal solutions. Reformulating a nonconvex QP as a MILP problem allows the use of current state-of-the-art MILP solvers to find its global optimal solution. To illustrate this, we compare the performance of this MILP-based solution approach, labeled quadprogIP, with quadprogBB, BARON, and CPLEX. In practice, quadprogIP is shown to typically outperform by orders of magnitude quadprogBB, BARON, and CPLEX on standard QPs. Also, unlike quadprogBB, quadprogIP is able to solve QP instances in which the dual feasible set is unbounded. The MATLAB code quadprogIP and the instances used to perform the reported numerical experiments are publicly available at https://***/xiawei918/quadprogIP.

关键词： non-convex quadratic programming global optimization mixed-integer linear programming KKT conditions branch and bound Hoffman bound

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Time-space network model and MILP formulation of the conflict-free routing problem of a capacitated AGV system

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COMPUTERS & INDUSTRIAL ENGINEERING 2020年 141卷 106270-106270页

作者： Murakami, Keisuke Kansai Univ 3-3-35 Yamate Suita Osaka 5648680 Japan

Automated guided vehicles (AGVs) are used to transport materials in flexible manufacturing systems. This paper addresses an AGV routing problem known as the dispatch and conflict-free routing problem of a capacitated AGV system (DCFRPC). In the problem, we consider the additional constraints of collision avoidance, AGV capacities, and capacities of the machine buffers. We use a time-space network (TSN) to model the DCFRPC and formulate it as a mixed-integer linear programming (MILP) problem. In the TSN, we consider the flows of the AGVs and materials separately and then synchronize these flows considering the constraints in the formulation. This approach allows us to formulate the DCFRPC as a MILP problem. The experimental results demonstrate that our proposed approach can find optimal solutions to the majority of instances examined in a previous study.

关键词： AGV system Optimization Time-space network mixed-integer linear programming

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Optimal Access Management for Cooperative Intersection Control

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2020年第5期21卷 2114-2127页

作者： Medina, Alejandro Ivan Morales Creemers, Falco Lefeber, Erjen van de Wouw, Nathan Eindhoven Univ Technol Dept Mech Engn NL-5612 AZ Eindhoven Netherlands Univ Minnesota Civil Environm & Geoengn Dept Minneapolis MN 55455 USA Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

This paper presents an intersection access management methodology that optimizes the crossing sequence of an automated intersection, where the low-level vehicle control is performed by a cooperative intersection control (CIC) strategy. While the CIC regulates the safe and efficient relative motion of vehicles in the intersection, a high-level hybrid queuing model is proposed to describe the dynamics of the vehicle queues associated to each intersection lane. This model, including constraints, is used to design an optimal access management approach based on the model predictive control that minimizes the time that the vehicles spend within the intersection, thereby optimizing the traffic throughput of the intersection. The performance of this methodology is studied by means of two representative examples. The impact of the design parameters of the optimal access management approach is shown for a T-intersection case study. Moreover, using a real-life five lane intersection case study, the proposed approach is compared to a vehicle-actuated traffic light approach, and a first come first served approach. The comparison shows the benefits of the automated optimal serving of vehicles from different lanes.

关键词： Roads Vehicle dynamics Throughput Cost function Predictive control Optimal intersection management cooperative intersection control hybrid dynamical queuing system model predictive control mixed-integer linear programming

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A near-optimal solution method for coordinated operation planning problem of power- and heat-interchange networks using column generation-based decomposition

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ENERGY 2020年第0期197卷 117118-000页

作者： Wakui, Tetsuya Hashiguchi, Moe Yokoyama, Ryohei Osaka Prefecture Univ Dept Mech Engn Naka Ku 1-1 Gakuen Cho Sakai Osaka 5998531 Japan

A near-optimal solution method for coordinated operation-planning problems of power- and heat-interchange networks using column generation-based decomposition was developed to enhance computational efficiency and scalability. The coordinated operation-planning problem, based on a mixed-integer linear programming (MILP) approach, was decomposed into a master problem concerning power and heat interchanges and subproblems for energy-supply systems on the basis of the Dantzig-Wolfe reformulation. To determine a near-optimal solution, heuristic finalization was developed, in which a final MILP problem is solved after fixing part of binary variables based on the lower bound result obtained through two-stage iterative column generation. The developed method was then applied to the coordinated operation planning of power- and heat-interchange networks consisting of 5-100 cogeneration systems using a 150-kWe gas engine and a 45-kWe polymer electrolyte fuel cell on a winter representative day. In the case of using 100 cogeneration systems, 93% of the binary variables expressing the on/off status of the cogeneration units and heat-interchange pumps were fixed in the heuristic finalization. The near-optimal solution, which has a lower daily energy cost than in the conventional solution method, can be obtained without optimization termination due to limits of computation time and memory usage. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Optimization Coordinated operation planning Energy network Dantzig-Wolfe decomposition Column generation mixed-integer linear programming

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Allocating Small Transporters to Large Jobs

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ALGORITHMS 2022年第2期15卷 60页

作者： Jami, Neil Leithaeuser, Neele Weiss, Christian Fraunhofer Inst Ind Math Fraunhofer Pl 1 D-67663 Kaiserslautern Germany

We optimize the assignment of transporters to several jobs. Each job consists of processing a large, decomposable volume. A fleet of transporters is given, each of which can only process a limited volume at a time. After processing its share, a transporter must rest for a short time before being able to process another part. This time is only dependent on the assigned job, not on the transporter. Other transporters can take over the processing while a transporter rests. Transporters assigned to the same job wait for their turn in a queue. A transporter can only be assigned to one job. Our goal is to simultaneously minimize the maximum job completion time and the number of assigned transporters by computing the frontier of Pareto optimal solutions. In general, we show that it is NP-hard in the strong sense to compute even a single point on the Pareto frontier. We provide exact methods and heuristics to compute the Pareto frontier for the general problem and compare them computationally.

关键词： transporter assignment bi-objective optimization heuristics mixed-integer linear programming logistics heterogeneous fleet

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Reverse logistics optimization of an industrial air conditioner manufacturing company for designing sustainable supply chain: a fuzzy hybrid multi-criteria decision-making approach

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WIRELESS NETWORKS 2020年第8期26卷 5759-5782页

作者： Ali, Sadia Samar Paksoy, Turan Torgul, Belkiz Kaur, Rajbir Coll Engn Dept Ind Engn GC Jeddah Saudi Arabia Fac Engn & Nat Sci Dept Ind Engn Konya Turkey

Magnified resource consumption and depletion of natural resources calls for non-flexible or strict regulations and penalties on industrial operations, increased rate of processing and reuse of waste material as a substitute for raw material and political and legal interventions at global scale. Product recovery involves reuse, repair, refurbishing, remanufacturing and materials recycling, requires an efficient network design known as reverse logistic network and offers economical benefits in terms of fewer procurement of raw material, inventory management and less disposal. In current study, a mixed integer linear programming model designed on a multi-stage reverse logistics network for product recovery is proposed which considers different recovery options-product remanufacturing, component reprocessing and material recycling for sustainable outcomes. The model is designed to find optimal solutions for fulfilling demand and revenue needs by focusing on strategic locations for collection centers, reprocessing centers, remanufacturing plants and transportation options and simultaneously achieving sustainability goals. The model is applied on an Indian based manufacturing unit of a Saudi Arabian Industrial Air conditioner manufacturing organization and the case is presented here. The model is converted into a multi-objective programming model in accordance with the importance of each objective suiting the business needs. All relevant objective functions are evaluated using BWM, AHP and FAHP methods to obtain weights for integration into a fuzzy linear programming model which eventually provides three separate results. The model applied has originality and uniqueness for applications to solve multi-objective problems under uncertain environment and tends to strike a balance between economic and environmental objectives. The study provides for a base for further scope covering uncertainty about the amount and quality of returned products and even can be implemented by p

关键词： BWM Fuzzy multi-objective linear programming mixed-integer linear programming Network design Product recovery Reverse logistics

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Stronger path-based extended formulation for the Steiner tree problem

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NETWORKS 2020年第1期75卷 3-17页

作者： Filipecki, Bartosz Van Vyve, Mathieu Tech Univ Chemnitz Fak Math Reichenhainer Str 39 D-09126 Chemnitz Germany Catholic Univ Louvain Ctr Operat Res & Econometr Louvain La Neuve Belgium

The Steiner tree problem (STP) is a classical NP-hard combinatorial optimization problem with applications in computational biology and network wiring. The objective of this problem is to find a minimum cost subgraph of a given undirected graph G with edge costs, that spans a subset of vertices called terminals. We present currently used linear programming formulations of the problem based on two different approaches-the bidirected cut relaxation (BCR) and the hypergraphic formulations (HYP), the former offering better computational performance, and the latter better bounds on the integrality gap. As our contribution, we propose a new hierarchy of path-based extended formulations for STP. We show that this hierarchy provides better integrality gaps on graph instances used to define the worst-case lower bounds on the integrality gap for both BCR and HYP. We prove that each consecutive level of our hierarchy is at least as strong as the previous one. Additionally, we also present numerical results showing that several difficult STP instances can be solved to integer optimality by using this hierarchy. Our approach can be adapted to variants of STP or applied to hypergraphic formulations for further potential improvement on the integrality gap bounds, in exchange for additional computational effort.

关键词： extended formulation flow-based formulation integrality gap linear programming relaxation mixed-integer linear programming Steiner tree

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Topology design of general tensegrity with rigid bodies

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2020年 202卷 278-298页

作者： Wang, Yafeng Xu, Xian Luo, Yaozhi Zhejiang Univ Coll Civil Engn & Architecture 866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China Swiss Fed Inst Technol EPFL Appl Comp & Mech Lab IMAC Sch Architecture Civil & Environm Engn ENAC CH-1015 Lausanne Switzerland

This study presents a general approach to the topology design of tensegrities with rigid bodies. To the best of the authors' knowledge, all existing topology design methods of tensegrities focus on tensegrities that only consist of members carrying axial forces, which are referred to herein as classic tensegrities. However, another category of tensegrities, referred to as general tensegrities, contains rigid bodies aside from axially loaded members. The equilibrium and stability conditions of general tensegrities are different from those of classic tensegrities because of the existence of rigid bodies, which makes the existing topology design methods invalid for general tensegrities. In this study, the equilibrium and stability conditions of general tensegrities are first derived. A topology design approach for general tensegrities is then proposed based on a mixed-integer linear programming optimization scheme. The topology (i.e., member connectivities) is treated as a binary variable, and the member forces are treated as continuous variables. Three essential attributes, namely self-equilibrium, unilateral member force, and class-k condition, of a general tensegrity, as well as some other practical requirements, are formulated as constraints. Different objective functions are employed to design different general tensegrities. Some well-known general tensegrities are reproduced, and various numerical examples are presented to verify the effectiveness and versatility of the proposed approach. The proposed topology design method is verified to be a truly general approach for the topology design of tensegrities with or without rigid bodies. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Topology design Topology optimization General tensegrity Rigid body mixed-integer linear programming

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Optimal Design of Electric Bus Transport Systems With Minimal Total Ownership Cost

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IEEE ACCESS 2020年 8卷 119184-119199页

作者： Lotfi, Mohamed Pereira, Pedro Paterakis, Nikolaos G. Gabbar, Hossam A. Catalao, Joao P. S. Univ Porto Fac Engn P-4200465 Porto Portugal Inst Syst & Comp Engn Technol & Sci INESC TEC P-4200465 Porto Portugal Ontario Tech Univ Fac Energy Syst & Nucl Sci Oshawa ON L1G 8C4 Canada Eindhoven Univ Technol TUe Dept Elect Engn NL-5600 MB Eindhoven Netherlands Ontario Tech Univ Fac Engn & Appl Sci Oshawa ON L1G 8C4 Canada

In this work, a generalized mathematical formulation is proposed to model a generic public transport system, and a mixed-integer linear programming (MILP) optimization is used to determine the optimal design of the system in terms of charging infrastructure deployment (with on-route and off-route charging), battery sizing, and charging schedules for each route in the network. Three case studies are used to validate the proposed model while demonstrating its universal applicability. First, the design of three individual routes with different characteristics is demonstrated. Then, a large-scale generic transport system with 180 routes, consisting of urban and suburban routes with varying characteristics is considered and the optimal design is obtained. Afterwards, the use of the proposed model for a long-term transport system planning problem is demonstrated by adapting the system to a 2030 scenario based on forecasted technological advancements. The proposed formulation is shown to be highly versatile in modeling a wide variety of components in an electric bus (EB) transport system and in achieving an optimal design with minimal TOC.

关键词： Electric buses mixed-integer linear programming charging infrastructure

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Mathematical model and bee algorithms for mixed-model assembly line balancing problem with physical human-robot collaboration

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APPLIED SOFT COMPUTING 2020年 93卷 106394-106394页

作者： Cil, Zeynel Abidin Li, Zixiang Mete, Suleyman Ozceylan, Eren Izmir Democracy Univ Dept Ind Engn Izmir Turkey Wuhan Univ Sci & Technol Key Lab Met Equipment & Control Technol Minist Educ Wuhan Hubei Peoples R China Wuhan Univ Sci & Technol Hubei Key Lab Mech Transmiss & Mfg Engn Wuhan Hubei Peoples R China Gaziantep Univ Dept Ind Engn Gaziantep Turkey

The collaboration of human workers and robots draws increasing attention from the manufacturing enterprises to embrace the Industry 4.0 paradigm in a competitive way. Motivated by the requirements of collaboration between human workers and robots in assembly lines, this study investigates the mixed-model assembly line balancing (MMALB) problem with the collaboration between human workers and robots. A mixed-integer linear programming (MILP) model is formulated to tackle the small-size problems optimally to minimize the sum of cycle times of models. Also, bee algorithm (BA) and artificial bee colony (ABC) algorithm are implemented and improved to solve the large-size problems due to the NP-hardness of this problem. The proposed BA algorithm utilizes a new employed bee phase to accelerate the evolution of the swarm and new scout phase to escape from being trapped into local optima and produce a high-quality and diverse population. The developed ABC proposes a new onlooker phase to accelerate the evolution of the whole swarm by removing the poor-quality solutions, new scout phase to achieve high-quality solutions while preserving the diversity of the swarm, and local search to enhance exploitation capacity. Computational study on a set of generated instances indicates that the improvements enhance the BA and ABC algorithm by a significant margin, and the proposed BA and ABC algorithm achieve competing performance in comparison with nine other algorithms, including the late acceptance hill-climbing algorithm, simulated annealing algorithm, genetic algorithm, particle swarm optimization algorithm, discrete cuckoo search algorithm, the original bee algorithm, and three artificial bee colony algorithms. (C) 2020 Elsevier B.V. All rights reserved.

关键词： mixed-model assembly line Human-robot collaboration Bee algorithm Artificial bee colony algorithm mixed-integer linear programming

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