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A computational study of the influence of the parameter big-M in a time-indexed MILP for assembly flowshop

IEEE LATIN AMERICA TRANSACTIONS 2022年第5期20卷 848-854页

作者： Santana, Jose R. Fuchigami, Helio Y. Univ Fed Goias UFG Fac Ciencia & Tecnol Aparecida Goias Goiania Go Brazil Univ Fed Sao Carlos UFSCar Sao Carlos SP Brazil

In this paper, a mixed integer linear programming model was proposed to solve the assembly flowshop scheduling problem. The objective of the study was to evaluate the impact on computational time (CPU) from the variation of the value of the big-M parameter considering three different dimensions. The performance of the mathematical model was evaluated from the application of a commercial solver that has different strategies in search of the optimal solution. 240 test-problems were solved on the optimality in an acceptable computational time, with the number of jobs ranging from 4 to 8, the number of products from 2 to 4 and the number of machines from 1 to 4. The performance profiles of Dolan and More (2002) were employed for a more accurate statistical analysis of the results, which indicated the most efficient value for the big-M parameter in the proposed mathematical formulation.

关键词： Computational modeling Mathematical models Visualization IEEE transactions Adaptation models Statistical analysis Software mixed integer linear programming Scheduling Assembly Flowshop big-M influence

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Autonomous Intersection Management for Connected and Automated Vehicles: A Lane-Based Method

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第9期23卷 15091-15106页

作者： Wu, Wei Liu, Yang Liu, Wei Zhang, Fangni Dixit, Vinayak Waller, S. Travis Changsha Univ Sci & Tectmol Key Lab Highway Engn Minist Educ Changsha 410114 Hunan Peoples R China Hong Kong Polytech Univ Dept Aeronaut & Aviat Engn Hong Kong Peoples R China Univ Hong Kong Dept Ind & Mfg Syst Engn Hong Kong Peoples R China Univ New South Wales Sch Civil & Environm Engn Res Ctr Integrated Transport Innovat Sydney NSW 2052 Australia

Most existing studies on autonomous intersection management (AIM) often focus on algorithms to accommodate conflicts among vehicles by assuming that the entrance lane and the exit lane of vehicles are exogenous inputs. This paper shows that allowing entrance lanes and exit lanes to be optimized can significantly improve traffic efficiency. In particular, this paper proposes all-direction lanes, where left-turn, through, and right-turn traffic is all allowed at the same lane. We develop two methods for optimizing entering time (i.e., when to enter the intersection) and route choice decisions (i.e., entrance lane and exit lane), including the sliding-time-window-based global optimum (GO-STW) and the first-come-first-served method with optimal route choices (FCFS-R). The developed lane-based methods can be formulated as mixed integer linear programming (MILP) problems, which can be solved using the CPLEX solver. A heuristic is further adopted to solve the MILP model in a timely manner, which illustrates the potential real-time applicability of the proposed method. Numerical analysis is conducted to examine performance and effectiveness of the proposed methods and heuristic. We found that the optimization of lane/route choices is often more critical than entering time.

关键词： Delays Autonomous vehicles Resource management Intelligent transportation systems Servers Numerical analysis mixed integer linear programming Autonomous intersection connected and autonomous vehicles lane-based method sliding time window

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Balancing cybersecurity in a supply chain under direct and indirect cyber risks

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2022年第2期60卷 766-782页

作者： Sawik, Tadeusz Reykjavik Univ Dept Engn IS-101 Reykjavik Iceland AGH Univ Sci & Technol Dept Operat Res Krakow Poland

Cybersecurity is an essential requirement for the sustainability of global supply chains. In this paper, a stochastic programming formulation is presented for optimisation of cybersecurity investment and selection of security controls to mitigate and balance the impact of direct and indirect (propagated) cyber risks in a multi-tier supply chain. Using a network transformation combined with the first-order Taylor series approximation of natural logarithm to linearise the nonlinear constraints, a nonlinear stochastic combinatorial optimisation model is approximated by its linear equivalent. The problem objective is to determine an optimal cybersecurity investment under limited budget and portfolio of security controls for each supply chain node to balance the cybersecurity over the entire supply chain. The minmax objective functions are applied to minimise either the maximum breach probability or the maximum loss of supply chain nodes. Alternatively, maxmin objectives are used to maximise either the minimum non-breach probability or the minimum saving of loss. The proposed integrated modelling approach is illustrated with results of computational study and a comparison of approximated and exact solution values is presented. The decision-making insights are provided and discussed.

关键词： Cyber risk management cybersecurity investment portfolio of security controls mixed integer linear programming supply chain cybersecurity

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A Novel Method for Inferring Chemical Compounds With Prescribed Topological Substructures Based on integer programming

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022年第6期19卷 3233-3245页

作者： Zhu, Jianshen Azam, Naveed Ahmed Zhang, Fan Shurbevski, Aleksandar Haraguchi, Kazuya Zhao, Liang Nagamochi, Hiroshi Akutsu, Tatsuya Kyoto Univ Grad Sch Informat Dept Appl Math & Phys Kyoto 6068501 Japan Kyoto Univ Grad Sch Adv Integrated Studies Human Survivabil Kyoto 6068306 Japan Kyoto Univ Inst Chem Res Bioinformat Ctr Uji 6110011 Japan

Drug discovery is one of the major goals of computational biology and bioinformatics. A novel framework has recently been proposed for the design of chemical graphs using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, an ANN is trained using data on existing chemical compounds. In the second phase, given a target chemical property, a feature vector is inferred by solving an MILP formulated from the trained ANN and then a set of chemical structures is enumerated by a graph enumeration algorithm. Although exact solutions are guaranteed by this framework, the types of chemical graphs have been restricted to such classes as trees, monocyclic graphs, and graphs with a specified polymer topology with cycle index up to 2. To overcome the limitation on the topological structure, we propose a new flexible modeling method to the framework so that we can specify a topological substructure of graphs and a partial assignment of chemical elements and bond-multiplicity to a target graph. The results of computational experiments suggest that the proposed system can infer chemical graphs with around up to 50 non-hydrogen atoms.

关键词： Chemicals Chemical compounds Vegetation Bioinformatics Computational biology Compounds Computational modeling QSAR QSPR molecular design chemical graph artificial neural network mixed integer linear programming enumeration of graphs

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A hierarchical model in short-term hydro scheduling with unit commitment and head-dependency

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ENERGY 2022年第0期251卷 1页

作者： Cheng, Xianliang Feng, Suzhen Zheng, Hao Wang, Jinwen Liu, Shuangquan Power Dispatch & Control Ctr China Southern Power Guangzhou 510663 Guangdong Peoples R China Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan 430074 Hubei Peoples R China Yunnan Elect Power Dispatch & Control Ctr Kunming 650011 Yunnan Peoples R China

The short-term hydro scheduling (STHS) problem has long been studied for decades, with great efforts having been made on improving their solution methods or algorithms. This work instead aims to solve a real-world problem with a hierarchical modeling strategy presented to decouple the STHS problem into two sub-problems: a load distribution (LD) and a unit commitment (UC), which are both solved with the mixed integer linear programming (MILP) and then coordinated through their coupling variables. The linearity errors in the model can be eliminated with an efficient successive water head updating pro-cedure that adjusts the searching range based on the improvement of the objective. Taking into account the hydraulic connection, unit operating zones, head-dependency, generation and water level targets, the optimal quarter-hourly schedule for Lancang Cascade that consists of 11 hydropower reservoirs and 56 units can be obtained in 1 min for not only all the hydro-plants in the cascade but also every unit within hydro plant. The application results demonstrate that the convergence of the water head updating procedure is intermittent yet guaranteed after about 20 iterations.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： Short -term hydro scheduling Unit commitment Head-dependency mixed integer linear programming Water head updating Cascaded reservoirs

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Weekly hydropower scheduling of cascaded reservoirs with hourly power and capacity balances

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APPLIED ENERGY 2022年 311卷 118620-118620页

作者： Feng, Suzhen Zheng, Hao Qiao, Yifan Yang, Zetai Wang, Jinwen Liu, Shuangquan Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn 1037 Luoyu Rd Wuhan 430074 Hubei Peoples R China Huazhong Univ Sci & Technol Joint Int Water Secur Res Ctr 1037 Luoyu Rd Wuhan 430074 Hubei Peoples R China Yunnan Elect Power Dispatch & Control Ctr 17 Chuncheng Rd Kunming 650011 Yunnan Peoples R China

A medium/long-term hydropower scheduling routinely assumes the energy produced in each week will be fully utilized in peak-shaving the power demands during every day in that week, ignoring the fluctuation of the hourly power loads. This work improves the traditional weekly hydropower scheduling by integrating the hourly power and capacity balances (HPCB), which has rarely been investigated, mainly due to great challenges imposed in solving the model. The HPCB are formulated into mixed integer linear constraints, involving the spare, maintenance, disabled, reserve and working capacities, as well as the order and levels of hydroplants in peak-shaving the hourly power load curve, all to be optimized. The formulation is then improved with successive strategies in updating water heads and peak-shaving hours, aiming to boost the solution efficiency by excluding more binary variables. The case studies involving 6 cascaded hydropower reservoirs in Lancang River reveal that the traditional weekly hydropower scheduling overestimates the benefits significantly, strongly suggesting the necessity to include the HPBC into a long/mid-term hydropower scheduling. The experiments also recommend an improved model formulation that achieves very consistent results on the top three prioritized objectives, while taking less than 0.1 s to solve the problem involving all six cascaded reservoirs, demonstrating a great prospect in solving problems in large scale.

关键词： Hydropower scheduling Large scale power system Power and capacity balances mixed integer linear programming Load balancing linearization

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The min-cost parallel drone scheduling vehicle routing problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期299卷 910-930页

作者： Nguyen, Minh Anh Dang, Giang Thi-Huong Ha, Minh Hoang Pham, Minh-Trien Phenikaa Univ ORLab Fac Comp Sci Hanoi Vietnam Univ Econ & Tech Ind Hanoi Vietnam VNU Univ Engn & Technol Hanoi Vietnam

Adopting unmanned aerial vehicles (UAV), also known as drones, into the last-mile-delivery sector and having them work alongside trucks with the aim of improving service quality and reducing the transportation cost gives rise to a new class of Vehicle Routing Problems (VRPs). In this paper, we introduce a new optimization problem called the min-cost Parallel Drone Scheduling Vehicle Routing Problem (PDSVRP). This problem is a variant of the well-known Parallel Drone Scheduling Traveling Salesman Problem (PDSTSP) recently introduced in the literature in which we allow multiple trucks and consider the objective of minimizing the total transportation costs. We formulate the problem as a mixed integer linear Program and then develop a Ruin and Recreate ( 7Z & 7Z ) algorithm. Exploiting PDSVRP solution characteristics in an effective manner, our heuristic manages to introduce "sufficient" rooms to a solution via new removal operators during the ruin phase. It is expected to enhance the possibilities for improving solutions later in the recreate phase. Multiple experiments on a new set of randomly generated instances confirm the performance of our approach. To explore the benefits of drone delivery as well as the insight into the impact of related factors on the contribution of drones' use to operational cost, a sensitivity analysis is conducted. We also adapt the proposed algorithm to solve the PDSTSP and validate it via benchmarks available in the literature. It is shown that our algorithm outperforms state-of-the-art algorithms in terms of solution quality. Out of 90 considered instances, it finds 26 new best known solutions. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Transportation Vehicle routing problem Drone parallel scheduling mixed integer linear programming Ruin and recreate metaheuristic

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A Selective Many-to-Many Pickup and Delivery Problem With Handling Cost in the Omni-Channel Last-Mile Delivery

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IEEE ACCESS 2022年 10卷 111284-111296页

作者： Li, Yali Huazhong Univ Sci & Technol Sch Management Wuhan 430074 Peoples R China

This paper introduces a selective many-to-many pickup and delivery problem with handling cost (SMMPDPH) arising in the omni-channel last-mile delivery. In SMMPDPH, each request is associated with multiple pickup and delivery nodes, which provide or require commodities. A request is to load commodities from the pickup nodes and transport them to the delivery nodes. Since the total supply is greater than the total demand, we need to determine the selected subset of pickup nodes to visit for each request. Based on the loading and unloading policy, we take into account the handling cost incurred by additional operations. SMMPDPH aims to obtain a routing plan with the minimum total cost, including the travel cost and handling cost, for a fleet of homogeneous vehicles with limited capacity and driving mileage to satisfy the requests. We present two mixed integer programming formulations of the problem and propose two algorithms, including an iterated local search (ILS) and a memetic algorithm (MA), with specially designed move operators to solve the problem. Experiments on small instances clearly indicate the effectiveness of the two heuristic methods. With a comparison of efficiency on large-scale instances, we find that MA outperforms ILS in terms of both the best and average solution quality.

关键词： Costs Routing Home appliances Search problems Traveling salesman problems Transportation Supply and demand Vehicle routing mixed integer linear programming Heuristic algorithms Supply chain management Vehicle routing problem pickup and delivery handling cost mixed integer programming heuristics

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Properties, Extensions and Application of Piecewise linearization for Euclidean Norm Optimization in R²

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2022年第2期195卷 418-448页

作者： Duguet, Alois Artigues, Christian Houssin, Laurent Ngueveu, Sandra Ulrich Univ Toulouse INP CNRS LAAS CNRS Toulouse France Univ Toulouse ISAE SUPAERO Toulouse France

This work considers nonconvex mixed integer nonlinear programming where nonlinearity comes from the presence of the two-dimensional euclidean norm in the objective or the constraints. We build from the euclidean norm piecewise linearization proposed by Camino et al. (Comput. Optim. Appl. https://***/10.1007/s10589-019-00083-z, 2019) that allows to solve such nonconvex problems via mixed-integer linear programming with an arbitrary approximation guarantee. Theoretical results are established that prove that this linearization is able to satisfy any given approximation level with the minimum number of pieces. An extension of the piecewise linearization approach is proposed. It shares the same theoretical properties for elliptic constraints and/or objective. An application shows the practical appeal of the elliptic linearization on a nonconvex beam layout mixed optimization problem coming from an industrial application.

关键词： mixed integer linear programming mixed integer nonlinear programming Euclidean norm linearization Approximation guarantee Multibeam satellites

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Solution to dynamic economic dispatch with prohibited operating zones via MILP

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第7期19卷 6455-6468页

作者： Pan, Shanshan Jian, Jinbao Yang, Linfeng Guangxi Univ Sci & Technol Sch Sci Liuzhou 545006 Peoples R China Guangxi Minzu Univ Coll Math & Phys Nanning 530006 Peoples R China Guangxi Univ Guangxi Key Lab Multimedia Commun & Network Techn Nanning 530004 Peoples R China

Dynamic economic dispatch (DED) problem considering prohibited operating zones (POZ), ramp rate constraints, transmission losses and spinning reserve constraints is a complicated non-linear problem which is difficult to solve efficiently. In this paper, a mixed integer linear programming (MILP) method is proposed to solve such a DED problem. Firstly, a novel MILP formulation for DED problem without considering the transmission losses, denoted by MILP-1, is presented by using perspective cut reformulation technique. When the transmission losses are considered, the quadratic terms in the transmission losses are replaced by their first order Taylor expansions, and then an MILP formulation for DED considering the transmission losses, denoted by MILP-2, is obtained. Based on MILP-1 and MILP-2, an MILP-iteration algorithm is proposed to solve the complicated DED problem. The effectiveness of the MILP formulation and MILP iteration algorithm are assessed by several cases and the simulation results show that both of them can solve to competitive solutions in a short time.

关键词： dynamic economic dispatch prohibited operating zones reformulation mixed integer linear programming iteration algorithm

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