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32nd Annual European Symposium on Algorithms, ESA 2024

作者： Brand, Cornelius Koutecký, Martin Lassota, Alexandra Ordyniak, Sebastian Faculty for Informatics and Computer Science University of Regensburg Germany Computer Science Institute Faculty of Mathematics and Physics Charles University Prague Czech Republic Eindhoven University of Technology Netherlands University of Leeds United Kingdom

ISBN: (纸本)9783959773386

We provide several novel algorithms and lower bounds in central settings of mixed-integer (non-)linear optimization, shedding new light on classic results in the field. This includes an improvement on record running time bounds obtained from a slight extension of Lenstra's 1983 algorithm [Math. Oper. Res.'83] to optimizing under few constraints with small coefficients. This is important for ubiquitous tasks like knapsack-, subset sum- or scheduling problems [Eisenbrand and Weismantel, SODA'18, Jansen and Rohwedder, ITCS'19]. Further, we extend our algorithm to an intermediate linear optimization problem when the matrix has many rows that exhibit 2-stage stochastic structure, which adds to a prominent line of recent results on this and similarly restricted cases [Jansen et al. ICALP'19, Cslovjecsek et al. SODA'21, Brand et al. AAAI'21, Klein, Reuter SODA'22, Cslovjecsek et al. SODA'24]. We also show that the generalization of two fundamental classes of structured constraints from these works (n-fold and 2-stage stochastic programs) to separable-convex mixed-integer optimization are harder than their mixed-integer, linear counterparts. This counters a widespread belief popularized initially by an influential paper of Hochbaum and Shanthikumar, namely that "convex separable optimization is not much harder than linear optimization" [J. ACM'90]. To obtain our algorithms, we employ the mixed Graver basis introduced by Hemmecke [Math. Prog.'03], and our work is the first to give bounds on the norm of its elements. Importantly, we use these bounds differently from how purely-integer Graver bounds are exploited in related approaches, and prove that, surprisingly, this cannot be avoided. © Cornelius Brand, Martin Koutecký, Alexandra Lassota, and Sebastian Ordyniak;licensed under Creative Commons License CC-BY 4.0.

关键词： mixed-integer linear programming

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A mixed-integer Charging Schedule for Electric Vehicles with Request-Dependent Pricing

A Mixed-Integer Charging Schedule for Electric Vehicles with...

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2024 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles and International Transportation Electrification Conference, ESARS-ITEC 2024

作者： Ghavami, Mahsa Liuzza, Davide Mostacciuolo, Elisa Iannelli, Luigi Vasca, Francesco Politecnico di Bari Dept. of El. and Inf. Engineering Bari Italy University of Sannio Dept. of Engineering Benevento Italy

ISBN: (纸本)9798350373905

A pricing mechanism for the charging schedule problem of Electric Vehicles (EVs) that takes into account the requests of EVs is proposed. Conventional price schemes adopted in the literature are typically affected by total energy demand and the time of use (TOU) tariff. These models do not capture the fact that, in real-world booking systems, by increasing the request in the presence of fixed limited resources, the price increases. In this paper, we propose a price function that, in addition to considering the effect of total energy demand and TOU tariff, it also accounts for satisfied and dissatisfied EVs due to fixed finite resources. The problem is modeled by using a mixed-integer linear cooperative structure by including the presence of infrastructural limitations such as the number of chargers and maximum demand from the grid. A corresponding optimization problem is defined whose cost function aims to reach a compromise between the demand from the grid during peak hours and the level of dissatisfaction with electric vehicles. Simulation results show that the proposed pricing mechanism, which also accounts for resource limitation, does not have adverse effects on energy peak shaving and allows a realistic balance for EV charging satisfaction. © 2024 IEEE.

关键词： mixed-integer linear programming

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Resilience-Oriented Allocation of DERs Considering the Fragility Model of Distribution System Components 16

Resilience-Oriented Allocation of DERs Considering the Fragi...

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16th IEEE PES Asia-Pacific Power and Energy Engineering Conference, APPEEC 2024

作者： Yang, Yun Zhang, Xiaochen Wei, Guangtao Li, Hui Wang, Yuehan Su, Yinghui Ma, Rui State Grid Beijing Electric Company Chaoyang Electric Company Beijing China School of Electrical and Electronics Engineering North China Electric Power University Beijing China

ISBN: (纸本)9798350386127

In this paper, a distributed energy resource (DER) allocation strategy is proposed to enhance the distribution system's resilience against extreme weather. The long-term planning problem is formulated as a two-stage stochastic mixed-integer programming (SMIP). The first stage is to make decisions on DG siting and sizing under the given budget constraint. In the second stage, a post-extreme-event-restoration (PEER) is employed to minimize the operating cost in an uncertain fault scenario. Finally, the SMIP is solved by the progressive hedging algorithm. The case studies of the IEEE 33-bus test system demonstrate the effectiveness of the proposed algorithm in reducing the expected energy not served (EENS), which is a critical criterion of resilience. © 2024 IEEE.

关键词： mixed-integer linear programming

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Optimizing subscriber migrations for a telecommunication operator in uncertain context

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第1期298卷 308-321页

作者： Cambier, Adrien Chardy, Matthieu Figueiredo, Rosa Ouorou, Adam Poss, Michael Orange Labs 44 Ave Republ F-92320 Chatillon France Avignon Univ LIA Avignon France Univ Montpellier UMR CNRS 5506 LIRMM Montpellier France

We consider a telecommunications company expanding its network capacity to face an increasing demand. The company can also invest in marketing to incentivize clients to shift to more recent technologies, hopefully leading to cheaper overall costs. To model the effect of marketing campaigns, previous works have relied on the Bass model. Since that model only provides a rough approximation of the actual shifting mechanism, the purpose of this work is to consider uncertainty in the shifting mechanism through the lens of robust optimization. We thus assume that the (discrete) shifting function can take any value in a given polytope and wish to optimize against the worst-case realization. The resulting robust optimization problem possesses integer recourse variables and non-linear dependencies on the uncertain parameters. We address these difficulties as follows. First, the integer recourse is tackled heuristically through a piece-wise constant policy dictated by a prior partition of the uncertainty polytope. Second, the non-linearities are handled by a careful analysis of the dominating scenarios. The scalability and economical relevance of our models are assessed through numerical experiments performed on realistic instances. In particular, we choose one of these instances to perform a case study with simulations illustrating the possible benefit of using robust optimization. (c) 2021 Elsevier B.V. All rights reserved.

关键词： OR in telecommunications Capacity expansion Bass model mixed-integer linear programming Robust optimization

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Integrated production and inventory routing planning of oxygen supply chains

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2022年 186卷 97-111页

作者： Lee, Yena Charitopoulos, Vassilis M. Thyagarajan, Karthik Morris, Ian Pinto, Jose M. Papageorgiou, Lazaros G. UCL Univ Coll London Sargent Ctr Proc Syst Engn Dept Chem Engn Torrington Pl London WC1E 7JE England Linde PLC Linde Digital Amer 10 Riverview Dr Danbury CT 06810 USA BOC EMEA Prod & Supply Bawtry Rd Brinsworth S60 5NT Rotherham England

In this work, we address a production and inventory routing problem for a liquid oxygen supply chain comprising production facilities, distribution network, and distribution re-sources. The key decisions of the problem involve production levels of production plants, delivery schedule and routing through heterogeneous vehicles, and inventory strategies for national stock-out prevention. Due to the problem complexity, we propose a two-level hybrid solution approach that solves the problem using both exact and metaheuristic methods. At the upper level, we develop a mixed-integer linear programming (MILP) model that determines production and inventory decisions and customer allocation. In the lower level, the original problem is reduced to several multi-trip heterogeneous ve-hicle routing problems by fixing the optimal production, inventory, and allocation deci-sions and clustering customers. A well-recognised metaheuristic, guided local search method, is adapted to solve the low-level routing problems. A real-world case study in the UK illustrates the applicability and effectiveness of the proposed optimisation framework. (c) 2022 The Author(s). Published by Elsevier Ltd on behalf of Institution of Chemical Engineers. CC_BY_4.0

关键词： Hybrid approach mixed-integer linear programming Metaheuristics Guided local search Integrated oxygen supply chain planning

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Design, dynamic simulation, and optimal size selection of a hybrid solar/wind and battery-based system for off-grid energy supply

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RENEWABLE ENERGY 2022年第0期187卷 1082-1099页

作者： Cao, Yan Taslimi, Melika S. Dastjerdi, Sajad Maleki Ahmadi, Pouria Ashjaee, Mehdi Xian Technol Univ Sch Mechatron Engn Xian 710021 Peoples R China Univ Tehran Coll Engn Sch Mech Engn POB 11155-4563 Tehran Iran

Remote energy systems are applicable, especially in critical circumstances like earthquakes, floods, etc. Besides, renewable energy systems are suitable energy sources in remote areas. Therefore, Due to high solar and wind potential and its location as an earthquake-prone, a solar-wind energy system for a remote application on a Conex is presented in this study. Considered wind turbines have power production of 1 kW and 3 kW. PV panels have an efficiency of about 20%. This Conex has 12 m(2) of the area and resides three to five people and supplies 520 W power consumption of equipment except for the HVAC unit. A considered lifetime of the Conex is 20 years. The considered capacity of batteries is about 100-200 Ah. Six cities are selected as representatives of the six major climate types in Iran. The studied system is optimized for each city. The heating and cooling demand of Conex in cities are specified using TRNSYS software. The heat pump's electricity requirement as a cooling and heating unit with COP of four, lighting (20 W), laptops (140 W), and refrigerators (360 W) is calculated for Conex in each city. mixed integer linear programming is employed to optimize an off-grid renewable energy system to supply this electricity demand. The system's total cost, which includes the initial and O & M cost of PV panels and wind turbines, and the capital and replacement cost of the batteries together with the loss of power supply probability during a year, are considered two objective functions. The interest rate is assumed to be 15%. Achieved results show that Iran's solar and wind potential can balance the required load of the Conex with a probability of power outage as low as 1% of a year. However, there is a variance in the cost of the required renewable energy system for supplying Conex power consumption for different climate zones: in the Mediterranean region, the system costs 500-5000 $ as the most expensive one, and in the hot coastal dry region, it costs 900 $-2000

关键词： Off-grid conex Multi-objective optimization Hybrid wind-solar power generation system mixed-integer linear programming Energy storage

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The flex-route transit planning problem with meeting points

The flex-route transit planning problem with meeting points

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作者： Li, Mingyang Wu, Lingxiao Wang, Yadong Tang, Jinjun Feng, Tao Smart Transportation Key Laboratory of Hunan Province School of Traffic and Transportation Engineering Central South University Changsha410075 China Department of Aeronautical and Aviation Engineering The Hong Kong Polytechnic University Hong Kong School of Economics and Management Nanjing University of Science and Technology Nanjing210094 China Department of Logistics and Maritime Studies Faculty of Business The Hong Kong Polytechnic University Hong Kong

As an innovative alternative to ridesharing, flex-route transit (FRT) is widely acknowledged as a promising solution, especially in scenarios in which transportation demand is low or dispersed. This paper addresses the FRT planning problem with meeting points (FRTPP-MP), which conceptualizes each passenger's pick-up/drop-off request as a set of points (i.e., a cluster) containing the designated pick-up/drop-off point and alternative points (i.e., meeting points), stipulating that only one point in each cluster needs to be visited to fulfill the request. The aim is to minimize both the travel cost of vehicles and the walking cost of passengers by simultaneously optimizing the routes of vehicles and the selection of nodes within their respective clusters. We formulate the FRTPP-MP as a mixed-integer programming (MIP) model and develop an exact branch-and-price (BAP) algorithm to solve it. To tackle the specific challenges of cluster visit restrictions in the pricing problem, we design a tailored bidirectional label correction algorithm (TBLCA), which is further enhanced by a novel acceleration strategy. Extensive computational experiments are conducted based on benchmark instances generated from a real-life FRT system. The numerical results highlight our solution algorithm's satisfactory performance. Furthermore, managerial insights from a sensitivity analysis suggest that introducing meeting points can substantially reduce the costs associated with FRT. © 2025 Elsevier Ltd

关键词： mixed-integer linear programming

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Exact optimization and decomposition approaches for shelf space allocation

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第2期299卷 432-447页

作者： Gencosman, Burcu Caglar Begen, Mehmet A. Bursa Uludag Univ Dept Ind Engn Bursa Turkey Western Univ Ivey Business Sch London ON Canada

A B S T R A C T Shelf space is one of the scarcest resources, and its effective management to maximize profits has become essential to gain a competitive advantage for retailers. We consider the shelf space allocation problem with additional features (e.g., integer facings, rectangular arrangement restrictions) motivated by litera-ture and our interactions with a local bookstore. We determine optimal number of facings of all products in two aspects (width and height of a rectangular arrangement space for each product), and allocate them as contiguous rectangles to maximize profit. We first develop a mixed-integer linear mathematical programming model (MIP) for our problem and propose a solution method based on logic-based Ben-ders decomposition (LBBD). Next, we construct an exact 2-stage algorithm (IP1/IP2), inspired by LBBD, which can handle larger and real-world size instances. To compare performances of our methods, we generate 100 test instances inspired by real-world applications and benchmarks from the literature. We observe that IP1/IP2 finds optimal solutions for real-world instances efficiently and can increase the local bookstore's profit up to 16.56%. IP1/IP2 can provide optimal solutions for instances with 100 products in minutes and optimally solve up to 250 products (assigned to 8 rows x 160 columns) within a time limit of 1800 s. This exact 2-stage IP1/IP2 solution approach can be effective in solving similar problems such as display problem of webpage design, allocation of product families in grocery stores, and flyer advertising. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Retailing Shelf space allocation Rectangular display problem mixed-integer linear programming Logic-based Benders decomposition 2-stage algorithm

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Uncertainty-aware non-supplied load minimization oriented demand response program for PV/FC power system with electrolyzer back-up

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INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2022年第19期47卷 10715-10735页

作者： Eren, Yavuz Yildiz Tech Univ Dept Control & Automat Davutpasa Campus TR-34220 Istanbul Turkey

This manuscript presents robust optimization framework with multi-objective approach for day-ahead operation of hybrid power system consisted of photovoltaic (PV) panel, fuel cell (FC) with electrolyzer (Elc) back-up. The multi-objective optimization model of PV/FC/ Elc has been developed by combining the physical and operational constraints with mathematical equivalence of affine forms as well as considering the uncertainties occurring in the load demand and PV power generation. As a novel contribution to the literature, three robust optimization approaches for scheduling the hybrid power systems have been presented through the conservatism approach. Moreover, the objective function has been described to integrate the different objectives as aiming to minimize non-supplied load, while maximize the utilization rate of the essential source. By this way, it has been aimed to accelerate the adaptation of the demand response strategies for the proposed system. Moreover, this hybrid scheme provides solutions to meet the power demands for the residential end-users located in off-grid areas or islands. The mixed integer linear programming (MILP) model is tested in GAMS v.24.1.3 using the solver CPLEX v.12 and the developed strategy is analyzed for different load patterns. The results are discussed and commented with some suggestions to prove the contribution of the paper. (c) 2022 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

关键词： Hybrid power sources mixed-integer linear programming Uncertainty Robust optimization Fuel cell Photovoltaic

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Research on the Optimization of Emergency Material Distribution Routes Considering Fairness and Efficiency 14

Research on the Optimization of Emergency Material Distribut...

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14th International Conference on Logistics and Systems Engineering

作者： Sun, Haobo Tong, Zeping School of Management Wuhan University of Science and Technology Wuhan430065 China

ISBN: (纸本)9798331314347

In post-disaster relief scenarios, achieving equitable and efficient humanitarian logistics is crucial for the timely delivery of relief materials and the alleviation of suffering among affected populations. This paper integrates the dual objectives of efficiency and equity in conducting optimization research on emergency material distribution routes. It employs deprivation costs arising from material shortages to quantify fairness. A mixed-integer nonlinear programming model was constructed with the goal of minimizing transportation and deprivation costs, and a variable neighborhood search-based metaheuristic algorithm was developed. Using the 2008 Wenchuan earthquake as a case study, the algorithm was implemented and solved using MATLAB 2020b software, yielding the optimal distribution routes and costs. The experimental results confirm that the model and algorithm proposed in this paper are practical and effective in optimizing emergency material distribution routes. © (2025) by Aussino Academic Publishing House All rights reserved.

关键词： mixed-integer linear programming

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