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A MILP model for the connected multidimensional maximum bisection problem

JOURNAL OF COMBINATORIAL OPTIMIZATION 2024年第4期48卷 1-17页

作者： Maksimovic, Zoran Lj. Univ Def Mil Acad Veljka Lukica Kurjaka 33 Belgrade 11000 Serbia

The Maximum Bisection Problem (MBP) is a well-known combinatorial optimization problem that has been proven to be NP-hard. The maximum bisection of a graph is the partition of its set of vertices into two subsets with an equal number of vertices, where the weight of the edge cut is maximal. This work introduces a connected multidimensional generalization of the Maximum Bisection Problem. In this NP-hard problem, weights on edges are vectors of non-negative numbers, and subgraphs induced by partitions must be connected. A mixed integer linear programming (MILP) formulation is proposed with proof of its correctness. The MILP formulation of the problem has a polynomial number of variables and constraints

关键词： Graph bisection mixed integer linear programming Combinatorial optimization Multidimensional weight of edge Connected graphs

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Solving a real-life multi-period trailer-truck waste collection problem with time windows

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EXPERT SYSTEMS WITH APPLICATIONS 2024年第PartA期237卷

作者： Van Engeland, Jens Lavigne, Carolien Belien, Jeroen De Jaeger, Simon Katholieke Univ Leuven Inst Mobil Leuven Belgium Katholieke Univ Leuven Fac Econ & Business Ctr Econ & Corp Sustainabil Campus Brussels Brussels Belgium Katholieke Univ Leuven Fac Econ & Business Operat Management Res Grp Campus Brussels Brussels Belgium

By introducing local recovery networks, regional and local environmental authorities can play an important role in facilitating the circular economy. This paper studies a network design problem that encompasses the recovery of separately collected household waste streams, which are collected in containers at civic amenity sites. We formulate a generic tactical-operational container collection problem that will be solved using a mixed integer linear programming approach. This paper makes both a theoretical and practical contribution. We are the first to study a two container vehicle capacity restriction combined with collection site inventory capacities, time windows, shift break time, and shift duration constraints. The model is applied to a number of real-life test instances and scenarios. The results provide insight in how different combinations of scenarios exactly affect the fleet requirements. This not only includes the number of trucks or information under which circumstances an additional truck would (not) be needed, but also the 12-day collection schedule for the collection crews.

关键词： Container collection Waste management mixed integer linear programming optimization Tactical-operational planning

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A new mathematical formulation and a hybrid evolutionary algorithm for re-entrant flow-shop problem with release date

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SCIENTIA IRANICA 2024年第6期31卷 500-517页

作者： Behmanesh, R. Kianfar, K. Naghshejahan Higher Educ Inst Dept Ind Engn Esfahan *** Iran Univ Isfahan Fac Engn Esfahan *** Iran

Tn this paper, we address the weighted multi-objective re-entrant flowshop scheduling problem considering release dates in order to minimize makespan, total completion time, total tardiness, maximum idle time, and number of tardy jobs. Each job is taken into account with deterministic processing times, and release dates. The flow-shop comprised of two workshops in whose jobs are entered to the main workshop and after the first part of the processing, they are transferred to the second workshop and after this stage, the jobs are returned to the main workshop for the last part of the processing. We model the problem by a new mixed integer programming based on formulating sum of idle time as a new concept. Moreover, a hybrid evolutionary algorithm is proposed based on some dispatching rules, ant colony optimization, and genetic algorithm. The performance of the proposed algorithm on some test instances is compared to the mixed integer linear programming model as well as the state-of-the-art algorithms called genetic algorithm, tabu search, bio-geography based optimization, and artificial bee colony. The computational experiments show that our proposed approach outperforms other algorithms and the results indicate efficiency and capability of the proposed algorithm in comparison with the traditional algorithms. (c) 2024 Sharif University of Technology. All rights reserved.

关键词： Re-entrant flow-shop scheduling Tdle time Release date Makespan Tardiness Hybrid evolutionary algorithm mixed integer linear programming

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Multi-Objective Resource Allocation for UAV-Assisted Air-Ground Integrated MC-NOMA Networks

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IEEE ACCESS 2024年 12卷 141000-141012页

作者： Wang, Tong Hubei Univ Econ Sch Informat Engn Wuhan 430205 Hubei Peoples R China

We consider a Multi-UAV multicarrier non-orthogonal multiple access (MC-NOMA) downlink network in which each UAV serves a group of ground users within its designated cell. Our goal is to maximize the total downlink rate for each cell by simultaneously optimizing the subcarrier assignment and power control. However, the need to maximize the downlink rate for each individual UAV cell introduces conflicts because the optimization objectives for different cells are inherently at odds with each other, making this a Multi-Objective Optimization Problem (MOOP). We applied the weighted Tchebycheff method to convert the MOOP into a Single-Objective Optimization Problem (SOOP). The resulting SOOP remains a mixed-integer Nonlinear programming (MINLP) problem. To address this, we first relax the combinatorial subcarrier assignment variables into continuous variables and then apply a penalty method to enforce binary constraints. To handle the nonconvexity of the objective function and constraints, we utilize the Big-M method and Successive Convex Approximation (SCA) to decouple the product terms and deal with nonconvexity. We then employed an iterative approach to obtain a suboptimal solution and continued the process until convergence was achieved. Simulations demonstrate that this method effectively balances the trade-offs among different cells, achieves significant performance improvements and successfully approximates Pareto optimal solutions.

关键词： NOMA Autonomous aerial vehicles Resource management Optimization Downlink Power control programming mixed integer linear programming Non-orthogonal multiple access (NOMA) power control subcarrier assignment multi-objective optimization problem (MOOP) mixed integer nonlinear problem (MINLP) big-m method successive convex approximation (SCA)

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Multi-Stage Planning of Distribution Network With High Penetration Renewable Energy Considering Reliability Index

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2024年第2期60卷 2344-2356页

作者： Liu, Jie Sun, Kaiqi Ding, Zhaohao Li, Ke-Jun Sun, Yuanyuan Shandong Univ Sch Elect Engn Jinan 250061 Peoples R China North China Elect Power Univ Sch Elect & Elect Engn Beijing 102206 Peoples R China

In this study, a multi-stage planning model of the distribution network with high photovoltaic (PV) penetration considering operational reliability is presented. The operation reliability cost consisting of three modified reliability indices is imposed in the objective function in the proposed distribution systems planning model. Additionally, the distribution network reconfiguration including microgrid is considered at the operation level to improve system operation reliability. Nonlinear expressions of modified reliability indices aggravate the complexity of the proposed planning model. To address the computational burden, the planning model is simplified as a mixed integer linear programming (MILP) model, which have an efficient computational behavior with exiting MILP solvers. The benefits of imposing operation reliability cost in the objective function and network reconfiguration including microgrid as operation strategies, are discussed. The effectiveness of the proposed model is tested by numerical results.

关键词： Planning Costs Distribution networks Power system reliability Reliability engineering Indexes Investment Distribution network multi-stage planning reliability index photovoltaic mixed integer linear programming

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Path Planning Optimization Based Interference Awareness for Mobile Robots in mmWave Multi Cell Networks

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2024年第9期73卷 13639-13650页

作者： Ren, Yijing Friderikos, Vasilis Kings Coll London Dept Engn London WC2R 2LS England

The emerging beyond fifth-generation (B5G) and envisioned sixth-generation (6G) wireless networks are considered as key enablers in supporting a diversified set of applications for industrial mobile robots (MRs). The scenario under investigation in this paper relates to mobile robots that autonomously roam on an industrial floor and perform a variety of tasks at different locations, whilst utilizing high directivity beamformers in millimeter wave (mmWave) small cells. In such scenarios, the potential close proximity of mobile robots connected to different base stations may cause excessive levels of interference having as a net result a decrease in the overall achievable data rate in the network. To resolve this issue, a novel MR optimal path planning scheme via a mixed integer programming formulation is proposed where robots' trajectory is considered jointly with the interference level at different beam sectors. To combat the curse of dimensionality, a geographical division clustering based MR path planning heuristic scheme is proposed to enable scalability and real-time decision making. The proposed heuristic aims to find a low interference path for each mobile robot whilst achieving a near-optimal performance. A wide set of numerical investigations reveal that the proposed optimal and heuristic path planning schemes for the mmWave connected mobile robots can improve the overall achievable throughput by up to 93% compared to an interference oblivious scheme without penalizing the total travel time.

关键词： Interference Robots Millimeter wave communication Optimization Mobile robots Service robots Trajectory Beamforming beyond 5G industry 4.0 mixed integer linear programming mobile robots path planning

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A multi-road quasi network flow model for the vertical alignment optimization of a road network

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ENGINEERING OPTIMIZATION 2024年第7期56卷 1140-1163页

作者： Ayman, Khandoker Md Hare, Warren Lucet, Yves Univ British Columbia Dept Comp Sci Okanagan Campus Kelowna BC Canada Univ British Columbia Dept Math Okanagan Campus Kelowna BC Canada

Minimizing earthwork costs is crucial in the optimization of vertical alignment. In this article, the previous quasi network flow model for the vertical alignment optimization of a single road is extended to a multi-road network. A 'one-at-a-time' method is first examined to solve the optimization problem and it is noted that this method is effectively what is currently used in practice. Two academic test problems are used to demonstrate that this method is not optimal. This leads to the development of three novel methods to solve the optimization problem: no-flow, with-flow and divide-and-conquer. It is noted that the with-flow method guarantees global optimality. All methods are compared on two real-world case studies. On small road networks, the with-flow method decreases costs by 7.4%, and achieves a 20 times speedup over the one-at-a-time method. On long road networks, the divide-and-conquer method is faster than all other methods without any notable cost difference. However, the divide-and-conquer method is an heuristic and cannot guarantee that it returns a global minimum.

关键词： Road network optimization vertical alignment mixed integer linear programming quasi network

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Long-term maintenance optimization for integrated mining operations

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OPTIMIZATION AND ENGINEERING 2024年第4期25卷 1817-1848页

作者： Yang, Yingying Loxton, Ryan Rohl, Andrew L. Bui, Hoa T. Curtin Univ ARC Training Ctr Transforming Maintenance Data Sc Perth WA Australia

Maintenance activities are inevitable and costly in integrated mining operations. Conducting maintenance may require the whole system, or sub-units of the system, to be shut down temporarily. These maintenance activities not only disrupt the unit being shut down, but they also have consequences for inventory levels and product flow downstream. In this paper, we consider an interconnected mining system in which there are complicated maintenance relationships and stock accumulation at intermediate nodes. We propose a time-indexed mixed-integer linear programming formulation to optimize the long-term integrated maintenance plan and maximize the total throughput. We also devise an algorithm, which combines Benders decomposition and Lagrangian relaxation, to accelerate the computational speed. To validate our mathematical model, we perform simulations for a real-world case study in the iron ore industry. The results show that our method can yield better solutions than CPLEX optimization solver alone in faster time.

关键词： Long-term maintenance planning Optimization mixed integer linear programming Integrated network Mining industry

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The road to net zero in a renewable energy-dominated electricity system: Impact of EV charging and social cost of emission on the optimal economic dispatch

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GREEN ENERGY AND INTELLIGENT TRANSPORTATION 2025年第3期4卷

作者： Sundararaman, Malolan Sambasivam, Balasubramanian Natl Inst Technol Dept Management Studies Tiruchirappalli India Mahindra Univ Ctr Sustainabil Hyderabad India

This study explores the intersection of two pivotal interventions aimed at achieving carbon neutrality: the electric vehicles (EVs) adoption and the renewable energy (RE) electricity generation. Focusing on a Renewable EnergyDominated (RED) electricity system, the research examines the interdependence between these interventions and their collective impact on economic dispatch. The study's objective is to determine optimal economic dispatch strategies that meet hourly electricity demand, considering two distinct supply scenarios across eight supply options. The first scenario assesses the maximum possible supply, while the second contemplates the minimum possible supply from each option. Additionally, the study delves into the influence of social cost of emissions on these economic dispatches. Employing an experimental design, the study generates representative load curves that incorporate EV charging demands for varied levels of EV penetration, alongside regular electricity demand. Data from Karnataka's RED electricity system provides a basis for the supply-side analysis. The economic dispatch for each supply scenario is formulated as a mixed integer linear Program (MILP), aiming to minimize both costs for generation and social costs of emissions, while adhering to operational constraints of the supply options. Key findings from this approach, highlight several critical insights: the significant role of incorporating social costs in economic dispatch decisions, the tangible impact of EV demand on supply shortages, and the importance of maintaining supply capacity to minimize these shortages.

关键词： EV demand Electricity load curves Social cost of emission mixed integer linear programming Experimental design

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Cost-based assembly line balancing and worker-cobot assignment problem under ergonomic constraints

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2024年第1期39卷 461-472页

作者： Bekdemir, Perihan Tasan, Seren Ozmehmet Eskisehir Tech Univ Fac Engn Dept Ind Engn TR-26555 Eskisehir Turkiye Dokuz Eylul Univ Fac Engn Dept Ind Engn TR-35390 Izmir Turkiye

For many years, the assembly line balancing problem (ALBP) has been discussed with different solution approaches in the literature. Recently, the use of collaborative robots (cobots) that can work at the same or different stations with the workers on the assembly line has become very popular. The problem of calculating the break times with the energy expenditure of the workers above a certain level has also been evaluated from the perspective of ergonomics. In this study, the cost-based assembly line balancing and worker-cobot assignment problem (ALBWCAP) under ergonomic constraints is discussed and a mixed integer linear programming model (MILP) is proposed to solve the problem. To evaluate the effectiveness of the cobots in assembly lines, a total of four different scenarios;i.e. cost-based assembly line only with the manual workforce, the cost-based ALBWCAP where the ergonomics perspective is ignored, cost-based ALBWCAP where the ergonomics perspective is ignored with different parameters in objective function, and the cost -based ALBWCAP where the ergonomics perspective is addressed-change in energy expenditures were considered and their results were compared. and their results were compared.

关键词： Cobot ergonomic issues mixed integer linear programming linearization cost-based

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