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two-stage heuristic algorithm with pseudo node-based model for electric vehicle routing problem

APPLIED SOFT COMPUTING 2024年 165卷

作者： Xia, Xiaoyun Zhuang, Helin Wang, Zijia Chen, Zefeng Jiaxing Univ Sch Informat Sci & Engn Jiaxing 314001 Peoples R China Jiaxing Vocat & Tech Coll Sch Internet Jiaxing 314036 Peoples R China Guangzhou Univ Sch Comp Sci & Cyber Engn Guangzhou 510006 Peoples R China Sun Yat Sen Univ Sch Artificial Intelligence Zhuhai 519082 Peoples R China

Electric vehicle routing problem (EVRP) is a special vehicle routing problem, which owns several specific characteristics of EV technology including the limited charging stations and the limited cruising range of EVs. This paper proposes a two-stage heuristic algorithm for EVRP with a kind of pseudo node, termed EVRPPN-TSH, which not only contributes to the model innovation but also to the algorithm design. In model innovation, the pseudo node is introduced into the EVRP model, forming EVRPPN, to reduce the search space and time complexity for obtaining service orders of customers from O ( n ) to O (1). Moreover, different from other research works which only use total distance as the fitness function, an improved fitness function is proposed, which takes all the distance, the electricity and capacity constraints compliance into consideration. In algorithm design, we first adopt the two-stage idea, which divides EVRP into the capacitated vehicle routing problem (CVRP) and a fixed route vehicle charging problem (FRVCP). Then we design a two-stage heuristic algorithm, termed as TSH. Specifically, for CVRP, a route division heuristic algorithm and a depot move heuristic algorithm are designed to divide routes. Further, an adjustment strategy with three operators is designed for adjusting the customer order. For FRVCP, an existing heuristic algorithm is adopted and enhanced by a variable extent shaking algorithm to avoid local trapped. Experimental results show that EVRPPN-TSH generally outperforms other state-of-the-art algorithms. Moreover, EVRPPN-TSH can obtain the best-known solution in all the 7 test cases, and update the best-known solution in test case E101 from 834.84 to 834.22.

关键词： Electric vehicle routing problem Pseudo node two-stage algorithm Route division

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An Online two-stage Classification Based on Projections

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年第1期44卷 387-415页

作者： Song, Aimin Wang, Yan Luan, Shengyang Dalian Jiaotong Univ Sch Sci Dalian 116028 Peoples R China Jiangsu Normal Univ Sch Elect Engn & Automat Xuzhou 221116 Peoples R China

Kernel-based online classification algorithms, such as the Perceptron, NORMA, and passive-aggressive, are renowned for their computational efficiency but have been criticized for slow convergence. However, the parallel projection algorithm, within the adaptive projected subgradient method framework, exhibits accelerated convergence and enhanced noise resilience. Despite these advantages, a specific sparsification procedure for the parallel projection algorithm is currently absent. Additionally, existing online classification algorithms, including those mentioned earlier, heavily rely on the kernel width parameter, rendering them sensitive to its choices. In an effort to bolster the performance of these algorithms, we propose a two-stage classification algorithm within the Cartesian product space of reproducing kernel Hilbert spaces. In the initial stage, we introduce an online double-kernel classifier with parallel projection. This design aims not only to improve convergence but also to address the sensitivity to kernel width. In the subsequent stage, the component with a larger kernel width remains fixed, while the component with a smaller kernel width undergoes updates. To promote sparsity and mitigate model complexity, we incorporate the projection-along-subspace technique. Moreover, for enhanced computational efficiency, we integrate the set-membership technique into the updates, selectively exploiting informative vectors to improve the classifier. The monotone approximation of the proposed classifier, based on the designed & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \epsilon $$\end{document}-insensitive function, is presented. Finally, we apply the proposed algorithm to equalize a nonlinear channel. Simulation results demonstrate that the proposed classifier achiev

关键词： Online classification two-stage algorithm Parallel projection Sparsification

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two-stage algorithms for covering array construction

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JOURNAL OF COMBINATORIAL DESIGNS 2019年第8期27卷 475-505页

作者： Sarkar, Kaushik Colbourn, Charles J. Arizona State Univ Sch Comp Informat & Decis Syst Engn POB 878809 Tempe AZ 85287 USA

Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to cause a fault. Covering arrays are used to test for interactions among components systematically. A two-stage framework, providing a number of concrete algorithms, is developed for the efficient construction of covering arrays. In the first stage, a time and memory efficient randomized algorithm covers most of the interactions. In the second stage, a more sophisticated search covers the remainder in relatively few tests. In this way, the storage limitations of the sophisticated search algorithms are avoided;hence, the range of the number of components for which the algorithm can be applied is extended, without increasing the number of tests. Many of the framework instantiations can be tuned to optimize a memory-quality trade-off, so that fewer tests can be achieved using more memory.

关键词： conditional expectation covering array Lovasz local lemma randomized algorithm two-stage algorithm

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A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling

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COMPUTERS & INDUSTRIAL ENGINEERING 2008年第1期55卷 183-194页

作者： Chtourou, Hedi Haouari, Mohamed Inst Preparatoire Etudes Ingn Sfax Dept Technol Sfax Tunisia Ecole Polytech Combinatorial Optimizat Res Grp ROI La Marsa 2078 Tunisia

Traditionally, the resource-constrained project scheduling problem (RCPSP) is modeled as a static and deterministic problem and is solved with the objective of makespan minimization. However, many uncertainties, such as unpredictable increases in processing times caused by rework or supplier delays, random transportation and/or setup, may render the proposed solution obsolete. In this paper, we present a two-stage algorithm for robust resource-constrained project scheduling. The first stage of the algorithm solves the RCPSP for minimizing the makespan only using a priority-rule-based heuristic, namely an enhanced multi-pass random-biased serial schedule generation scheme. The problem is then similarly solved for maximizing the schedule robustness while considering the makespan obtained in the first stage as an acceptance threshold. Selection of the best schedule in this phase is based on one out of 12 alternative robustness predictive indicators formulated for the maximization purpose. Extensive simulation testing of the generated schedules provides strong evidence of the benefits of considering robustness of the schedules in addition to their makespans. For illustration purposes, for 10 problems from. the well-known standard set J30, both robust and non-robust schedules are executed with a 10% duration increase that is applied to the same randomly picked 20% of the project activities. Over 1000 iterations per instance problem, the robust schedules display a shorter makespan in 55% of the times while the non-robust schedules are shown to be the best performing ones in only 6% of the times. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： resource-constrained project scheduling robustness stability two-stage algorithm priority rules

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two-stage Fault Classification algorithm for Real Fault Data in Transmission Lines

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IEEE ACCESS 2024年 12卷 121156-121168页

作者： Lim, Se-Heon Kim, Taegeun Lee, Kyeong-Yeong Song, Kyung-Min Yoon, Sung-Guk Soongsil Univ Dept Elect Engn Seoul 06978 South Korea

Fault classification in power transmission lines is important in distance relaying for identifying the accurate phases implicated in the fault occurrence. Generally, the accuracy of fault classification algorithms is evaluated by simulation data, which shows quite different characteristics from real fault data. Also, most of the previous works on fault classification used a single-stage method such as a rule-based algorithm or machine learning-based algorithm. Because of the diverse characteristics of real fault data, the performance of the single-stage method is limited. To address these issues, this paper proposes a novel two-stage algorithm that combines the strengths of rule-based and machine-learning algorithms to improve the accuracy of real fault data. A case study using real fault data shows that the proposed two-stage algorithm outperforms other conventional single-stage algorithms.

关键词： Classification algorithms Artificial neural networks Accuracy Random forests Machine learning algorithms Reviews Prediction algorithms Root mean square Power transmission lines two-stage algorithm rule-based artificial neural network root mean square

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two-stage recursive least squares parameter estimation algorithm for output error models

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MATHEMATICAL AND COMPUTER MODELLING 2012年第3-4期55卷 1151-1159页

作者： Duan, Honghong Jia, Jie Ding, Ruifeng Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China Nanchang Hangkong Univ Inst Aerosp Informat & Secur Technol Nanchang 330063 Peoples R China Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China

This paper presents a two-stage recursive least squares algorithm for output error models. The basic idea is to combine the auxiliary model identification idea and the decomposition technique and to decompose a system into two subsystems, which contain one parameter vector each. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm has less computational burden. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Least squares two-stage algorithm Auxiliary model Decomposition technique

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two-stage Vehicle Routing Optimization for Logistics Distribution Based on HSA-HGBS algorithm

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IEEE ACCESS 2022年 10卷 99646-99660页

作者： Sun, Qi Zhang, Haifei Dang, Jianwu Lanzhou Jiaotong Univ Key Lab Railway Ind BIM Engn & Intelligent Elect Lanzhou 730070 Peoples R China Jiangnan Univ Sch Artificial Intelligence & Comp Sci Wuxi 214122 Jiangsu Peoples R China Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Lanzhou Jiaotong Univ Sch Automat & Elect Engn Lanzhou 730070 Peoples R China

Aiming at the problems of complex urban road network, low efficiency of logistics distribution, and the difficulty of large-scale logistics distribution area division and routing planning, this paper proposes a two-stage logistics distribution vehicle routing optimization (VRP) method based on the establishment of a multi-factor complex road network constrained logistics distribution mathematical model. Considering the complex traffic elements and road network topological structure in logistics and distribution, in the first stage, a heuristic simulated annealing (HSA) distribution region partitioning algorithm is proposed with the objective of balancing vehicle task load to divide the urban logistics distribution network under complex road networks, so as to reduce the region scale and path search cost. In the second stage of route decision making, aiming at minimizing the total cost of logistics distribution, combining the VRP problem with complex road network conditions, a heuristic path search method combined with complex road network model constraints is proposed. In this stage, a hybrid genetic beam search(HGBS) algorithm is used to plan the path nodes, reduce the randomness of the model in the initial search for paths by heuristic genetic algorithms, then combine with Beam Search methods to reduce the space and time used for the search, and use optimization algorithms to improve the accuracy of independent sub-region routing optimization and the rationality of overall physical distribution route selection. Finally, the proposed method is validated in this paper with two practical cases. The experimental results show that the two-stage decision-making algorithm proposed in this paper has certain advantages in partitioning schemes, minimizing total cost and iteration times. Through comparison, the optimization ability of this method for logistics distribution networks is proved.

关键词： Logistics Road traffic Optimization Heuristic algorithms Search problems Vehicle routing Partitioning algorithms Urban areas Vehicle routing optimization complex road network two-stage algorithm heuristic simulated annealing hybrid genetic beam search

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Project scheduling for engineer-to-order assembly process with renewable energy

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 270卷

作者： Chen, Liangwei Zhang, Jingwen Demeulemeester, Erik Chen, Zhi Northwestern Polytech Univ Sch Management Xian 710072 Peoples R China Fac Econ & Business Res Ctr Operat Management B-3000 Leuven Belgium

In engineer-to-order (ETO) systems, assembling highly customized and complex products is comparable solving a project scheduling problem. In the execution of such projects, there is typically a significant amount of energy consumption. This paper investigates the synergistic utilization of diverse energy sources energy and power grid), taking inspiration from the energy internet, and investigates the optimization problem of ETO assembly projects under different power supply modes (power grid supply, solar energy and grid co-supply). Initially, an integer programming mathematical model was formulated with the optimization objectives of minimizing the total sum of delay costs, energy costs and carbon emissions costs. This aims to integrate project scheduling and electricity allocation, ultimately minimizing overall costs. Secondly, we analyzed the characteristics of the problem and designed a two-stage heuristic algorithm with embedded priority rules. Finally, the effectiveness of the model and algorithm was verified through experimental analysis. Meanwhile, the trends of different costs (delay costs, energy costs and carbon emissions costs) under different energy supply modes were explored. The case study demonstrates that utilizing renewable energy project execution reduces carbon emissions by an average of 78.19%, albeit with an 8.23% increase in costs.

关键词： Renewable energy Dual-energy hybrid Project scheduling two-stage algorithm

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A two-stage Rapid Trajectory Optimization algorithm for Hypersonic Entry

A Two-Stage Rapid Trajectory Optimization Algorithm for Hype...

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IEEE CSAA Guidance, Navigation and Control Conference (CGNCC)

作者： Wang, Jinbo Cui, Naigang Wei, Changzhu Harbin Inst Technol Aerosp Engn Dept Harbin 150001 Peoples R China

ISBN: (纸本)9781538611715

A novel two-stage rapid trajectory optimization algorithm is presented to solve the hypersonic entry trajectory optimization problem. To circumvent the issue of initial guess of nonlinear programming (NLP) based methods, and to increase the computation speed of the algorithm to accommodate online applications, a convex optimization based algorithm is designed as an initial trajectory generator, which is the first stage of the two-stage algorithm. The second stage is the NLP-based pseudospectral method. Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of single pseudospectral method.

关键词： Convex optimization Hypersonic entry Pseudospectral method Rapid trajectory optimization two-stage algorithm

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TS-TCP: two-stage Congestion Control algorithm for High Concurrency TCPs in Data center Networks 28

TS-TCP: Two-stage Congestion Control Algorithm for High Conc...

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28th International Conference on Computer Communications and Networks (ICCCN)

作者： Lu, Yifei Li, Yan Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing Peoples R China

ISBN: (纸本)9781728118567

Nowadays, TCP has been used as the de facto transport layer protocol on the Internet. However, TCP incast happens inevitably in data centers, where exist massive concurrent flows, leading to packets loss, unacceptable long transmission time, and throughput collapse. Furthermore, DCTCP is widely used to solve these problems. Unfortunately, DCTCP cannot work well under a high concurrency environment. To this end, in this paper, we introduce a two-stage congestion control algorithm (TS-TCP) for high concurrency flows. The first step is to reduce the congestion window of long-lived flows aggressively to release bandwidth for short-lived flows. The second step is to decline the sending rate by adjusting the sending interval. Through the above steps, the proposed algorithm can mitigate the TCP incast effectively. The results, by using extensive ns3 simulation, show that TS-TCP can significantly outperform the DCTCP and TCP NewReno in terms of throughput and flow completion time. Moreover, TS-TCP can support hundreds of concurrent flows while maintaining about 85% link utilization.

关键词： TCP incast Rate adjusting Congestion control two-stage algorithm Data Center Networks

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