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Gradual Optimization of University Course Scheduling Problem Using Genetic Algorithm and dynamic programming

ALGORITHMS 2025年第3期18卷 158-158页

作者： Han, Xu Wang, Dian Beijing Forestry Univ Sch Technol Beijing 100083 Peoples R China

The university course scheduling problem (UCSP) is a challenging combinatorial optimization problem that requires optimization of the quality of the schedule and resource utilization while meeting multiple constraints involving courses, teachers, students, and classrooms. Although various algorithms have been applied to solve the UCSP, most of the existing methods are limited to scheduling independent courses, neglecting the impact of joint courses on the overall scheduling results. To address this limitation, this paper proposed an innovative mixed-integer linear programming model capable of handling the complex constraints of both joint and independent courses simultaneously. To improve the computational efficiency and solution quality, a hybrid method combining a genetic algorithm and dynamic programming, named POGA-DP, was designed. Compared to the traditional algorithms, POGA-DP introduced exchange operations based on a judgment mechanism and mutation operations with a forced repair mechanism to effectively avoid local optima. Additionally, by incorporating a greedy algorithm for classroom allocation, the utilization of classroom resources was further enhanced. To verify the performance of the new method, this study not only tested it on real UCSP instances at Beijing Forestry University but also conducted comparative experiments with several classic algorithms, including a traditional GA, Ant Colony Optimization (ACO), the Producer-Scrounger Method (PSM), and particle swarm optimization (PSO). The results showed that POGA-DP improved the scheduling quality by 46.99% compared to that of the traditional GA and reduced classroom usage by up to 29.27%. Furthermore, POGA-DP increased the classroom utilization by 0.989% compared to that with the traditional GA and demonstrated an outstanding performance in solving joint course scheduling problems. This study also analyzed the stability of the scheduling results, revealing that POGA-DP maintained a high level of cons

关键词： genetic algorithms university course scheduling problem dynamic programming judgment mechanism forced mutation operation

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Optimal Control for Fractional Order Nonlinear Systems Based on Adaptive dynamic programming

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IEEE Transactions on Systems, Man, and Cybernetics: Systems 2025年第5期55卷 3086-3097页

作者： Yan, Yuqing Zhang, Huaguang Sun, Jiayue Yu, Shuhang Northeastern University College of Information Science and Engineering Shenyang110004 China Northeastern University State Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Shenyang110004 China

In this article, an adaptive dynamic programming (ADP)-based optimal control strategy for a series of fractional-order nonlinear systems (FONS) with unknown control directions is investigated. To eliminate the challenges posed by unknown control directions, fractional-order Nussbaum-type functions are introduced for FONS, expanding the range of possible applications. Additionally, since system performance is compromised by disturbances, a fractional-order disturbance observer is designed to counteract the effects of external disturbances and enhance system robustness. Furthermore, differential geometric methods are employed to investigate FONS, constructing appropriate diffeomorphism that provide equivalent systems for decoupled linearization. Then, an optimal control method is studied for a class of strictly feedback FONS, in which Nussbaum-type functions are combined with ADP theory during the backstepping design process. Finally, based on fractional Lyapunov stability theory and backstepping method, it is guaranteed that all signals of the closed-loop FONS are uniformly ultimately bounded (UUB). Numerical simulation and a PMSM model are utilized to verify the effectiveness of the presented method. © 2013 IEEE.

关键词： dynamic programming

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Adaptive dynamic programming with Event-Triggered Sampling Control for Path Following of Autonomous Vehicles

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JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2025年第2期29卷 316-324页

作者： Zhang, Haining Qin, Fengshuo Zhang, Pengfei Shandong Vocat & Tech Univ Int Studies Sch Informat Engn 99 Shanhai Rd Rizhao 276826 Shandong Peoples R China Southeast Univ Sch Cyber Sci & Engn 2 Southeast Daxue Rd Nanjing 211102 Jiangsu Peoples R China

Sampled-data control for dynamic programming of continuous-time system, which can facilitate to implement control actions under networked environments, is rarely considered in most existing works. In order to address this issue, an event-triggered dynamic programming sampling control (ET-DPSC) approach is investigated for networked path-following control of autonomous vehicles. The first goal is to establish the sampled-data-based event-triggered path-following control model using Hamilton-Jacobi-Bellman equation. Secondly, the asymptotic stability criterion in an input-to-state sense should be tackled by exploiting Lyapunov theory and input delay approach. As a third goal, the sampled-data controller based on dynamic programming method should be synthesized. Compared to most existing ADP-based control strategies, the proposed ET-DPSC approach not only guarantees the stability of path-following control but also provides significant benefits for control implementation under communication-constrained environments. In addition, Zeno behavior is naturally excluded by using periodic discrete-time sampling control fashion. At last, Simulink and CarSim joint simulations are conducted to show effectiveness of the proposed ET-DPSC scheme by comparing with linear quadratic regulation without considering input delay.

关键词： event-triggered control dynamic programming input delay path following

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A 3-space dynamic programming heuristic for the cubic knapsack problem

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2025年第4期49卷 1-32页

作者： Dije, Ibrahim Dan Fomeni, Franklin Djeumou Coelho, Leandro C. GERAD Grp Res Decis Anal 2920 Chemin Tour Montreal PQ H3T 1N8 Canada CIRRELT Interuniv Res Ctr Enterprise Networks Logi 2920 Chemin Tour Montreal PQ H3T 1N8 Canada Univ Quebec Montreal UQAM 320 Rue Sainte Catherine Est Montreal PQ H2X 1L7 Canada Univ Laval Canada Res Chair Integrated Logist 2325 Rue Univ Quebec City PQ G1V 0A6 Canada

The cubic knapsack problem (CKP) is a combinatorial optimization problem, which can be seen both as a generalization of the quadratic knapsack problem (QKP) and of the linear Knapsack problem (KP). This problem consists of maximizing a cubic function of binary decision variables subject to one linear knapsack constraint. It has many applications in biology, project selection, capital budgeting problem, and in logistics. The QKP is known to be strongly NP-hard, which implies that the CKP is also NP-hard in the strong sense. Unlike its linear and quadratic counterparts, the CKP has not received much of attention in the literature. Thus the few exact solution methods known for this problem can only handle problems with up to 60 decision variables. In this paper, we propose a deterministic dynamic programming-based heuristic algorithm for finding a good quality solution for the CKP. The novelty of this algorithm is that it operates in three different space variables and can produce up to three different solutions with different levels of computational effort. The algorithm has been tested on a set of 1570 test instances, which include both standard and challenging instances. The computational results show that our algorithm can find optimal solutions for nearly 98% of the standard test instances that could be solved to optimality and for 92% for the challenging instances. Finally, the computational experiments present comparisons between our algorithm, an existing heuristic algorithm for the CKP found in the literature, as well as adaptations to the CKP of some heuristic algorithms designed for the QKP. The results show that our algorithm outperforms all these methods.

关键词： Knapsack problem Integer programming dynamic programming Cubic Knapsack problem

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dynamic programming-based exact and heuristic algorithms for single machine scheduling with sequence-dependent setups

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 273卷

作者： Hu, Tengmu Tseng, Shih-Hsien Allen, Theodore T. Ohio State Univ Dept Integrated Syst Engn Columbus OH 43221 USA Natl Taiwan Univ Sci & Technol Dept Ind Management Sch Management Taipei 106 Taiwan

This study presents a novel algorithmic framework and an inventory flow mixed integer programming formulation designed to minimize total tardiness and the number of setups. The approach decomposes the problem into three stages: intra-family scheduling, family sequence optimization, and family-switch timing. We propose a specialized heuristic with O(n5 log n) complexity efficiently handles intra-family scheduling and is extended to accommodate subfamily groupings. dynamic programming is employed for family-switch optimization, with state complexity constrained to 2n + 1. In the last stage of algorithmic framework, we propose a branch-and-bound method to handle family-switch timing, utilizing lower bounds derived from the results of previous stages. Our overall proposed "branch-and-bound-regulated dynamic programming (B&B- DP)" algorithm excels in solving large-scale scheduling problems, demonstrating superior performance against four benchmark methods across 150 test cases. This algorithmic framework extends the capabilities of single- machine scheduling with family setup times to handle a large number of jobs. In our experiments, we show that the proposed algorithm reduces total tardiness by 10%-25% compared to other methods. This research not only advances the state of the art in single-machine scheduling but also provides a scalable and effective framework for addressing complex production scheduling challenges.

关键词： dynamic programming Branch and bound Heuristic Scheduling

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dynamic programming-based energy storage siting and sizing: Application to enhance flexibility of large-scale power grid

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JOURNAL OF ENERGY STORAGE 2025年 106卷

作者： Zhao, Yucan Bi, Yue Xu, Yao Gao, Yuan Hu, Sile Guo, Yu Yang, Jiaqiang Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China China Int Telecommun Construct Corp Beijing 100000 Peoples R China Inner Mongolia Power Grp Co Ltd Hohhot 010020 Peoples R China

To address the issues of limited Energy Storage System (ESS) locations and the flexibility unevenly distributed in the large-scale power grid planning, this paper introduces the dynamic programming (DP) theory into flexibility planning, and proposes a DP-based ESS siting and sizing method. This method reduces the computational complexity of siting and sizing to ensure a sufficient number of ESSs allocated. It provides each partitioning area with a certain degree of flexible ramping capability so that the flexibility is evenly distributed in the large-scale grid. The proposed method starts with a high-voltage pruning partition algorithm to hierarchically partition the large-scale grid, with the partitioning outcomes serving to divide the various DP stages. Then a state transition equation is established with the ESS rated power as the state variable, considering all nodes which satisfy the voltage level requirements as potential ESS sites to ensure a sufficient number of locations. Following this, a DP basic equation is formulated with the ESS capacity as the decision variable, setting flexibility constraints for all partitioning areas to achieve an even distribution of grid flexibility. By combining the state transition equation and the DP basic equation, the proposed method culminates in the energy storage allocation dynamic programming model, which determines the optimal locations, capacities, and rated powers of ESSs, along with the construction cost. This paper further explores the development of the Flexible Resource Allocation Intelligent Decision Software (FRAIDS) building upon the proposed method. Case analysis in an actual grid verifies that the calculations from FRAIDS significantly enhance the entire grid flexibility. Additionally, day-ahead dispatching results indicate that, following ESS allocation, net load fluctuates between 15,295.5 MW and 17,794.9 MW with the conventional method, compared to a more stable range of 16,309.8 MW to 17,417.4 MW with the

关键词： Energy storage Large-scale power grid Flexibility Planning dynamic programming Siting Sizing

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Construction and Preliminary Validation of a dynamic programming Concept Inventory 2025

Construction and Preliminary Validation of a Dynamic Program...

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56th Technical Symposium on Computer Science Education

作者： Ferland, Matthew Rao, Varun Nagaraj Arora, Arushi van der Poel, Drew Luu, Michael Huynh, Randy Reiber, Frederick Ossman, Sandra Poulsen, Seth Shindler, Michael Dickinson Coll Carlisle PA 17013 USA Princeton Univ Princeton NJ USA Univ Calif Irvine Irvine CA USA Northeastern Univ Boston MA USA Boston Univ Boston MA USA Utah State Univ Logan UT USA

ISBN: (纸本)9798400705311

Concept inventories are standardized assessments that evaluate student understanding of key concepts within academic disciplines. While prevalent across STEM fields, their development lags for advanced computer science topics like dynamic programming (DP)an algorithmic technique that poses significant conceptual challenges for undergraduates. To fill this gap, we developed and validated a dynamic programming Concept Inventory (DPCI). We detail the iterative process used to formulate multiple-choice questions targeting known student misconceptions about DP concepts identified through prior research studies. We discuss key decisions, tradeoffs, and challenges faced in crafting probing questions to subtly reveal these conceptual misunderstandings. We conducted a preliminary psychometric validation by administering the DPCI to 172 undergraduate CS students finding our questions to be of appropriate difficulty and effectively discriminating between differing levels of student understanding. Taken together, our validated DPCI will enable instructors to accurately assess student mastery of DP. Moreover, our approach for devising a concept inventory for an advanced theoretical computer science concept can guide future efforts to create assessments for other under-evaluated areas currently lacking coverage.

关键词： dynamic programming algorithms education concept inventory

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Student Utilization of Metacognitive Strategies in Solving dynamic programming Problems 2025

Student Utilization of Metacognitive Strategies in Solving D...

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56th Technical Symposium on Computer Science Education

作者： Liu, Jonathan Goodwin, Erica Franklin, Diana Univ Chicago Chicago IL 60637 USA

ISBN: (纸本)9798400705311

dynamic programming (DP) is commonly regarded as one of the most difficult topics in the upper-level algorithms curriculum. The teaching of metacognitive strategies may prove effective in helping students learn to design DP algorithms. To explore both whether students learn and use these strategies on their own and the effect of guidance about using these strategies, we conducted think-aloud interviews with structured guidance at two points in a college algorithms course: once immediately after students learned the concept and once at the end of the course. We explore 1) what metacognitive strategies are commonly employed by students, 2) how effectively they help students solve problems, and 3) to what extent structured guidance about using metacognitive strategies is effective. We find that these strategies generally help students make progress in solving DP problems, but that they can mislead students as well. We also find that the adoption of these strategies is an individualized process and that structured strategy guidance is often insufficient in allowing students to solve individual DP problems, indicating the need for more extensive strategy instruction.

关键词： dynamic programming Metacognitive Strategies Think-aloud Study Algorithms

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A segment-wise dynamic programming algorithm for BSDEs|

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Probability, Uncertainty and Quantitative Risk 2025年第1期10卷 103-134页

作者： Christian Bender Steffen Meyer Department of Mathematics Saarland UniversityCampus E 24D-66123 SaarbrückenGermany

We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.

关键词： Backward stochastic differential equations Empirical regression dynamic programming Monte Carlo methods

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Patient admission control and bed allocation during a pandemic using dynamic programming and simulation

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JOURNAL OF MODELLING IN MANAGEMENT 2025年第4期20卷 1284-1325页

作者： Zamani, Hamed Parvaresh, Fereshteh Isfahan Univ Technol Dept Ind & Syst Engn Esfahan Iran

PurposeThis paper aims to examine patient admission control (AC) policies aimed at reducing patient waiting times during a pandemic. Unlike previous studies that focused on AC within a single hospital, this research seeks to minimize waiting times across multiple hospitals. The primary objective is to ensure that patients are admitted to the most appropriate hospital to reduce congestion during a ***/methodology/approachThis paper proposes two stochastic dynamic programming (DP) models. The first model treats the number of available beds as a fixed parameter, while the second model considers the number of beds as a decision variable. In the first model, the main decision is determining which hospital a pandemic patient should be assigned to. Bed allocation is not addressed in this model. The rationale for presenting two models is based on the dynamic nature of hospital resource allocation. In some situations, hospital administrators must decide how to configure beds between pandemic and nonpandemic wards. In other scenarios, bed allocation is predetermined and remains constant throughout the pandemic. DP algorithms are used to precisely solve small-scale instances of the problem and generate policies for patient assignment. These policies are then evaluated against alternative heuristic policies using larger-scale problem instances and simulation *** results reveal that implementing an AC unit and adopting an appropriate patient allocation policy can reduce average patient waiting times by approximately 50%. Moreover, when equity is a consideration (when the objectives are in the form of min-max), the policies derived from the DP approach outperform heuristic policies. However, some heuristic policies are more effective when equity is not a primary ***/valueThe findings of this research can assist health-care managers in making informed decisions by highlighting the implications and performance of various strategies.

关键词： Admission control Pandemic Congestion management dynamic programming Simulation

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