Solution of Extraordinary Differential Equations with Physical Reasoning by Obtaining Modal Reaction Series by Shantanu Das

“…In this formulation of FDE by RL method it is found that there is no need to worry about the fractional initial states; instead one can use integer order initial states (the conventional ones) to arrive at solution of FDE. …”
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A mathematical model of the location problem for central and secondary warehouses in the multi-level supply chain network of perishable products by Seyyed Mostafa Mousavi, Majid Motamedi, Rasoul Karimi

“…In this research, the four-level supply chain in the field of food products, including the levels of supplier, customer, and central and secondary warehouses, has been investigated. A mixed integer mathematical model of the research problem is presented to minimize chain costs, including the setting up and preparation of warehouses, transportation between transfer levels, and holding products. …”
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On the number of residues of certain second-order linear recurrences by Accossato, Federico, Sanna, Carlo

“…We generalize this result by showing that $\mathcal{R}(X^2 - a_1 X - 1) = \mathbb{Z}^+$ for every nonzero integer $a_1$. As a corollary, we deduce that for all integers $a_1 \ge 1$ and $k \ge 2$ there exists $\xi \in \mathbb{R}$ such that the sequence of fractional parts $\bigl (\mathrm{frac}(\xi \alpha ^n)\big )_{n \ge 0}$, where $\alpha :=\big (a_1 + \sqrt{a_1^2 + 4}\,\big ) / 2$, has exactly $k$ limit points. …”
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Assessing the Role of Vaccination in the Control of Hand, Foot, and Mouth Disease Transmission by Zuhur Alqahtani, Mahmoud H. DarAssi, Yousef AbuHour, Areej Almuneef

“…The fractional-order model captures the memory effect in infectious disease dynamics, providing further insight into modeling HFMD transmission compared to a traditional integer-order model. The results would contribute to effective vaccination strategies and public health interventions against HFMD.…”
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Genetic Algorithm-Based Particle Swarm Optimization Approach to Reschedule High-Speed Railway Timetables: A Case Study in China by Mingming Wang, Li Wang, Xinyue Xu, Yong Qin, Lingqiao Qin

“…In this study, a mixed integer programming model is proposed to address timetable rescheduling problem under primary delays. …”
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Essential dimension of symmetric groups in prime characteristic by Edens, Oakley, Reichstein, Zinovy

“…The essential dimension $\operatorname{ed}_k(\operatorname{S}_n)$ of the symmetric group $\operatorname{S}_n$ is the minimal integer $d$ such that the general polynomial $x^n + a_1 x^{n-1} + \dots + a_n$ can be reduced to a $d$-parameter form by a Tschirnhaus transformation. …”
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Simulation of a multi-layered facility location model by cosidering queueing theory by Mahdi Yousefi Nejad Attari, Saeed Kolahi-Randji, Aniseh Neishabouri Jami

“…The proposed model is a nonlinear integer programming model and it is in the field of highly complex problems. …”
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Graph Pointer Network Based Hierarchical Curriculum Reinforcement Learning Method Solving Shuttle Tankers Scheduling Problem by Xiaoyong Gao, Yixu Yang, Diao Peng, Shanghe Li, Chaodong Tan, Feifei Li, Tao Chen

“…However, conventional approaches like Mixed Integer Linear Programming (MILP) or meta heuristic algorithms often fail in long running time. …”
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Designing High-Freedom Responsive Feeder Transit System with Multitype Vehicles by Zhengwu Wang, Jie Yu, Wei Hao, Tao Chen, Yi Wang

“…In order to improve the operation of the HFRFT system, the optimization design methods are suggested for vehicle routes, scheduling, and service area. A mixed integer programming model and its hybrid of a metaheuristic algorithm are proposed to efficiently and integrally solve the vehicle routes and scheduling parameters according to the reservation requirements. …”
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Optimal Scheduling of Energy Storage Systems with Private Ownership Based on a Stochastic-Robust Hybrid Optimization Model in Energy and Ancillary Services Markets by Mohammad Farahani, Abouzar Samimi, Hossein Shateri

“…The proposed formulation based on the Mixed Integer Nonlinear Programming (MINLP) model is implemented in the GAMS software environment and the results demonstrate the maximum profitability of BES in EM (21% more) and also show participation in providing ancillary services, such as reserve to provide security in incidents and reactive power to maintain stability and reduce cost and losses, despite the decrease in profit, leads to neutralizing the negative impact of uncertainties in the BES profit..…”
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A Multimodal Passenger-and-Package Sharing Network for Urban Logistics by Yuxiong Ji, Yujing Zheng, Jizhou Zhao, Yu Shen, Yuchuan Du

“…Packages are transported by metro on backbone links between the hubs and are carried by taxis or trucks between service stores and hubs, depending on the unit costs of these two modes and capacity constraint of the taxi. A mixed integer linear programming model for hub location problems—fusing the multiassignment p-hub median problem without capacity constraints and the capacitated multiassignment p-hub covering problem—is formulated to optimize the multimodal PPS network. …”
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A vibration damping optimization algorithm to solve flexible job shop scheduling problems with reverse flows by Esmaeil Mehdizadeh, Fatemeh Soleimaninia

“…The aim is to minimize the makespan of the jobs (the maximum completion time). A Mixed Integer Programming (MIP) is presented to model the problem and the Branch and Bound (B&B) method is used to solve the problem. …”
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Understanding the Complexity of Temperature Dynamics in Xinjiang, China, from Multitemporal Scale and Spatial Perspectives by Jianhua Xu, Yaning Chen, Weihong Li, Zuhan Liu, Chunmeng Wei, Jie Tang

“…The main conclusions are as follows (1) The integer CD values indicate that the temperature dynamics are a complex and chaotic system, which is sensitive to the initial conditions. (2) The complexity of temperature dynamics decreases along with the increase of temporal scale. …”
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Two-Stage Optimization Method for the Bearing Layout of Isolated Structure by Yu Dang, GenXiong Zhao, HongTu Tian, Guobao Li

“…Moreover, the cost of the isolation bearing layout should be as low as possible. An integer programming method is adopted to optimize the number of each type of isolator. …”
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An Optimization Method for the Train Service Network Design Problem by Jie Xiao, Yi Xie, Haowei Yu, Hongying Yan

“…It aims to determine the types of train services to be offered, how many trains of each service are to be dispatched per day (service frequency), and by which train services shipments are to be transported. An integer programming model is proposed to address this problem. …”
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Optimal PV‐storage capacity planning for rail transit self‐consistent energy systems considering extreme weather conditions by Siyu Guo, Liuyang Cai, Haiyi Wu, Guanghui Song, Li Lin, Yanbo Chen

“…Finally, the model is linearized as mixed‐integer linear programming and solved using Gurobi and the Yalmip toolbox. …”
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Design Guidelines for Fractional Order Cascade Control in DC Motors: A Computational Analysis on Pairing Speed and Current Loop Orders Using Oustaloup’s Recursive Method by Marta Haro-Larrode, Alvaro Gomez-Jarreta

“…Finding appropriate combinations of fractional exponents is therefore crucial to minimize experimental costs and achieve better dynamic response compared to integer-order cascade control. Additionally, mitigating adverse couplings between speed and current loops remains an underexplored area in fractional-order control design. …”
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Hypergraph-based resource allocation for Device-to-Device underlay H-CRAN network by Pan Zhao, Wenlei Guo, Datong Xu, Zhiliang Jiang, Jie Chai, Lijun Sun, He Li, Weiliang Han

“…To solve the non-convex mixed integer nonlinear optimization problem, the optimization model is decomposed into two sub-problems, which are all solvable quasi-convex power allocation and non-convex channel allocation. …”
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A multi-objective robust possibilistic programming approach to designing sustainable and reliable closed-loop supply chain network (case study: aluminum industry) by Sajad Amirian, Maghsoud Amiri, Mohammad Taghi Taghavifard

“…The mathematical model developed in this research is of mixed integer linear programming type, which is implemented in GAMS software to solve it and find Pareto optimal solutions.Findings: The accuracy of the overall performance of the proposed model has been evaluated with four examples (based on the coefficients of the objective functions) from a case study in the aluminium industry. …”
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A systematic literature review of aggregate production planning (APP): Social and economic perspectives by Wan Yee Leong, Kuan Yew Wong, Ali Anjomshoae

“…Findings: The outcome shows that most of the previous studies applied mixed-integer linear programming (MILP) methods in developing the APP models while stochastic and fuzzy methods are the most common approaches to deal with uncertainties. …”
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