Application of Escape Discrete Differential Evolution Algorithm in Optimal Design of Gear Transmission by Che Linxian, Yi Jian, He Bing

“…According to the equivalent mapping relation of decision variables,the constrained discrete optimization problems for gear transmission design are transformed into nonlinear constrained non- negative integer programming problems（ CNIPPs） and a discrete differential evolution（ DDE） algorithm is used to solve these problems. …”
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Traffic modeling for machine type communication and its overload control by Xin JIAN, Xiao-ping ZENG, Yun-jian JIA, Jun-yi YANG, Yuan HE

“…Machine type communications (MTC),defined as machine to machine communication over cellular mobile network,is an integral part of future ubiquitous network and has broad application prospects and market potentials.To carry out the performance analysis of network in context of MTC applications,a Beta/M/1 queue model was proposed for modeling the network with MTC applications and its full performance analysis wer iven out by deducing the analytical expression of Beta distribution’s moment generation function,in which the shape parameters of Beta distribut are as-sumed to be integer.In addition,to handle the congestion caused by mass concurrent data and signaling transmission from many MTC devices,three overload control measures were also presented,that is:1) inter-class grouping techniques; 2) re-shaping the inter-arrival time distribution of MTC devices; 3) segment-wise uniform back-off scheme.The Beta/M/1 mod-el and segment-wise uniform back-off scheme proposed here can be used as a preliminary model for different MTC ap-plication scenarios and serve as a fundamental traffic model and overload control method for future ubiquitous network.…”
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Model and Algorithm for Human Resource-Constrained R&D Program Scheduling Optimization by Junjie Chen, Shurong Tong, Hongmei Xie, Yafei Nie, Jingwen Zhang

“…A parameter and estimation formula to measure staff competency is presented, and a mixed-integer programming model is established for the problem. …”
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Service function chain embedding algorithm with wireless multicast in mobile edge computing network by Kan WANG, Nan ZHAO, Junhuai LI, Huaijun WANG

“…To resolve the excessive system overhead and serious traffic congestion in user-oriented service function chain (SFC) embedding in mobile edge computing (MEC) networks,a content-oriented joint wireless multicast and SFC embedding algorithm was proposed for the multi-base station and multi-user edge networks with MEC servers.By involving four kinds of system overhead,including service flow,server function sustaining power,server function service power and wireless transmission power,an optimization model was proposed to jointly design SFC embedding with multicast beamforming.Firstly,with Lagrangian dual decomposition,the problem was decoupled into two independent subproblems,namely,SFC embedding and multicast beamforming.Secondly,with the L<sub>p</sub> norm penalty term-based successive convex approximation algorithm,the integer programming-based SFC embedding problem was relaxed to an equivalent linear programming one.Finally,the non-convex beamforming optimization problem was transformed into a series of convex ones via the path following technique.Simulation results revealed that the proposed algorithm has good convergence,and is superior to both the optimal SFC embedding with unicasting and random SFC embedding with multicasting in terms of system overhead.…”
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Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product by Jia-Bao Liu, Sana Akram, Muhammad Javaid, Zhi-Ba Peng

“…The use of numerical numbers to represent molecular networks plays a crucial role in the study of physicochemical and structural properties of the chemical compounds. For some integer k and a network G, the networks SkG and RkG are its derived networks called as generalized subdivided and generalized semitotal point networks, where Sk and Rk are generalized subdivision and generalized semitotal point operations, respectively. …”
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Fractional Theoretical Model for Gravity Waves and Squall Line in Complex Atmospheric Motion by Liguo Chen, Liangui Yang

“…In order to explore more structural features of this solitary wave, the derived integer order model is transformed into the more practical time fractional-order model by using the variational method. …”
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MIP Models and Hybrid Algorithms for Simultaneous Job Splitting and Scheduling on Unrelated Parallel Machines by Duygu Yilmaz Eroglu, H. Cenk Ozmutlu

“…We developed mixed integer programming (MIP) models and hybrid genetic-local search algorithms for the scheduling problem of unrelated parallel machines with job sequence and machine-dependent setup times and with job splitting property. …”
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Spatial Decision Support System for Efficient School Location-Allocation by Marios Batsaris, Dimitris Kavroudakis, Euripides Hatjiparaskevas, Panagiotis Agourogiannis

“…For this purpose, a capacitated P-median approach is adopted and formulated as a mixed-integer linear problem. The SDSS is further evaluated using actual data for students' transition from primary to secondary education in the city of Mytilene, Greece. …”
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Advanced Fractional Mathematics, Fractional Calculus, Algorithms and Artificial Intelligence with Applications in Complex Chaotic Systems by Dumitru Baleanu, Yeliz Karaca

“…Moreover, Fractional Calculus (FC), related to the dynamics of complicated real-world problems, ensures emerging processes adopting fractional dynamics rather than the ordinary integer-ordered ones, which means the related differential equations feature non integer valued derivatives. …”
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Solving Fractional-Order Diffusion Equations in a Plasma and Fluids via a Novel Transform by Pongsakorn Sunthrayuth, Haifa A. Alyousef, S. A. El-Tantawy, Adnan Khan, Noorolhuda Wyal

“…The results we showed through graphs and tables for different fractional-order confirm that the results converge towards exact solution as the fractional-order tends towards integer-order. Moreover, it can solve physical problems having fractional order in different areas of applied sciences. …”
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Model predictive control for on–off charging of electrical vehicles in smart grids by Ye Shi, Hoang D. Tuan, Andrey V. Savkin, H. Vincent Poor

“…The joint coordination problem is formulated by a mixed integer non‐linear programming (MINP) with binary charging and continuous voltage variables and is solved by a highly novel computational algorithm. …”
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A Two-Disk Extended Jeffcott Rotor Model Distinguishing a Shaft Crack from Other Rotating Asymmetries by Xi Wu, Jim Meagher

“…When the general nonlinear models used in this study are constrained to reduce to linear torsional vibration, the peak responses occur at commonly reported integer ratios. Full spectrum analyses of the X and Y vibrations reveal distinct vibration characteristics of both cracked and asymmetric rotors including reverse vibration components. …”
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A Finite Difference Method for Solving Unsteady Fractional Oldroyd-B Viscoelastic Flow Based on Caputo Derivative by Fang Wang, Yu Wang

“…Viscoelastic characteristics of the unsteady Poiseuille flow are similar to the second-order fluid or integer-order Oldroyd-B fluid when the parameter is close to 0 or to 1. …”
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Pell’s equation, sum-of-squares and equilibrium measures on a compact set by Lasserre, Jean B.

“…We first interpret Pell’s equation satisfied by Chebyshev polynomials for each degree $t$, as a certain Positivstellensatz, which then yields for each integer $t$, what we call a generalized Pell’s equation, satisfied by reciprocals of Christoffel functions of “degree” $2t$, associated with the equilibrium measure $\mu $ of the interval $[-1,1]$ and the measure $(1-x^2)\mathrm{d}\mu $. …”
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Optimization of PLL frequency synthesizer by G. A. Koshuk, I. A. Tikhonov, B. A. Kosarev

“…The influence of different configurations of phase-locked loop frequency (PLL) with integer coefficients on parameters of the PLL loop of the frequency synthesizer is considered. …”
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Ranking of Search Requests in the Digital Information Retrieval System Based on Dynamic Neural Networks by Viera Bartosova, Svetlana Drobyazko, Sergii Bogachov, Olga Afanasieva, Maria Mikhailova

“…The ability to generate a ranked list of pages found as a result of the request in the digital information retrieval system can be provided by solving two problems of integer optimization: the problem of assignment of combinatorial sets of criteria for assessing the relevance of web page search and the problem of sorting of numbers—relevance values. …”
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Multi-echelon reverse logistics network design in the context of circular economy: a Hong Kong case study by Kai Kang, Bing Qing Tan

“…Consequently, construction industry leaders are advocating for development of reverse logistics networks for multiple types of CDW by solving a multi-objective mixed-integer linear programming model, which aims to restore waste for new structures toward circular economy. …”
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Station Location Optimization for the One-Way Carsharing System: Modeling and a Case Study by Yongjun Chen, Lulin Wang, Jingjing Tian

“…This paper develops a data-driven mixed-integer linear programming (MILP) model for planning one-way carsharing systems that consider the spatial distribution of demand and the interacting decisions between stations. …”
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On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions by Haobin Liu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu

“…It is observed that the solutions at various fractional orders are convergent to an integer-order solution of the problems. The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.…”
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Non-holomorphic modular S 4 lepton flavour models by Gui-Jun Ding, Jun-Nan Lu, S.T. Petcov, Bu-Yao Qu

“…Non-trivial polyharmonic Maaß forms exist for zero, negative and positive integer modular weights. Employing the finite modula group S 4 as a flavour symmetry group and assuming that the three left-handed lepton doublets furnish a triplet irreducible representation of S 4, we construct all possible 7- and 8-parameter lepton flavour models in which the neutrino masses are generated either by the Weinberg effective operator or by the type-I seesaw mechanism. …”
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