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Two heuristics for the Euclidean Steiner tree problem

JOURNAL OF GLOBAL OPTIMIZATION 1998年第1期13卷 95-106页

作者： Dreyer, DR Overton, ML Carnegie Mellon Univ Sch Comp Sci Pittsburgh PA 15213 USA NYU Courant Inst Math Sci Dept Comp Sci New York NY 10012 USA

The Euclidean Steiner tree problem is to find the tree with minimal Euclidean length spanning a set of fixed points in the plane, allowing the addition of auxiliary points to the set (Steiner points). The problem is NP-hard, so polynomial-time heuristics are desired. We present two such heuristics, both of which utilize an efficient method for computing a locally optimal tree with a given topology. The first systematically inserts Steiner points between edges of the minimal spanning tree meeting at angles less than 120 degrees, performing a local optimization at the end. The second begins by finding the Steiner tree for three of the fixed points. Then, at each iteration, it introduces a new fixed point to the tree, connecting it to each possible edge by inserting a Steiner point, and minimizes over all connections, performing a local optimization for each. We present a variety of test cases that demonstrate the strengths and weaknesses of both algorithms.

关键词： Euclidean Steiner tree interior-point algorithm

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A SYMMETRIC REDUCTION OF THE NT DIRECTION

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SIAM JOURNAL ON OPTIMIZATION 2014年第2期24卷 714-732页

作者： Jarre, Florian Hergenroeder, Chantal Univ Dusseldorf Math Inst D-40225 Dusseldorf Germany

A stable symmetrization of the linear systems arising in interior-point methods for solving linear programs is introduced. A comparison of the condition numbers of the resulting interior-point linear systems with other commonly used approaches indicates that the new approach may be best suitable for an iterative solution. It is shown that there is a natural generalization of this symmetrization to the Nesterov-Todd (NT) search direction for solving semidefinite programs. The generalization includes a novel pivoting strategy to minimize the norm of the right and side and heavily relies on the symmetry properties of the NT direction. The search directions generated by iterative solvers typically have fairly low relative accuracy. Nevertheless, in some preliminary numerical examples, a suitably adapted interior-point approach results in a rather small number of outer iterations.

关键词： linear program semidefinite program condition number quasi-minimal residual iteration interior-point algorithm

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Neuro-Evolutionary Computing Paradigm for the SIR Model Based on Infection Spread and Treatment

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NEURAL PROCESSING LETTERS 2023年第4期55卷 4365-4396页

作者： Gomez-Aguilar, J. F. Sabir, Zulqurnain Alqhtani, Manal Umar, Muhammad Saad, Khaled M. CONACyT Tecnol Nacl Mexico CENIDET Interior Internado Palmira S-N Cuernavaca 62490 Morelos Mexico Hazara Univ Dept Math & Stat Mansehra Pakistan Najran Univ Coll Sci & Arts Dept Math Najran Saudi Arabia

The intension of the present study is to solve the nonlinear biological susceptible, infected and recovered (SIR) models using Feed-Forward Artificial Neural Networks (FFANN) optimized with global search of genetic algorithm aided with rapid local search interior-point IP algorithms, i.e., FEANN-GAIP. An error-based cost function is formulated by exploiting FEANN models of differential equations and its associated conditions representing the SIR systems. The proposed FEANN-GAIP scheme is evaluated for three types of infection spread biological systems based on simple SIR, modified SIR and treatment-based SIR models. The reliability and correctness of the FEANN-GAIP scheme is substantiated with good agreement based on the results of the Adam numerical solver. The statistical outcomes further demonstrate the consistent precision, applicability, and robustness of the designed FEANN-GAIP based stochastic numerical solver.

关键词： HIV infection Particle swarm Hybrid approach interior-point algorithm Artificial neural networks Statistical analysis

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Improved complexity using higher-order correctors for primal-dual Dikin affine scaling

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MATHEMATICAL PROGRAMMING 1997年第1期76卷 117-130页

作者： Jansen, B Roos, C Terlaky, T Ye, Y DELFT UNIV TECHNOL FAC TECH MATH & INFORMATNL-2600 GA DELFTNETHERLANDS UNIV IOWA DEPT MANAGEMENT SCIIOWA CITYIA 52242

In this paper we show that the primal-dual Dikin affine scaling algorithm for linear programming of Jansen, Roos and Terlaky enhances an asymptotical O(root nL) complexity by using corrector steps, We also show that t... 详细信息

关键词： linear programming interior-point algorithm affine scaling complexity

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Adaptive hierarchical coding and modulation scheme over satellite channels

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IET COMMUNICATIONS 2019年第17期13卷 2834-2839页

作者： He, Rui Yang, Dewei Wang, Hua Kuang, Jingming Beijing Inst Technol Sch Informat & Elect Beijing Peoples R China

In this study, a new scheme called adaptive hierarchical coding and modulation has been proposed, based on Adaptive Coding and Modulation (ACM) and hierarchical modulation (HM). The primary contribution of this study is summarised as the following aspects. Firstly, 16- to 64-APSK constellations with size and labelling optimisation method are proposed for HM, which can be adapted to transmitting multiple hierarchies with different QoS streams and to the non-linear satellite channels due to a lower peak-to-average power ratio compared to traditional hierarchical QAM modulation. Bit channel capacity and Chernoff error bound are introduced to optimise size and labelling of the constellation with interior-point algorithm and modified binary switch algorithm for a specific channel model to get a better performance. Secondly, combining with optimised constellations, coding and modulation modes set is obtained from using constellation design and optimisation method, with different modulation orders and code rates. And over satellite channels with rain and location attenuation, the proposed scheme is able to adapt itself to a changing channel condition and increase the transmission rate compared with ACM schemes of DVB-S2 and DVB-S2X standard.

关键词： optimisation modulation coding phase shift keying quadrature amplitude modulation quality of service satellite communication error statistics channel capacity adaptive codes adaptive modulation wireless channels telecommunication switching adaptive hierarchical coding hierarchical modulation HM labelling optimisation method nonlinear satellite channels peak-to-average power ratio traditional hierarchical QAM modulation bit channel capacity specific channel model optimised constellations modulation modes constellation design code rates ACM schemes adaptive coding and modulation scheme modulation orders channel condition QoS streams 16-to 64-APSK constellations interior-point algorithm modified binary switch algorithm modulation modes set location attenuation rain attenuation transmission rate DVB-S2X standard DVB-S2 standard Chernoff error bound

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Solution of novel multi-fractional multi-singular Lane-Emden model using the designed FMNEICS

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NEURAL COMPUTING & APPLICATIONS 2021年第24期33卷 17287-17302页

作者： Sabir, Zulqurnain Raja, Muhammad Asif Zahoor Guirao, Juan L. G. Saeed, Tareq Hazara Univ Dept Math & Stat Mansehra Pakistan Natl Yunlin Univ Sci & Technol Future Technol Res Ctr 123 Univ RdSect 3 Touliu 64002 Yunlin Taiwan Tech Univ Cartagena Hosp Marina Dept Appl Math & Stat Cartagena 30203 Spain King Abdulaziz Univ Fac Sci Dept Math Nonlinear Anal & Appl Math NAAM Res Grp POB 80203 Jeddah 21589 Saudi Arabia

The present study is related to design a novel multi-fractional multi-singular Lane-Emden model (MFMS-LEM) by keeping the ideas of the literature LEM and by extension of the work of doubly singular multi-fractional LEM. This mathematical novel MFMS-LEM is numerically treated by applying the fractional Meyer neuro-evolution intelligent solver (FMNEICS). The optimization is performed using the mutual heuristics of fractional Mayer wavelet neural networks (FMW-NN), the global search aptitude of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e., FMW-NN-GAIPA. The derivation steps, details of the singular points, fractional terms, shape factors and singular points are also provided. The modeling strength of MW-NN is implemented to characterize the novel model in the sagacity of mean squared error of objective function and network optimization is performed with the integrated capability of GAIPA. The authentication, perfection and verification of FMNEICS is checked for three diverse cases of the novel model which are conventional via relative studies through the reference solutions based on accuracy, stability, robustness and convergence procedures. Furthermore, the explanations via the statistical measures validate the value of the designed stochastic solver FMW-NN-GAIPA.

关键词： Artificial neural networks Multi-fractional model based on Lane-Emden Multi-singular systems Mayer wavelet neural networks interior-point algorithm Genetic algorithms

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A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with O(√nL)-iteration complexity

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MATHEMATICAL PROGRAMMING 2004年第2期100卷 317-337页

作者： Potra, FA Univ Maryland Baltimore Cty Baltimore MD 21250 USA

An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is presented. The method has -iteration complexity and is superlinearly convergent even when the ... 详细信息

关键词： linear complementarity problem interior-point algorithm large neighbourhood superlinear convergence

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An improved computationally efficient identification method for errors-in-variables models based on v-gap optimisation

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INTERNATIONAL JOURNAL OF CONTROL 2019年第9期92卷 2150-2158页

作者： Geng, Li-Hui Tianjin Univ Technol & Educ Sch Automat & Elect Engn Tianjin Key Lab Informat Sensing & Intelligent Co Tianjin Peoples R China

A v-gap optimisation-based frequency-domain identification method is proposed to estimate a nominal normalised right graph symbol for errors-in-variables models. The proposed method follows the similar identification idea from a previous research work but with improved computational efficiency using interior-point (IP) algorithms. By imposing an inner function constraint instead of frequency point-wise constraints to normalise the graph symbol, the number of involved equality constraints for the v-gap optimisation is related to the nominal model order instead of the data length. As a consequence, the computational complexity of the proposed IP-based identification algorithm is much lower than that of linear matrix inequalities-based algorithms. Due to the fact that the data length is typically much larger than the finite nominal model order, the number of saved equality constraints is close to that of the employed data points. Finally, two numerical simulation examples are given to verify the proposed identification method.

关键词： V-gap optimisation computational efficiency errors-in-variables models interior-point algorithm

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Limit states of structures in n-dimensional loading spaces with limited kinematical hardening

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COMPUTERS & STRUCTURES 2015年第Jan.期147卷 4-13页

作者： Simon, Jaan-Willem Rhein Westfal TH Aachen Inst Appl Mech D-52074 Aachen Germany

The load bearing capacity of engineering structures subjected to varying thermo-mechanical loading can be determined most conveniently by shakedown analysis. Admittedly, if limited kinematical hardening is considered, shakedown analysis is, as yet, restricted to either one or two independently varying loads. In consequence, the aim of this paper is to extend existing formulations for arbitrary numbers of loading, which is inevitable for most technical applications. For this, limited kinematical hardening was incorporated into Melan's shakedown theorem by means of a two-surface model covering both alternating plasticity and ratcheting, generalized to n-dimensional loading spaces. As a result, the three-dimensional shakedown domain accounting for hardening is presented for a flanged pipe subjected to thermo-mechanical loading. (C) 2014 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

关键词： Shakedown analysis n-dimensional loading space Limited kinematical hardening interior-point algorithm Convex optimization Nonlinear programming

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Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

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IEEE ACCESS 2020年 8卷 86674-86695页

作者： Khan, Adnan Sulaiman, Muhammad Alhakami, Hosam Alhindi, Ahmad Abdul Wali Khan Univ Dept Math Mardan 23200 Pakistan Umm Al Qura Univ Dept Comp Sci Mecca 21955 Saudi Arabia Umm Al Qura Univ Ctr Innovat & Dev AI CIADA Mecca 21955 Saudi Arabia

This paper aims at the analysis of the VdP heartbeat mathematical model. We have analysed the conditionality of a mathematical model which represents the oscillatory behaviour of the heart. A novel neuroevolutionary approach is chosen to analyse the mathematical model. The characteristics of the cardiac pulse of the heart are examined by considering two major scenarios with sixteen different cases. Artificial neural networks (ANNs) are constructed to obtain the best solutions for the heartbeat model. Unknown weights are finely tuned by a combination of a global search technique the Harris Hawks Optimizer (HHO) and a local search technique the interior point algorithm (IPA). Stable behaviour of solutions obtained by considering different cases demonstrates that the model under consideration is well-conditioned. The accuracy of our novel procedure is established by getting the lowest residual errors in our solution for all cases. Graphical and statistical analysis are added to further elaborate the accuracy of our approach.

关键词： Cardiac pulse model hybridized soft computing artificial neural networks non-linear ordinary differential equations heuristics interior-point algorithm Harris Hawks optimizer

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