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Finding member connectivities and nodal positions of tensegrity structures based on force density method and mixed integer nonlinear programming

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ENGINEERING STRUCTURES 2018年 166卷 240-250页

作者： Xu, Xian Wang, Yafeng Luo, Yaozhi Zhejiang Univ Dept Civil Engn A-725 Anzhong Bldg866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China Zhejiang Univ Dept Civil Engn A-818 Anzhong Bldg866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China Zhejiang Univ Dept Civil Engn A-821 Anzhong Bldg866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China

An optimization approach based on force density method and mixed integer nonlinear programming is proposed for optimization of tensegrity structures on member connectivities and nodal positions. The member connectivities, nodal coordinates and force densities are simultaneously used as design variables and the number of nodes is the only necessary parameter needed to be given in advance, The proposed approach possesses a general-purpose formulation which can be degenerated into both conversional form-finding formulation and previous member connectivities-finding formulation. Various properties such as the number of cables, nodal coordinates and evenness of member internal forces can be controlled and optimized by introducing appropriate constraints and objective functions. Numerical examples are carried out to verify the proposed approach and illustrate that not only classical tensegrity systems but also novel tensegrity systems can be obtained by the proposed approach.

关键词： Tensegrity structures Member connectivities Nodal positions Optimization mixed integer nonlinear programming

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A trajectory-based method for mixed integer nonlinear programming problems

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JOURNAL OF GLOBAL OPTIMIZATION 2018年第3期70卷 601-623页

作者： Oliphant, Terry-Leigh Ali, M. Montaz Sch Comp Sci & Appl Math Johannesburg South Africa Fac Engn & Built Environm TCSE Johannesburg South Africa Univ Witwatersrand Private Bag 3 ZA-2050 Johannesburg South Africa

A local trajectory-based method for solving mixed integer nonlinear programming problems is proposed. The method is based on the trajectory-based method for continuous optimization problems. The method has three phases, each of which performs continuous minimizations via the solution of systems of differential equations. A number of novel contributions, such as an adaptive step size strategy for numerical integration and a strategy for updating the penalty parameter, are introduced. We have shown that the optimal value obtained by the proposed method is at least as good as the minimizer predicted by a recent definition of a mixed integer local minimizer. Computational results are presented, showing the effectiveness of the method.

关键词： Trajectory-based method mixed integer nonlinear programming System of ordinary differential equations Neighborhood Local minimizer Subproblem Pattern search

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Bilevel mixed-integer nonlinear programming for integrated scheduling in a supply chain network

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2019年第6-Sup期22卷 15517-15532页

作者： Yang, Jianchao Guo, Feng Luo, Li Ye, Xiaoming Sichuan Univ Business Sch Chengdu Sichuan Peoples R China Sichuan Univ Coll Comp Sci Chengdu Sichuan Peoples R China Chengdu Univ Informat Technol Sch Cybersecur Chengdu Sichuan Peoples R China

An integrated scheduling problem under a make-to-order supply chain network is addressed. This problem considers integrated production and transportation scheduling with realistic supply chain features such as unrelated parallel shop and product batch-based transportation. The mathematical model for this problem is presented, which is formulated as a bilevel mixed-integer nonlinear program. A novel bilevel evolutionary optimization model based on memetic algorithm is proposed to resolve this problem because the problem is hard-to-tackle for mathematical programming techniques and traditional intelligent techniques. The effectiveness of the proposed optimization model is validated through a series of numerical experiments. The experimental results also confirmed that the proposed optimization model is superior to other three intelligent optimization models.

关键词： Make-to-order supply chain scheduling mixed integer nonlinear programming Bilevel programming Memetic algorithm Bilevel evolutionary algorithms

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Inexact feasibility pump for mixed integer nonlinear programming

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INFORMATION PROCESSING LETTERS 2017年 118卷 110-116页

作者： Li, M. Liu, Q. Shandong Normal Univ Sch Math Sci Jinan Peoples R China

The mixed integer nonlinear programming (MINLP) problem as an optimization problem involves both continuous and discrete variables. Moreover, at least one of the functions defining the objective function or the constraints must be nonlinear. Because of its complexity, it is very difficult to obtain the exact optimal solution. Therefore, the heuristic methods for getting a feasible solution of MINLPs are very important in practice. The feasibility pump is one of the famous heuristic methods, which alternates between solving nonlinear programming (NLP) problems and mixed integer linear programming (MILP) relaxed master problems. In this paper, we will extend the feasibility pump to the case where the NLP problems are solved inexactly and propose the convergence of this method under some conditions. Moreover, we present the study of inexactness of the Lagrange multipliers (which are returned negative) of the NLP subproblems. (C) 2016 Elsevier B.V. All rights reserved.

关键词： mixed integer nonlinear programming Feasibility pump Algorithms Inexactness Heuristic

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A mixed Coding Scheme of a Particle Swarm Optimization and a Hybrid Genetic Algorithm with Sequential Quadratic programming for mixed integer nonlinear programming in Common Chemical Engineering Practice

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CHEMICAL ENGINEERING COMMUNICATIONS 2017年第8期204卷 840-851页

作者： Chanthasuwannasin, Manatsanan Kottititum, Bundit Srinophakun, Thongchai Kasetsart Univ Fac Engn Dept Chem Engn Bangkok Thailand Kasetsart Univ Natl Ctr Excellence Petr Petrochem & Adv Mat Fac Engn Dept Chem Engn Bangkok Thailand Kasetsart Univ Ctr Adv Studies Ind Technol Bangkok Thailand

In this paper, mixed integer nonlinear programming (MINLP) is optimized by PSO_GA-SQP, the mixed coding of a particle swarm optimization (PSO), and a hybrid genetic algorithm and sequential quadratic programming (GA-SQP). The population is separated into two groups: discrete and continuous variables. The discrete variables are optimized by the adapted PSO, while the continuous variables are optimized by the GA-SQP using the discrete variable information from the adapted PSO. Therefore, the population can be set to a smaller size than usual to obtain a global solution. The proposed PSO_GA-SQP algorithm is verified using various MINLP problems including the designing of retrofit heat exchanger networks. The fitness values of the tested problems are able to reach the global optimum.

关键词： Genetic algorithm Heat exchanger network mixed integer nonlinear programming mixed-coding Optimization Particle swarm Sequential quadratic programming

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The Multiplicative Weights Update Algorithm for mixed integer nonlinear programming: Theory, Applications, and Limitations

The Multiplicative Weights Update Algorithm for Mixed Intege...

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作者： Luca Mencarelli Ecole Polytechnique

学位级别：博士

This thesis presents a new algorithm for mixed integer nonlinear programming, inspi- red by the Multiplicative Weights Update frame- work and relying on a new class of reformulations, called the pointwise reformulations. mixed integer nonlinear programming is a hard and fascinating topic in Mathematical Optimiza- tion both from a theoretical and a computational viewpoint. Many real-world problems can be cast this general scheme and, usually, are quite challen- ging in terms of efficiency and solution accuracy with respect to the solving procedures. The thesis is divided in three main parts: a fore- word consisting in Chapter 1, a theoretical founda- tion of the new algorithm in Chapter 2, and the ap- plication of this new methodology to two real-world optimization problems, namely the Mean-Variance Portfolio Selection in Chapter 3, and the Multiple nonlinear Separable Knapsack Problem in Chap- ter 4. Conclusions and open questions are drawn in Chapter 5.

关键词： mixed integer nonlinear programming Multiplicative Weights Update Algorithm Mean-Variance Portfolio Multiple nonlinear Knapsack Problem

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A multi-objective mixed integer nonlinear programming model for construction site layout planning to minimise noise pollution and transport costs

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AUTOMATION IN CONSTRUCTION 2016年 61卷 73-85页

作者： Hammad, A. W. A. Akbarnezhad, A. Rey, D. Univ NSW Sch Civil & Environm Engn Sydney NSW Australia

The achievement of a sustainable industry in the construction sector requires the consideration of environmental and social impacts of the operations involved, along with the traditionally imperative economic factors affecting the construction project. An implicit social and environmental factor commonly linked with construction is the noise pollution resulting from activities taking placing during the various construction stages. The levels of sound recorded at receivers positioned in the vicinity of the construction site may be considerably affected by the site layout adopted. Site layout planning with the objective of minimising the construction noise levels has not been investigated in the available literature. To ensure a balance between economic, social and environmental impacts, the planning of the site should also account for the economic factors associated with the monetary costs of material transportation between facilities, rendering the problem a multi-objective one. This paper presents a novel multi-objective mixed integer nonlinear programming model that minimises noise levels at multiple receivers surrounding the construction site, as well as on-land material transportation costs, through site layout optimisation. An improved transportation cost model accounting for several transportation modes is presented. A Pareto front, listing nondominated global optimum solutions, is obtained for a case study tested using the 8-constraint method. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Construction site layout optimisation Construction noise pollution Site layout planning mixed integer nonlinear programming Multi-objective optimisation

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A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain

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COMPUTERS & OPERATIONS RESEARCH 2016年 65卷 93-103页

作者： Kaya, Onur Urek, Busra Anadolu Univ Dept Ind Engn Eskisehir Turkey Koc Univ Dept Ind Engn Istanbul Turkey

We analyze a network design problem for a closed-loop supply chain that integrates the collection of the used products with the distribution of the new products. We present a mixed integer nonlinear facility location-inventory-pricing model to decide on the optimal locations of the facilities, inventory amounts, prices for new products and incentive values for the collection of right amount of used products in order to maximize the total supply chain profit. We develop heuristics for the solution of this model and analyze the effectiveness of these heuristics and the effects of the parameters on this system through numerical experiments. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Closed-loop supply chain Facility location Pricing Inventory mixed integer nonlinear programming Heuristics

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Heterogeneous parallel method for mixed integer nonlinear programming

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COMPUTERS & CHEMICAL ENGINEERING 2014年 66卷 290-300页

作者： Zhou, Kai Chen, Xi Shao, Zhijiang Wan, Wei Biegler, Lorenz T. Zhejiang Univ Dept Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310003 Zhejiang Peoples R China Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In a heterogeneous parallel structure, two types of algorithms, Quesada Grossmann's (QG) algorithm and Tabu search (TS), are used to solve mixed integer nonlinear programming (MINLP) simultaneously. Communication is well designed between two threads running the two algorithms individually by exchanging three kinds of information during iterations. First, the best feasible solution in TS can become a valid upper bound for QG. Second, new linearization which can further tighten the lower bound of QG can be generated at the node provided by the TS. Third, additional integer variables can be fixed in QG, thus reducing the search space of TS. Numerical results show that good performance can be achieved by using the proposed method. Further analysis reveals that the heterogeneous method has the potential for superlinear speedup, which may surpass that of the traditional homogeneous parallel method for solving MINLPs. (c) 2013 Elsevier Ltd. All rights reserved.

关键词： mixed integer nonlinear programming Parallel computing Heterogeneous method

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Integrating nonlinear branch-and-bound and outer approximation for convex mixed integer nonlinear programming

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第2期60卷 373-389页

作者： Melo, Wendel Fampa, Marcia Raupp, Fernanda Univ Fed Rio de Janeiro Inst Grad Studies & Res Engn COPPE Rio De Janeiro Brazil Univ Fed Rio de Janeiro Inst Math Rio De Janeiro Brazil Univ Fed Rio de Janeiro COPPE BR-21945 Rio De Janeiro Brazil Pontificia Univ Catolica Rio de Janeiro Dept Ind Engn Rio De Janeiro Brazil Natl Lab Sci Comp Petropolis Brazil

In this paper, we present a new hybrid algorithm for convex mixed integer nonlinear programming (MINLP). The proposed hybrid algorithm is an improved version of the classical nonlinear branch-and-bound (BB) procedure, where the enhancements are obtained with the application of the outer approximation algorithm on some nodes of the enumeration tree. The two methods are combined in such a way that each one collaborates to the convergence of the other. Computational experiments with benchmark instances of the MINLP problem show the good performance of the proposed algorithm, which is compared to the outer approximation algorithm, the nonlinear BB algorithm and the hybrid algorithm implemented in the solver Bonmin.

关键词： mixed integer nonlinear programming Branch-and-bound Outer approximation Hybrid algorithm

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