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Orbital rendezvous mission planning using mixed integer nonlinear programming

ACTA ASTRONAUTICA 2011年第7-8期68卷 1070-1078页

作者： Zhang, Jin Tang, Guo-jin Luo, Ya-Zhong Li, Hai-yang Natl Univ Def Technol Coll Aerosp & Mat Engn Changsha Hunan Peoples R China

The rendezvous and docking mission is usually divided into several phases, and the mission planning is performed phase by phase. A new planning method using mixed integer nonlinear programming, which investigates single phase parameters and phase connecting parameters simultaneously, is proposed to improve the rendezvous mission's overall performance. The design variables are composed of integers and continuous-valued numbers. The integer part consists of the parameters for station-keeping and sensor-switching, the number of maneuvers in each rendezvous phase and the number of repeating periods to start the rendezvous mission. The continuous part consists of the orbital transfer time and the station-keeping duration. The objective function is a combination of the propellant consumed, the sun angle which represents the power available, and the terminal precision of each rendezvous phase. The operational requirements for the spacecraft-ground communication, sun illumination and the sensor transition are considered. The simple genetic algorithm, which is a combination of the integer-coded and real-coded genetic algorithm, is chosen to obtain the optimal solution. A practical rendezvous mission planning problem is solved by the proposed method. The results show that the method proposed can solve the integral rendezvous mission planning problem effectively, and the solution obtained can satisfy the operational constraints and has a good overall performance. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Orbital rendezvous Mission planning mixed integer nonlinear programming Genetic algorithm

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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 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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Coupling genetic algorithm with a grid search method to solve mixed integer nonlinear programming problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1997年第12期34卷 13-23页

作者： Cheung, BKS Langevin, A Delmaire, H GERAD École des Hautes Études Commerciales 3000 ch. de la Cote-Sainte-Catherine Montréal Québec Canada H3T 2A7

A new hybrid algorithm is being introduced for solving mixed integer nonlinear programming (MINLP) problems which arise from study of many real-life engineering problems such as the minimum cost development of oil fields and the optimization of a multiproduct batch plant. This new algorithm employs both the Genetic Algorithm and a modified grid search method interfacing in such a way that the resulting hybrid algorithm is capable of solving many MINLP problems efficiently and accurately. Testings indicate that this algorithm is efficient and robust even for some ill-conditioned problems with nonconvex constraints.

关键词： mixed integer nonlinear programming hybrid genetic method modified grid search heuristic multiproduct batch plant problems sizing and location of oil-platforms

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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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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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Two linear approximation algorithms for convex mixed integer nonlinear programming

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ANNALS OF OPERATIONS RESEARCH 2022年第2期316卷 1471-1491页

作者： Melo, Wendel Fampa, Marcia Raupp, Fernanda Univ Fed Uberlandia Coll Comp Sci Uberlandia MG Brazil Univ Fed Rio de Janeiro Inst Math Rio De Janeiro Brazil Univ Fed Rio de Janeiro COPPE Rio De Janeiro Brazil Minist Sci Technol Innovat & Commun Natl Lab Sci Comp Rio De Janeiro Brazil

We present two new algorithms for convex mixed integer nonlinear programming (MINLP), both based on the well known Extended Cutting Plane (ECP) algorithm proposed by Weterlund and Petersson. Our first algorithm, Refined Extended Cutting Plane (RECP), incorporates additional cuts to the MILP relaxation of the original problem, obtained by solving linear relaxations of NLP problems considered in the Outer Approximation algorithm. Our second algorithm, Linear programming based Branch-and-Bound (LP-BB), applies the strategy of generating cuts that is used in RECP, to the linear approximation scheme used by the LP/NLP based Branch-and-Bound algorithm. Our computational results show that RECP and LP-BB are highly competitive with the most popular MINLP algorithms from the literature, while keeping the nice and desirable characteristic of ECP, of being a first-order method.

关键词： mixed integer nonlinear programming Extended cutting plane Outer approximation Linear approximation

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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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Optimal exact designs of experiments via mixed integer nonlinear programming

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STATISTICS AND COMPUTING 2020年第1期30卷 93-112页

作者： Duarte, Belmiro P. M. Granjo, Jose F. O. Wong, Weng Kee Inst Politecn Coimbra Dept Chem & Biol Engn Inst Super Engn Coimbra Rua Pedro Nunes P-3030199 Coimbra Portugal Univ Coimbra Dept Chem Engn CIEPQPF Rua Silvio Lima Polo 2 P-3030790 Coimbra Portugal Univ Calif Los Angeles Dept Biostat Fielding Sch Publ Hlth 10833 Le Conte Ave Los Angeles CA 90095 USA

Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studying their properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariably applicable to the particular problem only. We propose a systematic approach to construct optimal exact designs by incorporating the Cholesky decomposition of the Fisher Information Matrix in a mixed integer nonlinear programming formulation. As examples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global or local optimizers. Our examples include design problems with constraints on the locations or the number of replicates at the optimal design points.

关键词： Model-based optimal designs Exact designs Constrained designs mixed integer nonlinear programming Global Optimization

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A mixed integer nonlinear programming model for biomass production

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OPERATIONAL RESEARCH 2019年第1期19卷 39-57页

作者： Contreras, J. Lara, H. Nouel-Borges, G. UCLA Apdo 400 Barquisimeto Venezuela Biominbloq CA Sarare Venezuela

In this paper, a nonlinear model to maximize biomass production with specific nutritional quality is proposed. The model decides about kind of grasses and legumes to cultivate, quantities of each grasses and legumes chosen, the use of resources, and the proper time of harvest at which the biomass with specific nutritional quality is maximized. Model works with sufficient information about biomass yield, nutrient content, water requirements and fertilizer requirements of several crops, and it can explore all possible harvest times and choose the right time in which biomass production is maximized with desired nutritional quality. Furthermore, the solution gives to the producers additional information on weekly irrigation plan and weekly fertilizers plan for m(2) of cultivated grass. The model was tested on six scenarios using GAMS and obtained solutions are the global solution in each scenario.

关键词： mixed integer nonlinear programming Animal farming Mix crops

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