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Bi-objective mixed-integer nonlinear programming for multi-commodity tri-echelon supply chain networks

JOURNAL OF INTELLIGENT MANUFACTURING 2018年第4期29卷 809-826页

作者： Alavidoost, M. H. Tarimoradi, Mosahar Zarandi, M. H. Fazel Amirkabir Univ Technol Dept Ind Engn Computat Intelligent Syst Lab 424 Hafez AvePOB 15875-4413 Tehran Iran Univ Toronto Knowledge Intelligent Syst Lab Toronto ON Canada

The competitive market and declined economy have increased the relevant importance of making supply chain network efficient. Up to now, this has resulted in great motivations to reduce the cost of services, and simultaneously, to improve their quality. A mere network model, as a tri-echelon, consists of Suppliers, Warehouses or Distribution Centers (DCs), and Retailer nodes. To bring it closer to reality, the majority of parameters in this network involve retailer demands, lead-time, warehouses holding and shipment costs, and also suppliers procuring and stocking costs which are all assumed to be stochastic. The aim is to determine the optimum service level so that total cost is minimized. Obtaining such conditions requires determining which supplier nodes, and which DC nodes in network should be active to satisfy the retailers' needs, an issue which is a network optimization problem per se. The proposed supply chain network for this paper is formulated as a mixed-integer nonlinear programming, and to solve this complicated problem, since the literature for the related benchmark is poor, three numbers of genetic algorithm called Non-dominated Sorting Genetic Algorithm (NSGA-II), Non-dominated Ranking Genetic Algorithm (NRGA), and Pareto Envelope-based Selection Algorithm (PESA-II) are applied and compared to validate the obtained results. The Taguchi method is also utilized for calibrating and controlling the parameters of the applied triple algorithms.

关键词： Supply chain management Tri-echelon network mixed-integer nonlinear programming NRGA NSGA-II PESA-II Taguchi method

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Plunge milling time optimization via mixed-integer nonlinear programming

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COMPUTERS & INDUSTRIAL ENGINEERING 2016年第0期98卷 434-445页

作者： Cafieri, Sonia Monies, Frederic Mongeau, Marcel Bes, Christian ENAC MAIAA F-31055 Toulouse France Univ Toulouse IMT F-31400 Toulouse France Univ Toulouse 3 ICA F-31062 Toulouse France

Plunge milling is a recent and efficient production mean for machining deep workpieces, notably in aeronautics. This paper focuses on the minimization of the machining time by optimizing the values of the cutting parameters. Currently, neither Computer-Aided Manufacturing (CAM) software nor standard approaches take into account the tool path geometry and the control laws driving the tool displacements to propose optimal cutting parameter values, despite their significant impact. This paper contributes to plunge milling optimization through a mixed-integer nonlinear programming (MINLP) approach, which enables us to determine optimal cutting parameter values that evolve along the tool path. It involves both continuous (cutting speed, feed per tooth) and, in contrast with standard approaches, integer (number of plunges) optimization variables, as well as nonlinear constraints. These constraints are related to the Computer Numerical Control (CNC) machine tool and to the cutting tool, taking into account the control laws. Computational results, validated on CNC machines and on representative test cases of engine housing, show that our methodology outperforms standard industrial engineering know-how approaches by up to 55% in terms of machining time. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Plunge milling mixed-integer nonlinear programming Optimized cutting parameters Machining time optimization

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mixed-integer nonlinear programming model for layout design of subsea satellite well system in deep water oil field

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AUTOMATION IN CONSTRUCTION 2021年 123卷 103524-103524页

作者： Hong, Cheng Estefen, Segen F. Wang, Yuxi Lourenco, Marcelo Igor Ningbo Univ Fac Maritime & Transportat Ningbo 315211 Peoples R China Univ Fed Rio de Janeiro Ocean Engn Dept COPPE BR-21941972 Rio De Janeiro Brazil State Key Lab Petr Pollut Control Beijing 102206 Peoples R China CNPC Res Inst Safety & Environm Technol Beijing 102206 Peoples R China

This paper focuses on the concept of a subsea satellite well system in deep water oil field, and a mixed-integer nonlinear programming model (MINLP) is proposed to help design the layout to minimize the payback period. The proposed model has two key aspects. First, the objective function, payback period, reflects the link between the total cost and production. And second, the Floating Production Storage and Offloading units (FPSOs), subsea wells, flowlines, and subsea obstacles are integrated for the modeling, presenting the interaction of the components from underground to the sea level. A decomposition strategy based on gradient descent algorithm is proposed to solve the model. The case studies indicate the model's feasibility. Besides, two different applications of the model are presented, one is to optimize the layout under given horizontal displacements and the other is the cost comparison between drilling horizontal well and vertical well, indicating the model's flexibility.

关键词： Subsea production system Satellite well system concept Layout design mixed-integer nonlinear programming Gradient descent algorithm

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mixed-integer nonlinear programming framework for combined heat and power units with nonconvex feasible operating region: Feasibility, optimality, and flexibility evaluation

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2019年第3期29卷

作者： Razavi, Seyed-Ehsan Javadi, Mohammad Sadegh Nezhad, Ali Esmaeel Univ Birjand Fac Elect & Comp Engn Birjand Iran Islamic Azad Univ Shiraz Branch Dept Elect Engn Shiraz Iran Univ Bologna Dept Elect Elect & Informat Engn Bologna Italy

This paper presents an optimization framework to determine the optimal operating points of combined heat and power (CHP) units with nonlinear, nonconvex feasible operating region (FOR). The mentioned problem is the economic dispatch (ED) of heat-only units, thermal units, and CHP units. Also, the electric units are of thermal technology while their valve-point impact is taken into consideration. Also, the heat power curve of heat-only units is nonlinear. It is noted that the FOR of CHP units has been defined both as convex and nonconvex regions. For those with nonconvex characteristic, a method is proposed to convert it into a convex characteristic. Accordingly, a separate binary variable must be defined to determine the optimal operating point in each convex region. Thus, the presented problem in this paper is of mixed-integer nonlinear programming (MINLP) type modeled in General Algebraic Modeling System (GAMS) software. In this respect, different case studies have been presented to assess the optimality, feasibility, and the flexibility of the model. It is noteworthy that the valve-point effect of thermal units and different FORs of CHP units as well as the electrical power losses have been considered.

关键词： economic heat and power dispatch mixed-integer nonlinear programming nonconvex feasible operating region

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A Branch and Bound Algorithm for Transmission Network Expansion Planning Using Nonconvex mixed-integer nonlinear programming Models

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IEEE ACCESS 2022年 10卷 39875-39888页

作者： Zoppei, Reinaldo T. Delgado, Marcos A. J. Macedo, Leonardo H. Rider, Marcos J. Romero, Ruben Fed Univ Rondonopolis Inst Exact & Nat Sci BR-78736900 Rondonopolis Mato Grosso Brazil Sao Paulo State Univ Dept Elect Engn BR-15385000 Ilha Solteira SP Brazil Univ Estadual Campinas Dept Syst & Energy BR-13083852 Campinas SP Brazil

The branch and bound (BB) algorithm is widely used to obtain the global solution of mixed-integer linear programming (MILP) problems. On the other hand, when the traditional BB structure is directly used to solve nonconvex mixed-integer nonlinear programming (MINLP) problems, it becomes ineffective, mainly due to the nonlinearity and nonconvexity of the feasible region of the problem. This article presents the difficulties and ineffectiveness of the direct use of the traditional BB algorithm for solving nonconvex MINLP problems and proposes the formulation of an efficient BB algorithm for solving this category of problems. The algorithm is formulated taking into account particular aspects of nonconvex MINLP problems, including (i) how to deal with the nonlinear programming (NLP) subproblems, (ii) how to detect the infeasibility of an NLP subproblem, (iii) how to treat the nonconvexity of the problem, and (iv) how to define the fathoming rules. The proposed BB algorithm is used to solve the transmission network expansion planning (TNEP) problem, a classical problem in power systems optimization, and its performance is compared with the performances of off-the-shelf optimization solvers for MINLP problems. The results obtained for four test systems, with different degrees of complexity, indicate that the proposed BB algorithm is effective for solving the TNEP problem with and without considering losses, showing equal or better performance than off-the-shelf optimization solvers.

关键词： Search problems Propagation losses Planning Metaheuristics Linear programming Biological system modeling programming profession Branch and bound algorithm mixed-integer nonlinear programming optimization transmission network expansion planning

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Maximizing the number of conflict-free aircraft using mixed-integer nonlinear programming

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COMPUTERS & OPERATIONS RESEARCH 2017年第Apr.期80卷 147-158页

作者： Cafieri, Sonia Rey, David Univ Toulouse ENAC F-31055 Toulouse France UNSW Univ New South Wales Australia Sch Civil & Environm Engn Sydney NSW 2052 Australia

We address the conflict detection and resolution problem in air traffic control, where an aircraft conflict is a loss of separation between aircraft trajectories. Conflict avoidance is crucial to ensure flight safety and remains a challenging traffic control problem. We focus on speed control to separate aircraft and consider two approaches: (i) maximize the number of conflicts resolved and (ii) identify the largest set of conflict-free aircraft. Both problems are modeled using mixed-integer nonlinear programming and a tailored greedy algorithm is proposed for the latter. Computational efficiency is improved through a preprocessing algorithm which attempts to reduce the size of the conflict resolution models by detecting the existence of pairwise potential conflicts. Numerical results are provided after implementing the proposed models and algorithms on benchmark conflict resolution instances. The results highlight the benefits of using the proposed pre-processing step as well as the versatility and the efficiency of the proposed models. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： mixed-integer nonlinear programming Conflict detection and resolution Air traffic control Deterministic global optimization Modeling

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Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON

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OPTIMIZATION METHODS & SOFTWARE 2018年第3期33卷 540-562页

作者： Kilinc, Mustafa R. Sahinidis, Nikolaos V. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In this paper, we present recent developments in the global optimization software BARON to address problems with integer variables. A primary development was the addition of mixed-integer linear programming relaxations to BARON's portfolio of linear and nonlinear programming relaxations, aiming to improve dual bounds and offer good starting points for primal heuristics. Since such relaxations necessitate the solution of NP-hard problems, their introduction to a branch-and-bound algorithm raises many practical issues regarding their effective implementation. In addition to describing BARON's dynamic strategy for deciding under what conditions to activate integer programming relaxations in the course of branch-and-bound, the paper also describes cutting plane and probing techniques that originate from the literature of integer linear programming and have been adapted in BARON to solve nonlinear problems. Finally, we describe BARON's primal heuristics for finding good solutions of mixed-integer nonlinear programmes. For all these techniques, we report extensive computational results on a public data set, aiming to analyse the impact of each technique in the solution process and identify techniques that expedite solution the most.

关键词： mixed-integer nonlinear programming global optimization primal heuristics portfolios of relaxations

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An Efficient Modified Particle Swarm Optimization Algorithm for Solving mixed-integer nonlinear programming Problems

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2019年第2期12卷 530-543页

作者： Sun, Ying Gao, Yuelin Hefei Univ Technol Sch Comp Sci & Informat Engn 193 Tunxi Rd Hefei 230009 Anhui Peoples R China North Minzu Univ Ningxia Prov Key Lab Intelligent Informat & Data 204 Wenchang North St Yinchuan 750021 Peoples R China

This paper presents an efficient modified particle swarm optimization (EMPSO) algorithm for solving mixed-integer nonlinear programming problems. In the proposed algorithm, a new evolutionary strategies for the discrete variables is introduced, which can solve the problem that the evolutionary strategy of the classical particle swarm optimization algorithm is invalid for the discrete variables. An update strategy under the constraints is proposed to update the optimal position, which effectively utilizes the available information on infeasible solutions to guide particle search. In order to evaluate and analyze the performance of EMPSO, two hybrid particle swarm optimization algorithms with different strategies are also given. The simulation results indicate that, in terms of robustness and convergence speed, EMPSO is better than the other algorithms in solving 14 test problems. A new performance index (NPI) is introduced to fairly compare the other two algorithms, and in most cases the values of the NPI obtained by EMPSO were superior to the other algorithms. (c) 2019 The Authors. Published by Atlantis Press SARL.

关键词： Particle swarm optimization mixed-integer nonlinear programming Constrained optimization Simulated annealing

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On Solving Nonsmooth mixed-integer nonlinear programming Problems by Outer Approximation and Generalized Benders Decomposition

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第3期181卷 840-863页

作者： Wei, Zhou Ali, M. Montaz Xu, Liang Zeng, Bo Yao, Jen-Chih Yunnan Univ Dept Math Kunming 650091 Yunnan Peoples R China Univ Witwatersrand Sch Comp Sci & Appl Math ZA-2050 Johannesburg South Africa Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA Zhejiang Normal Univ Dept Math Jinhua 321004 Peoples R China China Med Univ China Med Univ Hosp Res Ctr Interneural Comp Taichung 40402 Taiwan

In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.

关键词： mixed-integer nonlinear programming Outer approximation Generalized Benders decomposition Subgradient Master program 90C11 90C25 90C30

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MINLPLib - A collection of test models for mixed-integer nonlinear programming

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INFORMS JOURNAL ON COMPUTING 2003年第1期15卷 114-119页

作者： Bussieck, MR Drud, AS Meeraus, A GAMS Dev Corp Washington DC 20007 USA ARKI Consulting & Dev AS DK-2880 Bagsvaerd Denmark

The paper describes a new computerized collection of test models for mixed-integer nonlinear programming. Because there is no standard format for nonlinear models, the model collection is augmented with a translation server that can transform the models from their basic GAMS format into other formats, including AMPL, BARON, LGO, LINGO, and MINOPT. The translation server can also be used to transform industrial models that contain confidential information. Such transformations allow many of these models to be distributed to the research community as highly relevant algorithmic test models.

关键词： mixed-integer nonlinear programming testing modeling systems

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