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A polyhedral branch-and-cut approach to global optimization

MATHEMATICAL programming 2005年第2期103卷 225-249页

作者： Tawarmalani, M Sahinidis, NV Purdue Univ Krannert Sch Management W Lafayette IN 47907 USA Univ Illinois Dept Chem & Biomol Engn Urbana IL 61801 USA

A variety of nonlinear, including semidefinite, relaxations have been developed in recent years for nonconvex optimization problems. Their potential can be realized only if they can be solved with sufficient speed and reliability. Unfortunately, state-of-the-art nonlinear programming codes are significantly slower and numerically unstable compared to linear programming software. In this paper, we facilitate the reliable use of nonlinear convex relaxations in global optimization via a polyhedral branch-and-cut approach. Our algorithm exploits convexity, either identified automatically or supplied through a suitable modeling language construct, in order to generate polyhedral cutting planes and relaxations for multivariate nonconvex problems. We prove that, if the convexity of a univariate or multivariate function is apparent by decomposing it into convex subexpressions, our relaxation constructor automatically exploits this convexity in a manner that is much superior to developing polyhedral outer approximators for the original function. The convexity of functional expressions that are composed to form nonconvex expressions is also automatically exploited. Root-node relaxations are computed for 87 problems from globallib and minlplib, and detailed computational results are presented for globally solving 26 of these problems with BARON 7.2, which implements the proposed techniques. The use of cutting planes for these problems reduces root-node relaxation gaps by up to 100% and expedites the solution process, often by several orders of magnitude.

关键词： mixed-integer nonlinear programming outer approximation convexification factorable programming convexity identification

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An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization

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OPTIMIZATION AND ENGINEERING 2008年第4期9卷 311-339页

作者： Holmstroem, Kenneth Quttineh, Nils-Hassan Edvall, Marcus M. Malardalen Univ Dept Math & Phys S-72123 Vasteras Sweden Tomlab Optimizat Inc Pullman WA 99163 USA

Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems. In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) are described. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integer nonlinear problems (MINLP). Solvers in the TOMLAB Optimization Environment (http://***/tomlab/) have been compared, specifically the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integer nonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENO solver implementing a stochastic genetic algorithm. Results show that the deterministic derivative-free methods compare well with the derivative-based ones, but the stochastic genetic algorithm solver is several orders of magnitude too slow for practical use. When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.

关键词： global optimization radial basis functions response surface model surrogate model expensive function CPU-intensive optimization software splines mixed-integer nonlinear programming nonconvex derivative-free black-box linear constraints nonlinear constraints

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LaGO: a (heuristic) Branch and Cut algorithm for nonconvex MINLPs

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2008年第2期16卷 127-138页

作者： Nowak, Ivo Vigerske, Stefan Humboldt Univ Dept Math D-10099 Berlin Germany Lufthansa Syst Berlin Berlin Germany

We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integer nonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not require an algebraic representation of the problem, reformulation techniques for the construction of the convex relaxation cannot be applied, and we are restricted to sampling techniques in case of nonquadratic nonconvex functions. The linear relaxation is further improved by mixed-integer-rounding cuts. Also box reduction techniques are applied to improve efficiency. Numerical results on medium size test problems are presented to show the efficiency of the method.

关键词： global optimization branch and bound branch and cut outer approximation mixed-integer nonlinear programming

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Delivery drone route planning over a battery swapping network

Delivery drone route planning over a battery swapping networ...

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12th International Conference on Ambient Systems, Networks and Technologies (ANT) / 4th International Conference on Emerging Data and Industry 4.0 (EDI40)

作者： Cokyasar, Taner Argonne Natl Lab Energy Syst Div 9700 S Cass Ave Lemont IL 60439 USA

Many enterprises invest on drone delivery research and development to drop off packages at consumers' doorsteps in a matter of minutes. We study delivery drone route planning over a battery swapping network allowing farther reach by penetrating current battery capacity constraints. A mixed-integer nonlinear programming model is created to plan efficient drone routing over the swapping machines by minimizing the delivery lead time. We develop an exact solution method, evaluate its performance, and compare it with a straightforward nonlinear solver application. A case study highlights the applicability of the model. Data and source code to the solver are publicly shared. (C) 2021 The Authors. Published by Elsevier B.V.

关键词： Drone delivery drone routing drone battery swapping mixed-integer nonlinear programming optimization

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Day-Ahead Optimal Power Flow for Smart-Community Microgrid with Centralized Electrical Storage and Wind Turbine 11

Day-Ahead Optimal Power Flow for Smart-Community Microgrid w...

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11th International Conference on Smart Grid (IcSmartGrid)

作者： Arkhangelski, Jura Abdou-Tankari, Mahamadou Lefebvre, Gilles Univ Paris Est Creteil CERTES Lab Creteil France

ISBN: (纸本)9798350310665

This research presents the innovate method of Day-Ahead Optimal Power Flow (DA-OPF) management of Smart Community Microgrid (SCM) with a wind turbine generation and Centralized Energy Storage System (CESS). The developed DA-OPF is based on the Deep Learning (DL) Long Short-Term Memory (LSTM) network for the wind generation and community consumption data forecast. The Optimal Power Flow (OPF) problem is formulated to reduce Locational Average Marginal Price (LAMP) and is solved by mixed-integer nonlinear programming (MINLP) model. To take into account the forecast error of forecast system, also as its influence on the SCM system stability, this method includes the evaluation system based on the Monte-Carlo Simulation (MCS). This allows developing DA-OPF strategy assure not only the optimal operation, but also the resilience and stability of the SCM. The evaluation of the proposed method was realized on the case of conversion of real conventional community into SCM. This was made by the integration of CESS, a wind turbine and developed DA-OPF management. The practical evaluation and subsequent economic analysis show the efficiency of the proposed DA-OPF method and its good effect on reducing community energy price and to respect the energy transition process.

关键词： microgrid deep learning optimal power flow mixed-integer nonlinear programming long short-term memory monte carlo simulation

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A Resource Constraint Approach for One Global Constraint MINLP 20th

A Resource Constraint Approach for One Global Constraint MIN...

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20th International Conference on Computational Science and Its Applications (ICCSA)

作者： Muts, Pavlo Nowak, Ivo Hendrix, Eligius M. T. Hamburg Univ Appl Sci Hamburg Germany Univ Malaga Comp Architecture Malaga 29080 Spain

ISBN: (纸本)9783030588083;9783030588076

Many industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, where low-dimensional sub-problems are linked by a (linear) knapsack-like coupling constraint. This paper investigates exploiting this structure using decomposition and a resource constraint formulation of the problem. The idea is that one outer approximation master problem handles sub-problems that can be solved in parallel. The steps of the algorithm are illustrated with numerical examples which shows that convergence to the optimal solution requires a few steps of solving sub-problems in lower dimension.

关键词： Decomposition Parallel computing Column generation Global optimization mixed-integer nonlinear programming

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Optimal Location of DGs in DC Power Grids Using a MINLP Model Implemented in GAMS 9

Optimal Location of DGs in DC Power Grids Using a MINLP Mode...

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9th IEEE Power, Instrumentation and Measurement Meeting (EPIM)

作者： Montoya, O. D. Garrido, V. M. Grisales-Norena, L. F. Gil-Gonzalez, W. Garces, A. Ramos-Paja, C. A. Univ Tecnol Bolivar Ingn Elect & Ingn Elect Cartagena Colombia Inst Tecnol Metropolitano Dept Electromecan & Mecatron Medellin Colombia Univ Tecnol Pereira Programa Ingn Elect Pereira Colombia Univ Nacl Colombia Fac Minas Medellin Colombia

ISBN: (纸本)9781538678428

This paper addresses the problem of optimal location and sizing of distributed generators (DGs) in direct current (dc) power grids by using a mixed-integer nonlinear programming (MINLP) formulation. The reduction of the power losses in all branches of the network are considered as the objective function;while the restrictions are the power balance, voltage regulation, maximum penetration and maximum distributed generation units available. The general algebraic modeling system (GAMS) is selected as nonlinear optimizing package to solve this problem;besides, a small numerical example of energy production is introduced to illustrate the usability of using GAMS. Finally, a 21-node dc grid with two ideal generators, and multiple constant power loads, is used as test system.

关键词： Direct-current power grids distributed generators location and sizing general algebraic modeling system mixed-integer nonlinear programming power losses minimization

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A JOINT DETECTION AND RECONSTRUCTION METHOD FOR BLIND GRAPH SIGNAL RECOVERY

A JOINT DETECTION AND RECONSTRUCTION METHOD FOR BLIND GRAPH ...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Mao, Xianghui Gu, Yuantao Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

ISBN: (纸本)9781538646588

Sampling and reconstruction is a fundamentally important problem in the field of graph signal processing. Many works have been contributed to reconstructing bandlimited signals from measurements taken on a known subset of vertices. However, in some cases, the vertex defects occur randomly over the graph. In such situation, the existing graph signal reconstruction methods fail to deal with such blind reconstruction problem. In this paper, we formulate the blind reconstruction problem as mixed-integer nonlinear programming, and propose a Joint Detection and Reconstruction (JDR) method to simultaneously detect the vertices' working states and reconstruct the bandlimited signal. The convergence property of the proposed method is analyzed. In the experimental part, both synthetic dataset and real-world dataset are applied to verify the proposed methods.

关键词： blind reconstruction bandlimited graph signal mixed-integer nonlinear programming

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Solving reliability redundancy allocation problems with orthogonal simplified swarm optimization

Solving reliability redundancy allocation problems with orth...

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International Joint Conference on Neural Networks (IJCNN)

作者： Yeh, Wei-Chang Jiang, Yun-Zhi Chung, Vera Yuk Ying He, Xiangjian Natl Tsing Hua Univ Dept Ind Engn & Engn Managemen Hsinchu 300 Taiwan Jiangxi Agr Univ Sch Software Nanchang 330045 Peoples R China S China Univ Technol Sch Software Engn Guangzhou 510006 Guangdong Peoples R China Univ Sydney Sch Informat Technol Sydney NSW 2006 Australia Univ Technol Sydney Comp Vis & Recognit Lab Res Ctr Innovat IT Serv & Applicat iNEXT Broadway NSW 2007 Australia

ISBN: (纸本)9781479919598

This study applies a penalty guided strategy and the orthogonal array test (OA) based on the Simplified Swarm Optimization algorithm (SSO) to solve the reliability redundancy allocation problems (RRAP) in the series system, the series-parallel system, the complex (bridge) system, and the overspeed protection of gas turbine system. For several decades, the RRAP has been one of the most well known techniques. The maximization of system reliability, the number of redundant components, and the reliability of corresponding components in each subsystem have to be decided simultaneously with nonlinear constraints, acting as one difficulty for the use of the RRAP. In other words, the objective function of the RRAP is the mixed-integer programming problem with the nonlinear constraints. The RRAP is of the class of NP-hard. Hence, in this paper, the SSO algorithm is proposed to solve the RRAP and improve computation efficiency for these NP-hard problems. There are four RRAP problems used to illustrate the applicability and the effectiveness of the SSO. The experimental results are compared with previously developed algorithms in literature. Moreover, the maximum-possible-improvement (MPI) is used to measure the amount of improvement of the solution found by the SSO to the previous solutions. According to the results, the system reliabilities obtained by the proposed SSO for the four RRAP problems are as well as or better than the previously best-known solutions.

关键词： Reliability Redundancy allocation problem RRAP Simplified Swarm Optimization algorithm SSO mixed-integer nonlinear programming

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A single-stage supply chain system controlled by kanban under just-in-time philosophy

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2004年第5期55卷 485-494页

作者： Wang, S Sarker, BR Louisiana State Univ Dept Ind & Mfg Syst Engn Baton Rouge LA 70803 USA SE Missouri State Univ Cape Girardeau MO 63701 USA

The production system using kanban was pioneered by Toyota Motor Company in Japan and subsequently it was adopted by numerous other Japanese and US companies for applying the just-in-time manufacturing principles. This research studies a single-stage supply chain system that is controlled by kanban mechanism. The supply chain system is modelled as a mixed-integer nonlinear programming (MINLP) problem. It is solved optimally by branch-and-bound method to determine the number of kanbans, batch size, number of batches, and the total quantity over one period. Meanwhile. the kanban operation between two adjacent plants is worked out considering the factors of loading and unloading time. and transport time. Coupled with plant-wide efforts for cost control and management commitment to enhance other measures of performance, a logistics system for controlling the production as well,is the supply chain system is developed. which results in minimizing the total cost of the supply chain system. The results show that the improvements in reduction of inventory, wasted labour, and customer service in a supply chain are accomplished through the kanban mechanism.

关键词： kanban supply chain inventory control mixed-integer nonlinear programming

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