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Benchmarking multidisciplinary design optimization algorithms

OPTIMIZATION AND ENGINEERING 2010年第1期11卷 159-183页

作者： Tedford, Nathan P. Martins, Joaquim R. R. A. Univ Toronto Inst Aerosp Studies Toronto ON M3H 5T6 Canada

A comparison of algorithms for multidisciplinary design optimization (MDO) is performed with the aid of a new software framework. This framework, pyMDO, was developed in Python and is shown to be an excellent platform for comparing the performance of the various MDO methods. pyMDO eliminates the need for reformulation when solving a given problem using different MDO methods: once a problem has been described, it can automatically be cast into any method. In addition, the modular design of pyMDO allows rapid development and benchmarking of new methods. Results generated from this study provide a strong foundation for identifying the performance trends of various methods with several types of problems.

关键词： Multidisciplinary design optimization decomposition algorithms Nonlinear programming Sensitivity analysis

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Amultistage decision-dependent stochastic bilevel programming approach for power generation investment expansion planning

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IISE TRANSACTIONS 2018年第8期50卷 720-734页

作者： Zhan, Yiduo Zheng, Qipeng P. Univ Cent Florida Dept Ind Engn & Management Syst Orlando FL 32816 USA

In this article, we study the long-term power generation investment expansion planning problem under uncertainty. We propose a bilevel optimization model that includes an upper-level multistage stochastic expansion planning problem and a collection of lower-level economic dispatch problems. This model seeks for the optimal sizing and siting for both thermal and wind power units to be built to maximize the expected profit for a profit-oriented power generation investor. To address the future uncertainties in the decision-making process, this article employs a decision-dependent stochastic programming approach. In the scenario tree, we calculate the non-stationary transition probabilities based on discrete choice theory and the economies of scale theory in electricity systems. The model is further reformulated as a single-level optimization problem and solved by decomposition algorithms. The investment decisions, computation times, and optimality of the decision-dependent model are evaluated by case studies on IEEE reliability test systems. The results show that the proposed decision-dependent model provides effective investment plans for long-term power generation expansion planning.

关键词： Multistage stochastic programming bilevel optimization generation expansion decision-dependent probability decomposition algorithms

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A survey of network interdiction models and algorithms

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期283卷 797-811页

作者： Smith, J. Cole Song, Yongjia Clemson Univ Dept Ind Engn Clemson SC 29631 USA

This paper discusses the development of interdiction optimization models and algorithms, with an emphasis on mathematical programming techniques and future research challenges in the field. After presenting basic interdiction concepts and notation, we recount the motivation and models behind founding research in the network interdiction field. Next, we examine some of the most common means of solving interdiction problems, focusing on dualization models and extended formulations solvable by row-generation techniques. We then examine contemporary interdiction problems involving incomplete information, information asymmetry, stochasticity, and dynamic play. We conclude by discussing several emerging applications in the field of network interdiction. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Networks Network interdiction Min-max games Mixed integer programming formulations decomposition algorithms

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Training SVMs Without Offset

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JOURNAL OF MACHINE LEARNING RESEARCH 2011年第1期12卷 141-202页

作者： Steinwart, Ingo Hush, Don Scovel, Clint Univ Stuttgart Inst Stochast & Anwendungen Fak Math & Phys D-70569 Stuttgart Germany Los Alamos Natl Lab Los Alamos NM 87545 USA

We develop, analyze, and test a training algorithm for support vector machine classifiers without offset. Key features of this algorithm are a new, statistically motivated stopping criterion, new warm start options, and a set of inexpensive working set selection strategies that significantly reduce the number of iterations. For these working set strategies, we establish convergence rates that, not surprisingly, coincide with the best known rates for SVMs with offset. We further conduct various experiments that investigate both the run time behavior and the performed iterations of the new training algorithm. It turns out, that the new algorithm needs significantly less iterations and also runs substantially faster than standard training algorithms for SVMs with offset.

关键词： support vector machines decomposition algorithms

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Optimal production scheduling of food process industries

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COMPUTERS & CHEMICAL ENGINEERING 2020年第0期134卷 106682-000页

作者： Georgiadis, Georgios P. Marino Pampin, Borja Adrian Cabo, Daniel Georgiadis, Michael C. Aristotle Univ Thessaloniki Dept Chem Engn Thessaloniki 54124 Greece Ctr Res & Technol Hellas CERTH CPERI POB 60361 Thessaloniki 57001 Greece Frinsa Noroeste SA Ave Ramiro Carregal Rey Parcela 29 La Coruna Spain ASM Soft SL Crta Bembrive 109 Vigo Spain

The production scheduling problem of a real-life food industry is addressed in this work. An efficient MILP-based solution strategy is developed to optimize weekly schedules for a Spanish canned fish production plant. The multi-stage, multi-product facility under study consists of both continuous and batch operations resulting in an extremely complex scheduling problem. In order to reduce its computational complexity, an aggregated approach is cleverly proposed, in which the continuous processes are explicitly modeled, while valid feasibility constraints are introduced for the batch stage. Based on this approach, two MILP models are developed, using a mixed discrete-continuous time representation. All technical, operating and design constraints of the facility are considered, while salient characteristics of the canned-food industry, such as assurance of the end products' microbiological integrity, are aptly modeled. Both the minimization of makespan and changeovers is studied. In order to meet the computational limits imposed by the industry, an order-based decomposition algorithm is further investigated. The method is successfully applied to real-life case studies, generating near-optimal solutions in short CPU times. The suggested solution strategy can be easily extended to consider other real-life scheduling problems from the process industries sector that share similar production characteristics. (C) 2019 The Authors. Published by Elsevier Ltd.

关键词： Production scheduling Food industries Large-scale Industrial problems MILP models decomposition algorithms

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Application of regional earthquake mitigation optimization

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COMPUTERS & OPERATIONS RESEARCH 2007年第8期34卷 2478-2494页

作者： Dodo, Atsuhiro Davidson, Rachel A. Xu, Ningxiong Nozick, Linda K. Swiss Reinsurance Co Chiyoda Ku Tokyo 1000004 Japan Cornell Univ Sch Civil & Environm Engn Ithaca NY 14853 USA

A linear program was developed to help seismically active communities decide: (1) how much to spend on pre-earthquake mitigation that aims to reduce future losses versus waiting until after an event and paying for reconstruction, and (2) which of the many possible mitigation activities to fund so as to minimize overall risk. The mitigation alternatives considered are structural upgrading policies for groups of buildings. Benefits of mitigation are losses avoided in future earthquakes, including structural, non-structural, contents, and time-related losses, and casualties. The model is intended to be used as a too] to support the public regional mitigation planning process. In realistic applications, the model includes millions of variables, thus requiring a special solution method. This paper focuses on two efficient solution algorithms to solve the model-a Dantzig-Wolfe decomposition algorithm and a greedy heuristic algorithm. A comprehensive numerical study compares the two algorithms in terms of solution quality and solution time. The Study shows that, compared to the Dantzig-Wolfe algorithm, the heuristic algorithm is much faster as expected, and provides comparable solution quality. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： optimization investment planning earthquake mitigation decomposition algorithms

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Global mixed-integer dynamic optimization

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AICHE JOURNAL 2005年第8期51卷 2235-2253页

作者： Chachuat, B Singer, AB Barton, PI MIT Dept Chem Engn Proc Syst Engn Lab Cambridge MA 02139 USA

Recent advances in process synthesis, design, operations, and control have created an increasing demand for efficient numerical algorithms for optimizing a dynamic system coupled with discrete decisions;these problems are termed mixed-integer dynamic optimization (MIDO). In this communication, we develop a decomposition approach for a quite general class of MIDO problems that is capable of guaranteeing finding a global solution despite the nonconvexities inherent in the dynamic optimization subproblems. Two distinct algorithms are considered. On finite termination, the first algorithm guarantees finding a global solution of the MIDO within nonzero tolerance;the second algorithm finds rigorous bounds bracketing the global solution value, with a substantial reduction in computational expense relative to the first algorithm. A case study is presented in connection with the optimal design and operation of a batch process consisting of a series reaction followed by a separation with no intermediate storage. The developed algorithms demonstrate efficiency and applicability in solving this problem. Several heuristics are tested to enhance convergence of the algorithms;in particular, the use of bounds tightening techniques and the addition of cuts resulting from a screening model of the batch process are considered. (c) 2005 American Institute of Chemical Engineers

关键词： mixed-integer dynamic optimization nonconvex problems global optimization decomposition algorithms outer-approximation batch process design

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Designing a new mathematical model based on ABC analysis for inventory control problem: A real case study

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RAIRO-OPERATIONS RESEARCH 2021年第4期55卷 2309-2335页

作者： Abdolazimi, Omid Shishebori, Davood Goodarzian, Fariba Ghasemi, Peiman Appolloni, Andrea Kharazmi Univ Dept Econ Tehran Iran Yazd Univ Dept Ind Engn Yazd Iran Machine Intelligence Res Labs MIR Labs Sci Network Innovat & Res Excellence 113rd St NWPOB 2259 Auburn WA 98071 USA Islamic Azad Univ South Tehran Branch Dept Ind Engn Tehran Iran Univ Roma Tor Vergata Fac Econ Dept Management & Law Viale Columbia 2 I-00133 Rome Italy Sch Management Cranfield MK43 0AL Beds England

In modern business today, organizations that hold large numbers of inventory items, do not find it economical to make policies for the management of individual inventory items. Managers, thus, need to classify these items according to their importance and fit each item to a certain asset class. The method of grouping and inventory control available in traditional ABC has several disadvantages. These shortcomings have led to the development of an optimization model in the present study to improve the grouping and inventory control decisions in ABC. Moreover, it simultaneously optimizes the existing business relationships among revenue, investment in inventory and customer satisfaction (through service levels) as well as a company's budget for inventory costs. In this paper, a mathematical model is presented to classify inventory items, taking into account significant profit and cost reduction indices. The model has an objective function to maximize the net profit of items in stock. Limitations such as budget even inventory shortages are taken into account too. The mathematical model is solved by the Benders decomposition and the Lagrange relaxation algorithms. Then, the results of the two solutions are compared. The TOPSIS technique and statistical tests are used to evaluate and compare the proposed solutions with one another and to choose the best one. Subsequently, several sensitivity analyses are performed on the model, which helps inventory control managers determine the effect of inventory management costs on optimal decision making and item grouping. Finally, according to the results of evaluating the efficiency of the proposed model and the solution method, a real-world case study is conducted on the ceramic tile industry. Based on the proposed approach, several managerial perspectives are gained on optimal inventory grouping and item control strategies.

关键词： Improved ABC analysis inventory control decomposition algorithms ceramic tile industry limited budget inventory shortages

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Family of perturbation methods for variational inequalities

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1996年第2期89卷 423-452页

作者： MaklerScheimberg, S Nguyen, VH Strodiot, JJ UNIV FED RIO DE JANEIRO INST MATEMATBR-21945 RIO JANEIROBRAZIL FAC UNIV NOTRE DAME PAIX DEPT MATHUNITE OPTIMISATB-5000 NAMURBELGIUM

In recent years, the so-called auxiliary problem principle has been used to derive many iterative type algorithms for solving optimal control, mathematical programming, and variational inequality problems. In the present paper, we use this principle in conjunction with the epiconvergence theory to introduce and study a general family of perturbation methods for solving nonlinear variational inequalities over a product space of reflexive Banach spaces. We do not assume that the monotone operator involved in our general variational inequality problem is of potential type. Several known iterative algorithms, which can be obtained from our theory, are also discussed.

关键词： variational inequalities decomposition algorithms nonlinear complementarity monotone operators auxiliary problem principle epiconvergence

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Cut sharing for multistage stochastic linear programs with interstage dependency

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MATHEMATICAL PROGRAMMING 1996年第2期75卷 241-256页

作者： Infanger, G Morton, DP UNIV TEXAS DEPT MECH ENGNAUSTINTX 78712

Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on the state of the system. decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decomposition algorithms.

关键词： stochastic programming decomposition algorithms Monte Carlo sampling interstage dependency

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