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A graph-based algorithm for the multi-objective optimization of gene regulatory networks

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期270卷 784-793页

作者： Nghe, Philippe Mulder, Bela M. Tans, Sander J. FOM Inst AMOLF Sci Pk 104 NL-1098 XG Amsterdam Netherlands PSL Res Univ UMR CNRS ESPCI Chim Biol Innovat 8231 Lab Biochim ESPCI 10 Rue Vauquelin F-75005 Paris France

The evolution of gene regulatory networks in variable environments poses Multi-objective Optimization Problem (MOP), where the expression levels of genes must be tuned to meet the demands of each environment. When formalized in the context of monotone systems, this problem falls into a sub-class of linear MOPs. Here, the constraints are partial orders and the objectives consist of either the minimization or maximization of single variables, but their number can be very large. To efficiently and exhaustively find Pareto optimal solutions, we introduce a mapping between colored Hasse diagrams and polytopes associated with an ideal point. A dynamic program based on edge contractions yields an exact closed form description of the Pareto optimal set, in polynomial time of the number of objectives relative to the number of faces of the Pareto front. We additionally discuss the special case of series-parallel graphs with monochromatic connected components of bounded size, for which the running time and the representation of solutions can in principle be linear in the number of objectives. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Dynamic programming Monotone systems Gene regulatory networks Systems biology

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A new algorithm for linearly constrained c-convex vector optimization with a supply chain network risk application

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期247卷 359-365页

作者： Qu, Shaojian Goh, Mark Ji, Ying De Souza, Robert Shanghai Univ Sci & Technol Sch Business Shanghai 200093 Peoples R China Harbin Inst Technol Ctr Nat Sci Harbin Heilongjiang Peoples R China Natl Univ Singapore Logist Inst Asia Pacific Singapore 117548 Singapore Natl Univ Singapore NUS Business Sch Singapore 117548 Singapore

We study a class of vector optimization problems with a C-convex objective function under linear constraints. We extend the proximal point algorithm used in scalar optimization to vector optimization. We analyze both the global and local convergence results for the new algorithm. We then apply the proximal point algorithm to a supply chain network risk management problem under bi-criteria considerations. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： multiple objective programming Pareto optimum C-convex Proximal point algorithm Supply chain network risk management

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Min-ordering and max-ordering scalarization methods for multi-objective robust optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期275卷 446-459页

作者： Schmidt, M. Schoebel, Anita Thom, Lisa Erasmus Univ Rotterdam Sch Management Dept Technol & Operat Management POB 1738 NL-3000 DR Rotterdam Netherlands Univ Gottingen Inst Numer & Angew Math Lotzestr 16-18 D-37083 Gottingen Germany

Several robustness concepts for multi-objective uncertain optimization have been developed during the last years, but not many solution methods. In this paper we introduce two methods to find min-max robust efficient solutions based on scalarizations: the min-ordering and the max-ordering method. We show that all point-based min-max robust weakly efficient solutions can be found with the max-ordering method and that the min-ordering method finds set-based min-max robust weakly efficient solutions, some of which cannot be found with formerly developed scalarization based methods. We then show how the scalarized problems may be approached for multi-objective uncertain combinatorial optimization problems with special uncertainty sets. We develop compact mixed-integer linear programming formulations for multi-objective extensions of bounded uncertainty (also known as budgeted or Gamma-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems. (C) 2018 The Authors. Published by Elsevier B.V.

关键词： multiple objective programming Robust optimization Multi-objective robust optimization Combinatorial optimization Scalarization

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Energy planning in buildings under uncertainty in fuel costs: The case of a hotel unit in Greece

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ENERGY CONVERSION AND MANAGEMENT 2003年第8期44卷 1303-1321页

作者： Mavrotas, G Demertzis, H Meintani, A Diakoulaki, D Natl Tech Univ Athens Dept Chem Engn Lab Ind & Energy Econ Athens 15780 Greece

Energy planning for individual large energy consumers becomes increasingly important due to several supply options competing and/or complementing each other and the high uncertainty associated with fuel prices. Hotel units are among the largest energy consumers in the building sector, where energy planning may greatly facilitate investment decisions for efficiently meeting energy demand. The present paper presents a linear programming model, including both continuous and integer variables, which represent energy flows and discrete energy technologies, respectively. Furthermore, the model comprises fuzzy parameters in order to handle adequately the uncertainties regarding energy costs. The obtained fuzzy linear programming model is then translated into the equivalent multiple objective linear programming model, which provides a set of efficient solutions, each one characterized by quantification of the risk associated with the uncertain energy costs. The proposed methodology is illustrated with a case study referring to a large hotel unit located nearby Athens. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： energy planning hotels fuzzy numbers multiple objective programming

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A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第3期169卷 943-959页

作者： Paquete, L Stützle, T Tech Univ Darmstadt Dept Comp Sci Intellect Grp D-64283 Darmstadt Germany

This paper studies the performance of two stochastic local search algorithms for the biobjective Quadratic Assignment Problem with different degrees of correlation between the flow matrices. The two algorithms follow two fundamentally different ways of tackling multiobjective combinatorial optimization problems. The first is based on the component-wise ordering of the objective value vectors of neighboring solutions, while the second is based on different scalarizations of the objective function vector. Our experimental results suggest that the performance of the algorithms with respect to solution quality and computation time depends strongly on the correlation between the flow matrices. In addition, some variants of these stochastic local search algorithms obtain very good solutions in short computation time. (c) 2004 Elsevier B.V. All rights reserved.

关键词： combinatorial optimization stochastic local search multiple objective programming

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Trade-off preservation in inverse multi-objective convex optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期270卷 25-39页

作者： Chan, Timothy C. Y. Lee, Taewoo Univ Toronto Mech & Ind Engn 5 Kings Coll Rd Toronto ON M5S 3G8 Canada Univ Houston Ind Engn 4722 Calhoun Rd Houston TX 77204 USA

Given an input solution that may not be Pareto optimal, we present a new inverse optimization methodology for multi-objective convex optimization that determines a weight vector producing a weakly Pareto optimal solution that preserves the decision maker's trade-off intention encoded in the input solution. We introduce a notion of trade-off preservation, which we use as a measure of similarity for approximating the input solution, and show its connection with minimizing an optimality gap. We propose a linear approximation to the inverse model and a successive linear programming algorithm that balance between trade-off preservation and computational efficiency, and show that our model encompasses many of the existing inverse optimization models from the literature. We demonstrate the proposed method using clinical data from prostate cancer radiation therapy. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Convex programming Inverse optimization OR in cancer therapy

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Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期284卷 644-659页

作者： Selcuklu, Saltuk Bugra Coit, David W. Felder, Frank A. Erciyes Univ Energy Syst Engn Kayseri Turkey Rutgers State Univ Ind & Syst Engn Piscataway NJ USA Tsinghua Univ Ind Engn Dept Beijing Peoples R China Rutgers State Univ Ctr Energy Econ & Environm Policy Piscataway NJ USA

Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality to show the trade-off between objectives. Pareto optimality involves the identification of solutions that are not dominated by other solutions based on their respective objective functions. However, the Pareto optimality concept does not contain any information about the uncertainty of solutions. Evaluation and comparison of solutions becomes difficult when the objective functions are subjected to uncertainty. A new metric, the Pareto Uncertainty Index (PUI), is presented. This metric includes uncertainty due to the stochastic coefficients in the objective functions as part of the Pareto optimality concept to form an extended probabilistic Pareto set, we define as the p-Pareto set. The decision maker can observe and assess the randomness of solutions and compare the promising solutions according to their performance of satisfying objectives and any undesirable uncertainty. The PUI is an effective and convenient decision-making tool to compare promising solutions with multiple uncertain objectives. (C) 2020 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Uncertainty modeling Pareto

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Locating series FACTS devices for multi-objective congestion management improving voltage and transient stability

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第2期236卷 763-773页

作者： Esmaili, Masoud Shayanfar, Heidar Ali Moslemi, Ramin Islamic Azad Univ Dept Elect Engn West Tehran Branch Tehran Iran Iran Univ Sci & Technol Ctr Excellence Power Syst Automat & Operat Tehran Iran

Transmission congestion management is a vital task in electricity markets. Series FACTS devices can be used as effective tools to relieve congestion mostly employing Optimal Power Flow based methods, in which total cost as the objective function is minimized. However, power system stability may be deteriorated after relieving congestion using traditional methods leading to a vulnerable power system against disturbances. In this paper, a multi-objective framework is proposed for congestion management where three competing objective functions including total operating cost, voltage and transient stability margins are simultaneously optimized. This leads to an economical and robust operating point where enough levels of voltage and transient security are included. The proposed method optimally locates and sizes series FACTS devices on the most congested branches determined by a priority list based on Locational Marginal Prices. Individual sets of Pareto solutions, resulted from solving multi-objective congestion management for each location of FACTS devices, are merged together to create the comprehensive Pareto set. Results of testing the proposed method on the well-known New-England test system are discussed in details and confirm efficiency of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Congestion management FACTS devices Electricity markets Power system stability margin

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A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期180卷 1011-1027页

作者： Sylva, John Crema, Alejandro Cent Univ Venezuela Escuela Computac Fac Ciencias Caracas 1041A Venezuela Cent Univ Venezuela Fac Ingn Dept Matemat Aplicada Caracas 1041A Venezuela

We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors. (c) 2006 Elsevier B.V. All rights reserved.

关键词： integer programming multiple objective programming parametric programming

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Resource allocation in dynamic PERT networks with finite capacity

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第3期215卷 670-678页

作者： Yaghoubi, Saeed Noori, Siamak Azaron, Amir Tavakkoli-Moghaddam, Reza Univ Coll Dublin Michael Smurfit Grad Sch Business Dublin 2 Ireland Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Dept Ind Engn Fac Engn Tehran Iran Reykjavik Univ Dept Financial Engn & Engn Management Sch Sci & Engn Reykjavik Iceland

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Project management Markov processes multiple objective programming

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