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Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

OPTIMIZATION 2015年第3期64卷 641-661页

作者： Eronen, Ville-Pekka Makela, Marko M. Westerlund, Tapio Univ Turku Dept Math & Stat Turku Finland Abo Akad Univ Proc Design & Syst Engn Lab Turku Finland

In this article, a generalization of the ECP algorithm to cover a class of nondifferentiable mixed-integer NonLinear programming problems is studied. In the generalization constraint functions are required to be -pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also -pseudoconvex case is considered. Furthermore, the gradients used in the ECP algorithm are replaced by the subgradients of Clarke subdifferential. With some additional assumptions, the resulting algorithm shall be proven to converge to a global minimum.

关键词： generalized convexity mixed-integer programming pseudoconvex function alpha ECP nonsmooth optimization nonsmooth MINLP subgradient extended cutting plane algorithm 26A27 90C56 90C11 90C26

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Solving Infrastructure Monitoring Problems with Multiple Heterogeneous Unmanned Aerial Vehicles 15

Solving Infrastructure Monitoring Problems with Multiple Het...

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International Conference on Autonomous Agents and Multiagent Systems

作者： Jakub Ondracek Ondrej Vanek Michal Pechoucek Agent Technology Center Faculty of Electrical Engineering Czech Technical University

ISBN: (纸本)9781450337717

A number of critical infrastructures, such as gas or oil pipelines operate in a sensitive environment and any damage done to the infrastructure significantly harms the surrounding fauna and flora and poisons water supplies. The infrastructure thus needs to be monitored and any damage or failure has to be detected and reported as quickly as possible. We focus on the enhancement of the monitoring systems - we propose a first holistic solution for a set of heterogeneous unmanned aerial vehicles (UAVs) which monitor the infrastructure under current technological restrictions such as speed, battery endurance and sensing radius. We solve the problem of (1) the allocation of charging/maintenance stations in the area, (2) the assignment of the UAVs to the stations and (3) the computation of their trajectories with respect to the environment sensitivity. We propose a formal graph-based model capturing problem constraints and requirements. We explore possible decompositions of the problem and we propose a number of algorithms allowing to choose between algorithm runtime and solution quality. The results show that our approach can be used to monitor real-world sized infrastructures of a length of tens of kilometers using up to five UAVs.

关键词： Unmanned Aerial Vehicles Critical Infrastructure Protection mixed-integer programming Trajectory Planning

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Solving a multi-floor layout design model of a dynamic cellular manufacturing system by an efficient genetic algorithm

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JOURNAL OF MANUFACTURING SYSTEMS 2014年第1期33卷 218-232页

作者： Kia, R. Khaksar-Haghani, F. Javadian, N. Tavakkoli-Moghaddam, R. Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran Islamic Azad Univ Najafabad Branch Dept Ind Engn Esfahan Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Univ Tehran Coll Engn Engn Optimizat Res Grp Tehran Iran

This paper presents a mixed-integer programming model for a multi-floor layout design of cellular manufacturing systems (CMSs) in a dynamic environment. A novel aspect of this model is to concurrently determine the cell formation (CF) and group layout (GL) as the interrelated decisions involved in the design of a CMS in order to achieve an optimal (or near-optimal) design solution for a multi-floor factory in a multi-period planning horizon. Other design aspects are to design a multi-floor layout to form cells in different floors, a multi-rows layout of equal area facilities in each cell, flexible reconfigurations of cells during successive periods, distance-based material handling cost, and machine depot keeping idle machines. This model incorporates with an extensive coverage of important manufacturing features used in the design of CMSs. The objective is to minimize the total costs of intra-cell, inter-cell, and inter-floor material handling, purchasing machines, machine processing, machine overhead, and machine relocation. Two numerical examples are solved by the CPLEX software to verify the performance of the presented model and illustrate the model features. Since this model belongs to NP-hard class, an efficient genetic algorithm (GA) with a matrix-based chromosome structure is proposed to derive near-optimal solutions. To verify its computational efficiency in comparison to the CPLEX software, several test problems with different sizes and settings are implemented. The efficiency of the proposed GA in terms of the objective function value and computational time is proved by the obtained results. (C) 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

关键词： Dynamic cellular manufacturing systems Multi-floor layout mixed-integer programming Genetic algorithm

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Using integer programming for balancing return and risk in problems with individual chance constraints

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COMPUTERS & OPERATIONS RESEARCH 2014年 49卷 59-70页

作者： Shen, Siqian Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

In this paper, we study probabilistically constrained problems involving individual chance constraints, random univariate right-hand sides, and risk tolerances defined as decision variables which affect part of the objective function. Built on the concept of efficient points, we formulate the problems as mixed-integer programs by using binary variables to determine an optimal risk tolerance for each chance constraint. We develop two benchmark approaches, both of which solve chance-constrained programs with fixed risk values in a bisection algorithm or by enumeration. We specify our approaches for a minimum cost flow problem and a network capacity design problem, both of which involve chance constraints for bounding the risk of demand shortages. We test instances with diverse size and complexity of the two network problems, and demonstrate the computational efficacy as well as give managerial insights. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Chance-constrained programming Risk management mixed-integer programming Minimum cost flow Network capacity design

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Generalized Elastic Flow Rerouting Scheme

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NETWORKS 2015年第4期66卷 267-281页

作者： Fouquet, Yoann Nace, Dritan Pioro, Michal Poss, Michael Zotkiewicz, Mateusz Univ Technol Compiegne Univ Paris 04 CNRS Heudiasyc UMR 7253 F-60203 Compiegne France Warsaw Univ Technol Inst Telecommun PL-00661 Warsaw Poland Lund Univ Dept Elect & Informat Technol S-22100 Lund Sweden Univ Montpellier 2 UMR CNRS LIRMM 5506 F-34392 Montpellier 5 France

The present study deals with Elastic Flow Rerouting (EFR)-an original traffic restoration strategy for protecting traffic flows in communication networks (including wireless networks) against multiple link failures. EFR aims at alleviating the trade-off between practicability of traffic restoration and the cost of network resources observed in existing networking solutions. We present an extension of EFR capable of managingmultiple partial link failures. We describe EFR and its extension, formulate the EFR related optimization problems, and discuss approaches for their resolution. We also discuss numerical results illustrating effectiveness of EFR in terms of the link capacity cost. (c) 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(4), 267-281 2015

关键词： survivability traffic restoration mixed-integer programming partial link failures

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A hybrid heuristic approach to the problem of the location of vehicle charging stations

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期70卷 195-204页

作者： You, Peng-Sheng Hsieh, Yi-Chih Natl ChiaYi Univ Dept Mkt & Logist Transportat Chiayi 600 Taiwan Natl Formosa Univ Dept Ind Management Huwei 632 Yunlin Taiwan

In order to reduce the negative impact of fuel-powered vehicles on the environment, the use of alternative-fuel vehicles (AFVs), which produce far less pollution than traditional fuel-powered vehicles, is being introduced in many countries around the world. However, compared to the fuel-powered vehicles, AFVs such as electric vehicles require frequent recharging of their electrical energy storages (batteries), which results in a short vehicle driving range. Thus, AFV users who want to travel from home to a terminal location and back again must consider whether their AFVs can be recharged on the way. One of the approaches to solve this problem is to install alternative fuel charging stations on suitable locations to provide recharging services. However, when the budget is limited, the selection of locations and the types of alternative fuel charging stations becomes a decision problem, since it will directly affect the number of potential AFV users that can be served. This paper develops a mixed-integer programming model to address this problem and to maximize the number of people who can complete round-trip itineraries. A hybrid heuristic approach is proposed to solve this model. Numerical results show that the proposed heuristic approach only requires a small amount of CPU time to attain confident solutions. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Charging stations Location Heuristic approach mixed-integer programming

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A bi-objective analysis of the r-all-neighbor p-center problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期72卷 114-128页

作者： Medal, Hugh R. Rainwater, Chase E. Pohl, Edward A. Rossetti, Manuel D. Mississippi State Univ Dept Ind & Syst Engn Starkville MS 39762 USA Univ Arkansas Dept Ind Engn Fayetteville AR 72701 USA

In this paper we consider a generalization of the p-center problem called the r-all-neighbor p-center problem (RANPCP). The objective of the RANPCP is to minimize the maximum distance from a demand point to its rth-closest located facility. The RANPCP is applicable to facility location with disruptions because it considers the maximum transportation distance after (r - 1) facilities are disrupted. While this problem has been studied from a single-objective perspective, this paper studies two bi-objective versions. The main contributions of this paper are (1) algorithms for computing the Pareto-efficient sets for two pairs of objectives (closest distance vs rth-closest distance and cost vs. rth-closest distance) and (2) an empirical analysis that gives several useful insights into the RANPCP. Based on the empirical results, the RANPCP produces solutions that not only minimize vulnerability but also perform reasonably well when disruptions do not occur. In contrast, if disruptions are not considered when locating facilities, the consequence due to facility disruptions is much higher, on average, than if disruptions had been considered. Thus, our results show the importance of optimizing for vulnerability. Therefore, we recommend a bi-objective analysis. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Facility location Interdiction mixed-integer programming Bi-objective programming Disruptions Risk assessment

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A robust optimization approach to diet problem with overall glycemic load as objective function

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APPLIED MATHEMATICAL MODELLING 2014年第19-20期38卷 4926-4940页

作者： Bas, Esra Istanbul Tech Univ Dept Ind Engn TR-34367 Istanbul Turkey

The main purpose of the paper is to introduce a mixed-integer programming model for the diet problem with glycemic load (GL) values of foods as objective function parameters. It is assumed that the glycemic load values are subject to uncertainty. The diet problem with minimum cost function is well-known in the literature. However, the diet problem with minimum total daily GL values of foods that satisfies the daily nutritional and serving size requirements has not been proposed. Robust optimization approach is used to account for uncertainty in the GL values of foods. The decision maker is flexible to tune the degree of uncertainty rather than assuming a worst-case scenario. An experimental analysis with a total of 177 foods is performed based on the nutritional and serving size requirements and the basic food groups recommended by the U.S. Department of Health and Human Services & U.S. Department of Agriculture (USDA). The results of the experimental analysis with different scenarios give different solutions for different degrees of uncertainty. However, some foods are frequently found to be in the optimum solutions. These foods are in good agreement with the literature advising them as a part of a daily diet for attaining low level of blood glucose levels. Although we believe that the proposed diet problem with minimum total GL has contributions for satisfying the daily nutritional and serving size requirements with a minimum level of effect on blood glucose levels, it has several limitations. It is a basic diet problem, and assumes that the overall GL is a linear combination of number of serving sizes with the GL values of foods. It also does not consider any other factors such as several combinations of foods and their varying effects on blood glucose levels. These factors should be considered for the next research. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Diet problem Glycemic index Glycemic load Robustness mixed-integer programming

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Optimizing fuzzy p-hub center problem with generalized value-at-risk criterion

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APPLIED MATHEMATICAL MODELLING 2014年第15-16期38卷 3987-4005页

作者： Yang, Kai Liu, Yankui Yang, Guoqing Hebei Univ Coll Math & Comp Sci Risk Management & Financial Engn Lab Baoding 071002 Hebei Peoples R China

In this study, we reduce the uncertainty embedded in secondary possibility distribution of a type-2 fuzzy variable by fuzzy integral, and apply the proposed reduction method to p-hub center problem, which is a nonlinear optimization problem due to the existence of integer decision variables. In order to optimize p-hub center problem, this paper develops a robust optimization method to describe travel times by employing parametric possibility distributions. We first derive the parametric possibility distributions of reduced fuzzy variables. After that, we apply the reduction methods to p-hub center problem and develop a new generalized value-at-risk (VaR) p-hub center problem, in which the travel times are characterized by parametric possibility distributions. Under mild assumptions, we turn the original fuzzy p-hub center problem into its equivalent parametric mixed-integer programming problems. So, we can solve the equivalent parametric mixed-integer programming problems by general-purpose optimization software. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the efficiency of the proposed solution methods. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Parametric possibility distribution Uncertainty reduction Hub location problem Parametric programming mixed-integer programming

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A novel MIQCP method for FACTS allocation in complex real-world grids

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2014年 62卷 735-743页

作者： Chang, Robert W. Saha, Tapan K. Univ Queensland Sch Informat Technol & Elect Engn Brisbane Qld 4072 Australia

This paper presents a novel Flexible AC Transmission Systems (FACTS) placement method based on mixed integer quadratically constrained programming (MIQCP). The method is capable of allocating both Static VAR Compensator (SVC) and Thyristor-Controlled Series Capacitor (TCSC) either separately or simultaneously, to determine concurrently their numbers, locations as well as sizes. The optimization objective is to maximize loadability and minimize compensation. The proposed MIQCP formulation partially incorporates key quadratic constraints, which were absent in mixed integer linear programming (MILP) placement methods reported in the past. The authors demonstrate significant improvements in accuracy over past MILP methods, with case studies presented on the simplified Southeast Australian network, and on a large scale real-world power system, Powerlink Queensland's HV transmission network, with 886 buses and 1087 branches. In addition, results and observations for simultaneous allocation of multiple TCSCs and SVCs in these networks are demonstrated in this paper. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： FACTS devices Optimal allocation mixed-integer programming SVC TCSC

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