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Modelling the mobile target covering problem using flying drones

OPTIMIZATION LETTERS 2016年第5期10卷 1021-1052页

作者： Pugliese, Luigi Di Puglia Guerriero, Francesca Zorbas, Dimitrios Razafindralambo, Tahiry Univ Calabria Dept Mech Energy & Management Engn I-87036 Arcavacata Di Rende CS Italy Inria Lille Nord Europe Villeneuve Dascq France

This paper addresses the mobile targets covering problem by using unmanned aerial vehicles (UAVs). It is assumed that each UAV has a limited initial energy and the energy consumption is related to the UAV's altitude. Indeed, the higher the altitude, the larger the monitored area and the higher the energy consumption. When an UAV runs out of battery, it is replaced by a new one. The aim is to locate UAVs in order to cover the piece of plane in which the target moves by using a minimum number of UAVs. Each target has to be monitored for each instant time. The problem under consideration is mathematically represented by defining mixed integer non-linear optimization models. Heuristic procedures are defined and they are based on restricted mixed integer programming (MIP) formulation of the problem. A computational study is carried out to assess the behaviour of the proposed models and MIP-based heuristics. A comparison in terms of efficiency and effectiveness among models and heuristics is carried out.

关键词： Targets tracking Unmanned aerial vehicles non-linear programming Matheuristic

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A joint optimization of product variety and ordering approach

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COMPUTERS & OPERATIONS RESEARCH 1998年第7-8期25卷 557-566页

作者： Jayaraman, V Srivastava, R Benton, WC Washington State Univ Coll Business & Econ Vancouver WA 98686 USA USAF Inst Technol AFIT LAL Wright Patterson AFB OH 45433 USA Ohio State Univ Dept Management Sci Columbus OH 43210 USA

It has been generally recognized that the product variety or product line decision is one of critical importance to marketing and product managers. Product line composition is one of the most pervasive problems that includes analysis of product additions as well deletions and the degree of complementarity and substitutability among the different items within the product line. Equally important is the ordering decision which determines the order size and timing of the order for replenishing the stock of each of the products that constitute the given product line. We develop a model, OPROVAR (optimization of product variety and ordering strategy) that considers simultaneously the order quantity decision of a product and the stocking decision of a product line to maximize total profits. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： non-linear programming inventory planning and control marketing

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Operating rules of an irrigation purposes reservoir using multi-objective optimization

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WATER RESOURCES MANAGEMENT 2008年第5期22卷 551-564页

作者： Consoli, Simona Matarazzo, Benedetto Pappalardo, Nello Univ Catania Dept Agr Engn I-95123 Catania Italy Univ Catania Dept Econ & Quantitat Methods I-95129 Catania Italy

A multi-objective optimization technique for the operation of an irrigation reservoir is presented in this paper. The study deals with two different objective functions (OF): the minimization of reservoir release deficit from the irrigation demand (OF1) and the maximization of net benefit by the demand sector (OF2). In the first step, monthly optimization of each individual objective was performed with a deterministic non-linear programming (NLP) algorithm, that gave the lower and upper bounds for the multi-objective analysis. In the second step, multi-objective optimization was performed through the Constraint method that operates by optimising the objective function OF1, while the other (OF2) was constrained to satisfy release strategies generated by the optimization. non-dominated set of release strategies is generated by parametrically varying the bounds of the constraints obtained from the individual optimal solutions. In the third step, the interactive analytical Step method was applied to find the best compromise solution, between the two OFs, by minimizing the distance of each non-dominated solution to an ideal solution that represents the utopian optimum for both OF1 and OF2. Furthermore, the interactive approach allows to improve the performance of the reservoir in terms of compromise irrigation releases, by changing the OF values until the satisfaction of predetermined criteria fixed by the planners and decision makers. The proposed water allocation model was applied to the Pozzillo reservoir operation, that supplies the Catania Plain irrigation area (Eastern Sicily).

关键词： interactive approach multi-objective optimization net benefit non-linear programming reservoir operating rules water deficits

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SENSITIVITY ANALYSIS FOR non-linear PROGRAMS WITH linear CONSTRAINTS

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OPERATIONS RESEARCH LETTERS 1987年第6期6卷 275-280页

作者： KYPARISIS, J Department of Decision Sciences and Information Systems College of Business Administration Florida International University Miami FL 33199 USA

We extend the principal sensitivity analysis results for parametric non-lieear programs with linear constraints. In particular, we obtain sufficient conditions for the existence, continuity and differentiability of a locally unique perturbed local minimum. We also show that the local optimal value function is differentiable under these conditions.

关键词： non-linear programming sensitivity analysis perturbed solution optimal value function

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Performance of the Equivalent Reservoir Modelling Technique for Multi-Reservoir Hydropower Systems

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WATER RESOURCES MANAGEMENT 2010年第12期24卷 3101-3114页

作者： Brandao, Joao Luiz B. Univ Sao Paulo Sao Carlos Sch Engn Sao Carlos SP Brazil

This paper investigates the validity of a simplified equivalent reservoir representation of a multi-reservoir hydroelectric system for modelling its optimal operation for power maximization. This simplification, proposed by Arvanitidis and Rosing (IEEE Trans Power Appar Syst 89(2):319-325, 1970), imputes a potential energy equivalent reservoir with energy inflows and outflows. The hydroelectric system is also modelled for power maximization considering individual reservoir characteristics without simplifications. Both optimization models employed MINOS package for solution of the non-linear programming problems. A comparison between total optimized power generation over the planning horizon by the two methods shows that the equivalent reservoir is capable of producing satisfactory power estimates with less than 6% underestimation. The generation and total reservoir storage trajectories along the planning horizon obtained by equivalent reservoir method, however, presented significant discrepancies as compared to those found in the detailed modelling. This study is motivated by the fact that Brazilian generation system operations are based on the equivalent reservoir method as part of the power dispatch procedures. The potential energy equivalent reservoir is an alternative which eliminates problems with the dimensionality of state variables in a dynamic programming model.

关键词： Hydro power plants Optimization models Reservoir operation Equivalent reservoir non-linear programming

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The economic value of improved agrometeorological information to irrigators amid climate variability

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INTERNATIONAL JOURNAL OF CLIMATOLOGY 2012年第4期32卷 567-581页

作者： Mushtaq, Shahbaz Chen, Charlie Hafeez, Mohsin Maroulis, Jerry Gabriel, Hamza Univ So Queensland Australian Ctr Sustainable Catchments Toowoomba Qld 4350 Australia Charles Sturt Univ Int Ctr Water Food Secur Wagga Wagga NSW 2678 Australia CSIRO Black Mt CSIRO Canberra ACT Australia

In Australia, climate variability and the predicted impact of climate change help in making seasonal rainfall less predictable and seasonal irrigation supplies more uncertain, eroding agricultural production prospects and profitability. Water allocation forecasts have economic value to irrigators for making informed cropping decisions. This study estimated the economic value of improved irrigation allocation forecasts in the Coleambally irrigation area (CIA) in southeastern Australia using a non-linear programming model. The model uses production and profit functions to estimate yield and gross margins for various water allocation levels rather than using given crop yields and gross margins. The model also captures the tactical response of improved cropping decisions made by irrigators based on water allocation announcements throughout the irrigation season. Tactical responses include changing the winter crop combinations, abandoning irrigation for a percentage of the summer crops, temporary purchase or sale of water, and deficit irrigation. The estimated economic benefit of improved seasonal water allocation forecasts to the CIA irrigators ranges from AU$1.33 ha(-1) to AU$9.58 ha(-1) (AU$1 = US$0.77). The economic analysis of water allocation forecasts shows that the potential total gross margin for the irrigators at the 100% allocation level was AU$47.6 m, assuming accurate forecast of the end-of-season allocations. A more realistic scenario generates a forecast value of AU$8.9 million reduction in the gross margin (pessimistic water allocation outlook) and AU$1.60 million in the forgone gross margin (optimistic water allocation outlook) for only 5% variation in outlook above or below the actual allocation level of 60%. This suggests that losses far exceed when water allocations are over-estimated by irrigators, as resources and inputs could be overly committed to execute the less-informed cropping plans. The knowledge benefits from forecasts are far greater at th

关键词： water allocation water policy forecasting economic value non-linear programming Australia

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Energy and B-spline interproximation

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COMPUTER-AIDED DESIGN 1997年第7期29卷 485-496页

作者： Wang, XF Cheng, FH Barsky, BA UNIV KENTUCKY DEPT COMP SCI LEXINGTON KY 40506 USA UNIV CALIF BERKELEY EECS DIV COMP SCI BERKELEY CA 94720 USA

In this paper, we study B-spline curve interproximation with different energy forms and parametrization techniques, and present an interproximation scheme for B-spline surfaces. It shows that the energy form has a much bigger impact on the generated curve than the parametrization technique. With the same energy form, different parametrization techniques generate relatively small difference on the corresponding curves. With the same parametrization technique, however, different energy forms make significant difference on the shape and smoothness of the resulting curves. Furthermore, interproximating B-spline curves generated by minimizing approximated energy forms are far from being good approximations to the optimal curves. They tend to generate flatter regions and sharper turns than curves generated by minimizing the exact energy form. The interproximation scheme for surfaces is aimed at generating a smooth surface to interpolate a grid of data which could either be a point or a region. This is achieved by minimizing a strain energy based on squared principal curvatures for bicubic B-spline surfaces. The surface interproximation process is also studied with different energy forms and parametrization techniques. The test results of the surface interproximation process also show the same conclusion as the curve interproximation process. (C) 1997 Elsevier Science Ltd.

关键词： B-splines interpolation approximation interproximation non-linear programming centripetal model relative chord length parametrization constrained optimization

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A decision-support system to assist forest industry planning and investment when data are scarce: the case of hardwood veneering in subtropical eastern Australia

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AUSTRALIAN FORESTRY 2021年第2期84卷 59-72页

作者： Venn, T. J. McGavin, R. L. Univ Queensland Fac Sci Sch Agr & Food Sci St Lucia Qld 4072 Australia Queensland Govt Dept Agr & Fisheries Agrisci Queensland Salisbury SA Australia Univ Queensland Sch Civil Engn Fac Engn Architecture & Informat Technol St Lucia Qld Australia

An aspatial mathematical model has been developed to simultaneously support log processing investment decisions with respect to processing scale, facility location and log procurement when data are scarce. A key design principle was to make the model suitable for use by industry. The objective function maximises gross margins per hour of log processing time, and the model accounts for potential processing efficiencies with larger-diameter logs. To support log procurement decisions, the model estimates mill-delivered log costs at which a log procurement officer should be indifferent between purchasing alternative log types. The utility of the model is demonstrated with an application to rotary veneer processing of hardwood logs in subtropical eastern Australia. Complex interactions between processing scale, facility location and log procurement strategies were revealed by substantial differences in gross margins between modelled scenarios. Log procurement decisions were found to have the greatest potential impact on gross margins, followed by facility location and processing scale. The model highlighted that substantially higher returns can be earned from optimal log procurement strategies relative to approaches that either minimise log costs, maximise product recovery or do not differentiate between log types and simply utilise all available log volume.

关键词： operations research non-linear programming processing scale facility location log procurement rotary veneer financial performance

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Optimal vaccination and control strategies against dengue

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2019年第10期42卷 3496-3507页

作者： Fischer, Anne Chudej, Kurt Pesch, Hans Josef Univ Bayreuth Lehrstuhl Ingenieurmath Bayreuth Germany Univ Bayreuth Lehrstuhl Wissensch Rechnen D-95440 Bayreuth Germany

This article focuses on the mathematical modelling of a disease outbreak of dengue fever. A cost-efficient fighting strategy, which simultaneously uses vaccination, application of insecticides to adult and aquatic mosquitoes, and an approach to decrease the number of man-made breeding places for the mosquitoes, is computed using optimal control. Vaccination includes a paediatric vaccination and an imperfect random mass vaccination with waning immunity.

关键词： Asian tiger mosquito dengue insecticide non-linear programming optimal control vaccination

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Modified differential evolution: a greedy random strategy for genetic recombination

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2005年第3期33卷 255-265页

作者： Bergey, PK Ragsdale, C N Carolina State Univ Dept Business Management Raleigh NC 27695 USA Virginia Polytech Inst & State Univ Dept Business Informat Technol Blacksburg VA 24061 USA

Over the past three decades Evolutionary Algorithms have emerged as a powerful mechanism for finding solutions to large and complex problems. A promising new evolutionary algorithm known as Differential Evolution (DE) was recently introduced and has garnered significant attention in the research literature. This paper introduces a modification to DE that enhances its rate of convergence without compromising solution quality. DE was recently shown to outperform several well-known stochastic optimization methods on an extensive set of test problems. Our Modified Differential Evolution (MDE) algorithm utilizes selection pressure to develop offspring that are more fit to survive than those generated from purely random operators. We demonstrate that MDE requires less computational effort to locate global optimal solutions to well-known test problems in the continuous domain. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： artificial intelligence evolutionary algorithms non-linear programming optimization

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