Relevant bibliographies by topics / Nonlinear optimisation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Nonlinear optimisation'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Nonlinear optimisation"

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Wang, Jiakun Liu &. Xu-Jia. "Light Refraction is Nonlinear Optimisation." Journal of Mathematical Study 54, no. 2 (June 2021): 142–63. http://dx.doi.org/10.4208/jms.v54n2.21.02.

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Diouf, Serigne, Mamadou M. Diop, and Alassane Sy. "NUMERICAL IMAGING USING NONLINEAR OPTIMISATION." International Journal of Numerical Methods and Applications 20, no. 1 (January 10, 2021): 1–16. http://dx.doi.org/10.17654/nm020010001.

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Dobersek, D., and D. Goricanec. "Optimisation of tree path pipe network with nonlinear optimisation method." Applied Thermal Engineering 29, no. 8-9 (June 2009): 1584–91. http://dx.doi.org/10.1016/j.applthermaleng.2008.07.017.

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Safari, Sina, and Julián Londoño Monsalve. "Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems." Vibration 4, no. 3 (August 5, 2021): 648–65. http://dx.doi.org/10.3390/vibration4030036.

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Characterisation and quantification of nonlinearities in the engineering structures include selecting and fitting a good mathematical model to a set of experimental vibration data with significant nonlinear features. These tasks involve solving an optimisation problem where it is difficult to choose a priori the best optimisation technique. This paper presents a systematic comparison of ten optimisation methods used to select the best nonlinear model and estimate its parameters through nonlinear system identification. The model selection framework fits the structure’s equation of motions using time-domain dynamic response data and takes into account couplings due to the presence of the nonlinearities. Three benchmark problems are used to evaluate the performance of two families of optimisation methods: (i) deterministic local searches and (ii) global optimisation metaheuristics. Furthermore, hybrid local–global optimisation methods are examined. All benchmark problems include a free play nonlinearity commonly found in mechanical structures. Multiple performance criteria are considered based on computational efficiency and robustness, that is, finding the best nonlinear model. Results show that hybrid methods, that is, the multi-start strategy with local gradient-based Levenberg–Marquardt method and the particle swarm with Levenberg–Marquardt method, lead to a successful selection of nonlinear models and an accurate estimation of their parameters within acceptable computational times.
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Liu, Hanmin, Xuesong Yan, and Qinghua Wu. "An Improved Pigeon-Inspired Optimisation Algorithm and Its Application in Parameter Inversion." Symmetry 11, no. 10 (October 15, 2019): 1291. http://dx.doi.org/10.3390/sym11101291.

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Pre-stack amplitude variation with offset (AVO) elastic parameter inversion is a nonlinear, multi-solution optimisation problem. The techniques that combine intelligent optimisation algorithms and AVO inversion provide an effective identification method for oil and gas exploration. However, these techniques also have shortcomings in solving nonlinear geophysical inversion problems. The evolutionary optimisation algorithms have recognised disadvantages, such as the tendency of convergence to a local optimum resulting in poor local optimisation performance when dealing with multimodal search problems, decreasing diversity and leading to the prematurity of the population as the number of evolutionary iterations increases. The pre-stack AVO elastic parameter inversion is nonlinear with slow convergence, while the pigeon-inspired optimisation (PIO) algorithm has the advantage of fast convergence and better optimisation characteristics. In this study, based on the characteristics of the pre-stack AVO elastic parameter inversion problem, an improved PIO algorithm (IPIO) is proposed by introducing the particle swarm optimisation (PSO) algorithm, an inverse factor, and a Gaussian factor into the PIO algorithm. The experimental comparisons indicate that the proposed IPIO algorithm can achieve better inversion results.
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Özcan, Dinçer, Ümit Sönmez, and Levent Güvenç. "Optimisation of the Nonlinear Suspension Characteristics of a Light Commercial Vehicle." International Journal of Vehicular Technology 2013 (February 18, 2013): 1–16. http://dx.doi.org/10.1155/2013/562424.

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The optimum functional characteristics of suspension components, namely, linear/nonlinear spring and nonlinear damper characteristic functions are determined using simple lumped parameter models. A quarter car model is used to represent the front independent suspension, and a half car model is used to represent the rear solid axle suspension of a light commercial vehicle. The functional shapes of the suspension characteristics used in the optimisation process are based on typical shapes supplied by a car manufacturer. The complexity of a nonlinear function optimisation problem is reduced by scaling it up or down from the aforementioned shape in the optimisation process. The nonlinear optimised suspension characteristics are first obtained using lower complexity lumped parameter models. Then, the performance of the optimised suspension units are verified using the higher fidelity and more realistic Carmaker model. An interactive software module is developed to ease the nonlinear suspension optimisation process using the Matlab Graphical User Interface tool.
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Beran, Václav, and Petr Dlask. "Nonlinear optimisation and rational cash flow." Engineering, Construction and Architectural Management 14, no. 3 (May 8, 2007): 277–92. http://dx.doi.org/10.1108/09699980710744917.

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Ławryńczuk, Maciej. "A Family of Model Predictive Control Algorithms With Artificial Neural Networks." International Journal of Applied Mathematics and Computer Science 17, no. 2 (June 1, 2007): 217–32. http://dx.doi.org/10.2478/v10006-007-0020-5.

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A Family of Model Predictive Control Algorithms With Artificial Neural NetworksThis paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used on-line to determine local linearisation and a nonlinear free trajectory. Single-point and multi-point linearisation methods are discussed. The MPC-NPL structure is far more reliable and less computationally demanding in comparison with the MPC-NO one because it solves a quadratic programming problem, which can be done efficiently within a foreseeable time frame. At the same time, closed-loop performance of both algorithm classes is similar. Finally, a hybrid MPC algorithm with Nonlinear Prediction, Linearisation and Nonlinear optimisation (MPC-NPL-NO) is discussed.
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Skworcow, P., D. Paluszczyszyn, and B. Ulanicki. "Pump schedules optimisation with pressure aspects in complex large-scale water distribution systems." Drinking Water Engineering and Science Discussions 7, no. 1 (February 10, 2014): 121–49. http://dx.doi.org/10.5194/dwesd-7-121-2014.

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Abstract. This paper considers optimisation of pump and valve schedules in complex large-scale water distribution networks (WDN), taking into account pressure aspects such as minimum service pressure and pressure-dependent leakage. An optimisation model is automatically generated in GAMS language from a hydraulic model in EPANET format and from additional files describing operational constraints, electricity tariffs and pump station configurations. The paper describes in details how each hydraulic component is modelled. To reduce the size of the optimisation problem the full hydraulic model is simplified using module reduction algorithm, while retaining the nonlinear characteristics of the model. Subsequently, a nonlinear programming solver CONOPT is used to solve the optimisation model, which is in the form of Nonlinear Programming with Discontinuous Derivatives (DNLP). The results produced by CONOPT are processed further by heuristic algorithms to generate integer solution. The proposed approached was tested on a large-scale WDN model provided in EPANET format. The considered WDN included complex structures and interactions between pump stations. Solving of several scenarios considering different horizons, time steps, operational constraints, demand levels and topological changes demonstrated ability of the approach to automatically generate and solve optimisation problems for variety of requirements.
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Ha, Manh Hung, Viet Hung Truong, and Minh Phuong Nguyen. "Rao algorithm-based method for optimisation of steel frames using nonlinear inelastic analysis." Ministry of Science and Technology, Vietnam 63, no. 8 (August 30, 2021): 35–39. http://dx.doi.org/10.31276/vjst.63(8).35-39.

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Metaheuristic optimisation algorithms have been increasingly used because of their superior ability to find globally optimal solutions. Theoretically, these algorithms are very powerful and can be applied in all types of optimisation problems. However, in reality, their performance depends on the characteristics of each optimisation problem class. In addition, the complexity of an algorithm is an important factor affecting its application in specific design problems. In this paper, the Rao optimisation algorithm, one of the newest metaheuristic algorithms, is presented for the optimisation algorithm of steel frame structures. The advantage of the Rao algorithm is that it is quite simple with few parameters, so engineers can easily apply it in daily design tasks. A nonlinear inelastic analysis is used to consider the nonlinear behaviors of the steel structure. A two-story space steel frame is studied. The results show that Rao-1 is more stable and converged more quickly but easily trapped in local solutions than Rao-2 and Rao-4. Rao-4 is more efficient in global search but its stability is less than other algorithms. Keywords:nonlinear inelastic analysis, optimisation, Rao algorithm, steel frame.
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Dissertations / Theses on the topic "Nonlinear optimisation"

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Backhouse, Allan R. "Nonlinear optimisation on multicommodity networks." Thesis, Backhouse, Allan R. (1996) Nonlinear optimisation on multicommodity networks. PhD thesis, Murdoch University, 1996. https://researchrepository.murdoch.edu.au/id/eprint/51547/.

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The purpose of the work described by this thesis is the exploration and comparison of a selection of methods for the solution of multicommodity network optimisation problems that have a nonlinear objective function, bound constraints, and both linear and nonlinear side constraints (these problems are denoted by MSC-NL). The motivation for this work was an important class of problems that arise in the petroleum industry. These problems typically have a relatively small number of nonlinear constraints which are, unfortunately, not convex. In many cases, a realistic model of a "real world" problem leads to optimisation problems which, for nonlinear programming problems, are medium to large in size and yet it is desirable for local optima to be able to be determined using easily accessible computing environments. Hence, it is important for methods to be available that are able to exploit the sparsity and structure inherent in the problem, are efficient in computer processing time and memory use, and are reliable and numerically stable. A variety of methods that potentially meet these requirements have been implemented in an experimental computer code called NLNET. Three different general nonlinear programming methods are considered: projected Lagrangian, penalty multiplier, and generalised reduced gradient. For each of these methods, the implementation in NLNET uses the same multicommodity network solver. This solver is an implementation of the active set feasible direction method that is specialised for multicommodity network optimisation problems with a nonlinear objective function and linear side constraints. Within this solver a number of different approaches, for details such as partitioning of the constraint matrix and determining a search direction, have been implemented. It is very common to encounter degenerate bases when using NLNET to solve problems of type MSC-NL and hence cycling is of concern. Consequently, methods are considered that either avoid generating an infeasible search direction or determine a feasible direction if an infeasible direction has been obtained. The multicommodity network solver is, in turn, based on a well known specialisation of the revised simplex algorithm to linear multicommodity network problems that has been extended to be able to handle side constraints. A major thrust of this work is the comparison of different combinations of a number of selected methods and approaches, some of which have been mentioned above, that can be used to solve MSC-NL. This comparison is made by presenting and analysing the results obtained by using NLNET on a test problem set consisting of thirteen "real world" petroleum industry problems.
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Njabeleke, Ignatius Andem. "Mathematical modelling of nonlinear dynamic systems." Thesis, University of Westminster, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319624.

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Chenery, Samara Davide. "Process controllability analysis using linear and nonlinear optimisation." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286291.

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Liao, Weiheng. "Constraints and optimisation in linear and nonlinear control." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442601.

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Johnson, Holly. "Nonlinear dynamics of wake vortices." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX101/document.

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Les tourbillons de sillage d’avion sont sources de problèmes économiques, environnementaux et de sécurité, et par conséquent ont fait l’objet de très nombreuses recherches depuis plusieurs dizaines d’années. Le sillage est composé d’une paire de tourbillons contrarotatifs qui perdurent longtemps après le passage de l’avion. Dans cette thèse la dynamique non linéaire de ces tourbillons desillage est examinée par Simulation Numérique Directe. L’objectif est d’étudier les comportements non linéaires des tourbillons de sillage et d’évaluer le potentiel de destruction anticipée des tourbillons par la perturbation optimale. Dans un premier temps, le potentiel destructeur de la perturbation optimale linéaire est estimé en l’appliquant aux tourbillons avec une amplitude initiale croissante et en observant la réponse non linéaire de l’écoulement. Une amplitude raisonnable suffit pour que la perturbation optimale linéaire réduise de moitié la durée de vie des tourbillons en accélérant une perte de cohérence des structures après l’étape de reconnexion. Par la suite, l’outil d’optimisation non linéaire développé au cours de la thèse est validé par la reproduction de résultats existants concernant un écoulement simple: un toubillon 2D isolé. De nouveaux résultats d’optimisation non linéaire sont obtenus et analysés. En particulier, la perturbation optimale non linéaire 2D d’un tourbillon isolé peut générer une croissance transitoire bien plus élevée que la perturbation optimale linéaire. Dans certains cas la perturbation optimale non linéaire provoque une transition vers un état non axisymétrique quasi-stationnaire,contournant ainsi le processus naturel d’axisymétrisation. De plus, l’effet de la distribution de vorticité dans le coeur du tourbillon sur les perturbations optimales est étudié. Les tourbillons ayant un profil plus raide que les tourbillons Gaussiens subissent une croissance transitoire linéaire plus élevée mais une croissance non linéaire plus faible. Enfin, l’analyse de perturbation optimale non linéaire est étendue aux perturbations 3D. Bien que les perturbations optimales non linéaires 3D produisent moins d’amplification, des transitions vers des états énergétiques et persistants sont observées
Aircraft wakes have been the subject of extensive research for several decades as it poses economic, safety and environmental issues. The wake is composed of powerful counter-rotating vortices that persist long after the aircraft has passed. In this thesis, the nonlinear dynamics of aircraft wake vortices is investigated through Direct Numerical Simulation. The aim is to explore the nonlinear effects on wake vortex behaviour and evaluate the potential for the anticipated destruction of the vortices through optimal perturbation. First the disruptive potential of the linear optimal perturbation of the flow is evaluated by applying it with increasing initial amplitude and observing the nonlinear response of the flow. With sufficient yet reasonable initial amplitude the linear optimal perturbation halves the life-span of the vortex pair by accelerating the loss of coherence of the vortices after the linking phase. Next the nonlinear gradient-based optimisation tool that was developed during the thesis is validated by reproducing existing results concerning a simple vortical flow: an isolated two-dimensional vortex. In doing so new nonlinear optimisation results are obtained and analysed. In particular it is shown that the 2D nonlinear optimal perturbation of an isolated vortex can induce considerably greater transient growth than the linear optimal. In some cases the nonlinear optimal causes a transition to a quasisteady asymmetric state, bypassing the natural axisymmetrisation process. The effect of the vortex vorticity profile on the optimal perturbations is also studied. Vortices with sharper profiles experiencefar greater linear perturbation growth, however the nonlinear growth is significantly inferior. Finally the nonlinear optimal perturbation analysis of the isolated vortex is extended to three dimensions. Although the 3D nonlinear optimals produce less growth than their linear counterparts, they can lead to quasi-permanent high energy states
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Naegele, Philipp Alexander. "An infeasible-path-following algorithm for nonlinear multiobjective optimisation problems." Thesis, University of Birmingham, 2010. http://etheses.bham.ac.uk//id/eprint/813/.

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The subject area of multiobjective optimisation deals with the investigation of optimisation problems that possess more than one objective function. Usually, there does not exist a single solution that optimises all functions simultaneously, quite the contrary, in general the set of so-called efficient points, these are solutions to multiobjective optimisation problems, is large. Since it is important for the decision maker to obtain as much information as possible about this set, our research objective is to determine a well-defined and meaningful approximation of the solution set for nonlinear multiobjective optimisation problems. In order to achieve this target we develop an algorithm that employs the optimality conditions introduced by Karush, Kuhn and Tucker for a scalarised objective function and computes solutions to the corresponding system of equations via a modified Newton method. In particular, we utilise an infeasible interior-point technique which determines solutions in the neighbourhood of a central path and therefore, constitutes a path-following approach. We proof the convergence of our algorithm under certain assumptions and develop a warm-start strategy to compute different solutions for varying weighting parameters. Furthermore we examine our numerical implementation in MATLAB and present the results we obtained for several suites of test problems from the literature.
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Karakuzu, Huseyin. "Design and optimisation of micro-structured waveguides in nonlinear crystals." Thesis, Aston University, 2017. http://publications.aston.ac.uk/33631/.

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Direct femtosecond laser inscription has emerged as one of the most efficient methods for direct three dimensional micro-fabrication of integrated optical circuits in dielectric crystals. Lithium niobate is one of the most widely used dielectric crystal for a wide range of optical functions. Using the direct femtosecond inscription technology, it is possible to produce almost circular tracks of 1-2:5μm diameters with negative refractive index changes up to -0:012 in lithium niobate crystals. Those tracks can be used as a cladding region to confine the propagating light inside a core region of a micro-structured waveguide. This dissertation is focused on the numerical investigation of the propagation properties of depressed-cladding,buried micro-structured waveguides in z-cut lithium niobate crystals which can be fabricatedby direct fs laser inscription method. First of all, we discuss how experimentally achievable parameters of cladding tracks such as their position, total number, refractive index contrasts between the low index cladding structure and the core region can be used to design buried micro-structured waveguides with good confinement properties and to achieve any control over the propagation properties of different polarisation modes specific to a wide range of applications of lithium niobate. Numerical analysis of micro-structured waveguides are implemented by using finite element method. The high nonlinear coefficient and wide transparency region of lithium niobate enable its use for frequency conversion applications towards mid-infrared wavelength ranges. In this thesis, optimisation of the guiding properties, specifically the confinement losses, of microstructured waveguides in lithium niobate is realised for both around telecom and mid-infrared wavelength regions. Optimisation is based on a practical approach which takes into account the variation of experimentally achieved track parameters over cladding region. It is shown that the spectral region where confinement losses are below 1 dB/cm can be extended up to a wavelength of 3:5μm. In recent years, a variety of design geometries for micro-structured waveguides has been a focus of research interest as a means of manipulating and controlling the properties of propagating light. The flexibility of writing tracks at various depths inside lithium niobatecrystals allows direct fabrication of micro-structured waveguides with advanced design geometries. The ability to write tracks at varying sizes by femtosecond laser inscription method enables the fabrication of micro-structured waveguides with highly complex spiral geometries. Here, we explore design issues of equiangular, Fermat and Archimedes spiral geometries in accordance with experimentally available track parameters. Optimisation of each geometry is separately implemented for telecom and mid-infrared wavelength ranges. The primary advantage of designing waveguides with spiral geometries is a much finer control and better manipulation of propagating light stemming from a higher number of parameters available for design. Also, it is found that the spectral region where confinement losses are below 1dB/cm can be further extended up to a wavelength of 3:66 μm.
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Lynch, Paul Kieran. "The generation of knowledge based systems for interactive nonlinear constrained optimisation." Thesis, Queen's University Belfast, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388221.

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Nasieva, Irina O. "Analysis and optimisation of the performance of nonlinear optical communication systems." Thesis, Aston University, 2006. http://publications.aston.ac.uk/8242/.

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We investigate the feasibility of simultaneous suppressing of the amplification noise and nonlinearity, representing the most fundamental limiting factors in modern optical communication. To accomplish this task we developed a general design optimisation technique, based on concepts of noise and nonlinearity management. We demonstrate the immense efficiency of the novel approach by applying it to a design optimisation of transmission lines with periodic dispersion compensation using Raman and hybrid Raman-EDFA amplification. Moreover, we showed, using nonlinearity management considerations, that the optimal performance in high bit-rate dispersion managed fibre systems with hybrid amplification is achieved for a certain amplifier spacing – which is different from commonly known optimal noise performance corresponding to fully distributed amplification. Required for an accurate estimation of the bit error rate, the complete knowledge of signal statistics is crucial for modern transmission links with strong inherent nonlinearity. Therefore, we implemented the advanced multicanonical Monte Carlo (MMC) method, acknowledged for its efficiency in estimating distribution tails. We have accurately computed acknowledged for its efficiency in estimating distribution tails. We have accurately computed marginal probability density functions for soliton parameters, by numerical modelling of Fokker-Plank equation applying the MMC simulation technique. Moreover, applying a powerful MMC method we have studied the BER penalty caused by deviations from the optimal decision level in systems employing in-line 2R optical regeneration. We have demonstrated that in such systems the analytical linear approximation that makes a better fit in the central part of the regenerator nonlinear transfer function produces more accurate approximation of the BER and BER penalty. We present a statistical analysis of RZ-DPSK optical signal at direct detection receiver with Mach-Zehnder interferometer demodulation
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Boulmier, Simon. "Optimisation globale avec LocalSolver." Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM037.

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LocalSolver est un logiciel de programmation mathématique.Originellement pensé pour traiter les grands problèmes d’optimisation combinatoire rencontrés dans l’industrie, son fonctionnement repose sur des heuristiques de recherche locale.Cette approche de résolution pragmatique, couplée à des structures de modélisation expressives, non linéaires et ensemblistes, lui ont permis de s'imposer dans le catalogue des solveurs commerciaux.L'objet de cette thèse est le développement d'une approche duale, complémentaire à la recherche locale, qui fournira des bornes aux problèmes traités.L'intérêt principal est de qualifier la qualité des solutions retournées, voire de prouver leur optimalité, permettant ainsi d'interrompre plus rapidement la résolution.Ce n'est cependant pas le seul, puisque les techniques nécessaires au calcul de bornes permettent par exemple de prouver l'inconsistance d'un problème.Cette fonctionnalité est utile en phase de développement, où des erreurs de modélisation ou de données sont fréquentes.Trois difficultés principales se présentent alors.D'abord, les problèmes traités sont génériques, et peuvent être combinatoires, non linéaires ou encore non différentiables.Ensuite, l'intégration à un logiciel industriel impose un haut niveau de fiabilité et de qualité logicielle, ainsi que la capacité à passer à l'échelle en temps et en mémoire.Enfin, tous les besoins de reformulation doivent être pris en compte en interne, afin de permettre aux utilisateurs de LocalSolver de modéliser leurs problèmes le plus naturellement possible.Ainsi, le module dual implémenté au sein de LocalSolver commence par transformer le problème d'optimisation fourni en un programme non linéaire en variables mixtes (MINLP).Ce programme est représenté sous une forme standard facilitant l'implémentation de divers outils utiles au calcul de bornes : génération de relaxations convexes, techniques de réduction de bornes ou encore actions de emph{presolve}.Ces outils sont ensuite intégrés dans une recherche arborescente de type emph{branch-and-reduce}, qui interagit avec les autres modules de LocalSolver grâce à des techniques de programmation concurrente.Si l'approche décrite ci-dessus est classique, plusieurs spécificités et choix d'implémentation se différentient de l’état de l’art.En effet, les opérateurs mathématiques supportés et la technique de reformulation utilisée permettent de calculer des bornes sur plus de problèmes que les solveurs d'optimisation globale de référence.Ensuite, ces solveurs exploitent principalement des relaxations linéaires, alors que l'un de nos objectifs est de montrer que des relaxations non linéaires peuvent être compétitives.Dans cette optique, nous avons implémenté un solveur non linéaire sur-mesure, dédié au calcul de bornes inférieures d'un problème convexe, et adapté aux relaxations non linéaires utilisées.Enfin, un résultat de dualité sous contraintes de bornes est obtenu.Celui-ci permet d'améliorer la performance du solveur non linéaire et d'y inclure une méthode robuste de détection de l'inconsistance, mais aussi de garantir la fiabilité des bornes inférieures calculées par LocalSolver
LocalSolver is a mathematical programming solver.Originally designed to solve large scale combinatorial optimization problems such as those found in the industry, it mainly relies on local search heuristics.This pragmatic solution approach, coupled with expressive nonlinear and set-based modeling techniques, has allowed LocalSolver to establish itself as a successful commercial solver.The purpose of this thesis is to implement a complementary dual approach for the computation of lower bounds within LocalSolver.The main stake is to qualify the solutions found by the solver and to potentially prove their optimality, thus allowing an early stop of the search.Furthermore, lower bounds have many other applications, such as the detection of inconsistent problems.This is useful in the development phase where modeling errors are frequent.We face three major challenges.First, the problems we address are generic and can be combinatorial, nonlinear or even nonsmooth.Then, the integration to an industrial software requires to produce reliable and high-quality code that can scale in time and memory.Finally, any reformulation need must be managed in-house, to allow LocalSolver's users to model their problems in the easiest way possible.The dual module provided to LocalSolver starts by reformulating the given optimization problem into a mixed-integer nonlinear program (MINLP).This program is stored under a standard form that facilitates the implementation of various techniques aiming at computing lower bounds.Examples of such techniques are the generation of convex relaxations, bound tightening techniques and presolve actions.These building blocks are then integrated into a partitioning scheme called the branch-and-reduce algorithm, and interact with the primal modules thanks to concurrent computing techniques.While this approach remains traditional, several choices and implementation features vary from the state of the art.The operators we support and the reformulation technique we use allow us to compute lower bounds on more problems than most global optimization solvers.These solvers also mainly use linear relaxations, whereas our goal is to show that nonlinear relaxations can be competitive.For this purpose, we implement a nonlinear solver dedicated to the computation of lower bounds to our convex relaxations.At last, we establish a duality result under bound constraints that allow us to improve the performance of our custom nonlinear solver.It is also exploited to certify the validity of the lower bounds computed by LocalSolver and to obtain robust inconsistency certificates
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Books on the topic "Nonlinear optimisation"

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Nonlinear Programming. Belmont, MA, USA: Athena Scientific, 1995.

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Riddalls, C. Frequency-domain theory and optimisation for nonlinear systems. Sheffield: Univeristy of Sheffield, Dept. of Automatic Control and Systems Engineering, 1997.

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Anciant, M. Optimisation methods for solving separable nonlinear least squares problems. Southampton, England: University of Southampton, Institute of Sound and Vibration Research, 1993.

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Dodu, J. C. Méthodes de quasi-Newton en optimisation non linéaire. Clamart: Electricité de France, Direction des études et recherches, Service études de réseaux, Département Méthodes d'optimisation et de simulation, 1990.

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1961-, Yang Jian-Bo, and Whidborne J. F. 1960-, eds. Multiobjective optimisation and control. Baldock, Hertfordshire, England: Research Studies Press, 2003.

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Zeidler, Eberhard. Nonlinear functional analysis and its applications. New York, N.Y., U.S.A: Springer-Verlag, 1986.

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Zeidler, Eberhard. Nonlinear functional analysis and its applications. New York: Springer, 1988.

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Zeidler, Eberhard. Nonlinear functional analysis and its applications. New York: Springer-Verlag, 1985.

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Floudas, Christodoulos A. A collection of test problems for constrained global optimization algorithms. Berlin: Springer-Verlag, 1990.

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P, Kamat Manohar, ed. Structural optimization: Status and promise. Washington, DC: American Institute of Aeronautics and Astronautics, 1993.

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Book chapters on the topic "Nonlinear optimisation"

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McKeown, J. J. "An Expert Systems Approach to Nonlinear Optimisation." In Flow Control of Congested Networks, 141–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86726-2_9.

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Denimal, E., R. Chevalier, L. Renson, and L. Salles. "Shape Optimisation for Friction Dampers with Stress Constraint." In Nonlinear Structures & Systems, Volume 1, 65–73. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04086-3_10.

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Amman, Hans M., and David A. Kendrick. "Matrix Methods for Solving Nonlinear Dynamic Optimisation Models." In Innovations in Multivariate Statistical Analysis, 257–76. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4603-0_19.

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Kulikov, Gennady G., and Haydn A. Thompson. "Nonlinear Model Structure Selection Using Evolutionary Optimisation Methods." In Advances in Industrial Control, 159–76. London: Springer London, 2004. http://dx.doi.org/10.1007/978-1-4471-3796-2_9.

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Worden, K., I. Antoniadou, O. D. Tiboaca, G. Manson, and R. J. Barthorpe. "Linear and Nonlinear System Identification Using Evolutionary Optimisation." In Simulation-Driven Modeling and Optimization, 325–45. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27517-8_13.

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Tanyi, B. A., J. Darlington, C. C. C. Pantelides, and B. Rustem. "Robust Optimisation of Nonlinear Systems under Parametric Uncertainty." In Operations Research Proceedings, 43–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60744-8_9.

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Biss, D., and K. G. Woodgate. "Gas Turbine Control Using Mixed Sensitivity H∞-Optimisation." In Robust Control of Linear Systems and Nonlinear Control, 255–65. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-4484-4_23.

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Schmidt, Martin, and Zbigniew Michalewicz. "Test-Case Generator TCG-2 for Nonlinear Parameter Optimisation." In Parallel Problem Solving from Nature PPSN VI, 539–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-45356-3_53.

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Denimal, Enora, Ludovic Renson, and Loic Salles. "Topological Optimisation of Friction Dampers for Nonlinear Resonances Mitigation." In NODYCON Conference Proceedings Series, 3–13. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81166-2_1.

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Dervilis, N., K. Worden, D. J. Wagg, and S. A. Neild. "Simplifying Transformations for Nonlinear Systems: Part I, An Optimisation-Based Variant of Normal Form Analysis." In Nonlinear Dynamics, Volume 1, 315–20. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-15221-9_28.

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Conference papers on the topic "Nonlinear optimisation"

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Streun, Andreas. "SLS dynamic aperture optimisation." In Nonlinear dynamics in particle accelerators: Theory and experiments. AIP, 1995. http://dx.doi.org/10.1063/1.48985.

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Gukov, Ilya, Sonia Boscolo, Christophe Finot, and Sergei K. Turitsyn. "Performance Optimisation of Dual-Pump NALM Fibre Laser Using Machine Learning Inference." In Nonlinear Photonics. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/np.2018.npm2c.6.

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Morelle, Patrick, and Alain Remouchamps. "Comparison of Various Optimisation Algorithms for Crash and Nonlinear Optimisation Problems." In 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-5414.

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"Control and optimisation of nonlinear evolutionary systems." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_others09.

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Petchsasithon, Arthit, and Peter Gosling. "Coupled Morphology Optimisation of Geometrically Nonlinear Shell." In 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-2211.

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Hutchings, D. C., and T. C. Kleckner. "Quasi-phase-matching in semiconductor waveguides using intermixing: optimisation considerations." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: OSA, 2001. http://dx.doi.org/10.1364/nlgw.2001.wa5.

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Kamalian, Morteza, Jaroslaw E. Prilepsky, Stanislav A. Derevyanko, Son T. Le, and Sergei K. Turitsyn. "Energy based transmission optimisation in nonlinear Fourier domain." In 2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC). IEEE, 2017. http://dx.doi.org/10.1109/cleoe-eqec.2017.8086930.

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Tiwari, Manish, and Vijay Janyani. "Supercontinuum Generation and Optimisation in Nonlinear Photonic Crystal Fibres." In 2010 Second International Conference on Computer and Network Technology. IEEE, 2010. http://dx.doi.org/10.1109/iccnt.2010.124.

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Diala, Uchenna, Rajintha Gunawardena, Yunpeng Zhu, and Zi-Qiang Lang. "Nonlinear Design and Optimisation of a Vibration Energy Harvester." In 2018 UKACC 12th International Conference on Control (CONTROL). IEEE, 2018. http://dx.doi.org/10.1109/control.2018.8516821.

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Eele, Alison, and Arthur Richards. "Multi Vehicle Avoidance Using Nonlinear Branch and Bound Optimisation." In AIAA Guidance, Navigation, and Control Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-5780.

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Reports on the topic "Nonlinear optimisation"

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Nobile, F., Q. Ayoul-Guilmard, S. Ganesh, M. Nuñez, A. Kodakkal, C. Soriano, and R. Rossi. D6.5 Report on stochastic optimisation for wind engineering. Scipedia, 2022. http://dx.doi.org/10.23967/exaqute.2022.3.04.

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Abstract:
This report presents the latest methods of optimisation under uncertainties investigated in the ExaQUte project, and their applications to problems related to civil and wind engineering. The measure of risk throughout the report is the conditional value at risk. First, the reference method is presented: the derivation of sensitivities of the risk measure; their accurate computation; and lastly, a practical optimisation algorithm with adaptive statistical estimation. Second, this method is directly applied to a nonlinear relaxation oscillator (FitzHugh–Nagumo model) with numerical experiments to demonstrate its performance. Third, the optimisation method is adapted to the shape optimisation of an airfoil and illustrated by a large-scale experiment on a computing cluster. Finally, the benchmark of the shape optimisation of a tall building under a turbulent flow is presented, followed by an adaptation of the optimisation method. All numerical experiments showcase the open-source software stack of the ExaQUte project for large-scale computing in a distributed environment.
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