Nonconvex Separable Programming Problem for Optimal Raw Material Mix in Flexible Polyurethane Foam Production

Nonconvex Separable Programming (NSP)  for selecting optimal raw material mix for flexible polyurethane foam production (FPFP) was developd. With unit cost function () as objective function;,Density(P1); compression set (P2); elongation(P3); hardness-index(P4) and tensile strength (P5) and other boundary conditions as constraints, an NSP foam raw material mix problem was defined and solved. Twelve existing formulation were used for validation .The cost and physical properties were determined and compared to the existing products using t-test. The optimal raw material mix 1.00, 0.4366, 0.0398, 0.0066, 0.0115, 0.0026, 0.0046 kg of polyol, toluene-di-isocynate, water, amine, silicone-oil, stannous-octoate and methylene-chloride respectively, were significantly different from  the existing formulations. The validated values of P1, P2, P3, P4, P5 from optimally formulated foams were 23.83kgm-3, 8.6%, 159.35%, 143.19N, and 117.33kNm-2, respectively and conformed to standard. The associated costs per metric tonne of the optimal mixes were lower than that of existing mixes.   Keywords: Polyurethane foam, Optimal-mix, Separable  programming , nonconvex, elongation

Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies

Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has grown: several new applications have arisen where the problem at hand constitutes a subproblem, and several new algorithms have been developed for its efficient solution. This paper therefore serves three purposes. First, it provides an up-to-date extension of the survey of the literature of the field, complementing the survey in Patriksson (2008) with more then 20 books and articles. Second, it contributes improvements of some of these algorithms, in particular with an improvement of the pegging (that is, variable fixing) process in the relaxation algorithm, and an improved means to evaluate subsolutions. Third, it numerically evaluates several relaxation (primal) and breakpoint (dual) algorithms, incorporating a variety of pegging strategies, as well as a quasi-Newton method. Our conclusion is that our modification of the relaxation algorithm performs the best. At least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

Methods for Estimating Capacities and Rates of Gaussian Quantum Channels

Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is dealt with multiple uses (multi-mode) channel where the capacity dependence from the (multi-mode) environment state is analyzed when both total environment energy and environment purity are fixed. This allows a fair comparison among different environments, thus understanding the role of memory (inter-mode correlations) and phenomenon like superadditivity of the capacity. The developed methods are also used for deriving transmission rates with heterodyne and homodyne measurements at the channel output. Classical capacity and transmission rates are presented within a unique framework where the rates can be treated as logarithmic approximations of the capacity.Comment: 39 pages, 30 figures. New results and graphs were added. Errors and misprints were corrected. To appear in IEEE Trans. Inf. T

Modelling and Optimisation of GSM and UMTS Radio Access Networks

The size and complexity of mobile communication networks have increased in the last years making network management a very complicated task. GSM/EDGE Radio Access Network (GERAN) systems are in a mature state now. Thus, non-optimal performance does not come from typical network start-up problems, but, more likely, from the mismatching between traffic, network or propagation models used for network planning, and their real counterparts. Such differences cause network congestion problems both in signalling and data channels. With the aim of maximising the financial benefits on their mature networks, operators do not solve anymore congestion problems by adding new radio resources, as they usually did. Alternatively, two main strategies can be adopted, a) a better assignment of radio resources through a re-planning approach, and/or b) the automatic configuration (optimisation, in a wide sense) of network parameters. Both techniques aim to adapt the network to the actual traffic and propagation conditions. Moreover, a new heterogenous scenario, where several services and Radio Access Technologies (RATs) coexist in the same area, is now common, causing new unbalanced traffic scenarios and congestion problems. In this thesis, several optimisation and modelling methods are proposed to solve congestion problems in data and signalling channels for single- and multi-RAT scenarios

Indefinite Knapsack Separable Quadratic Programming: Methods and Applications

Quadratic programming (QP) has received significant consideration due to an extensive list of applications. Although polynomial time algorithms for the convex case have been developed, the solution of large scale QPs is challenging due to the computer memory and speed limitations. Moreover, if the QP is nonconvex or includes integer variables, the problem is NP-hard. Therefore, no known algorithm can solve such QPs efficiently. Alternatively, row-aggregation and diagonalization techniques have been developed to solve QP by a sub-problem, knapsack separable QP (KSQP), which has a separable objective function and is constrained by a single knapsack linear constraint and box constraints. KSQP can therefore be considered as a fundamental building-block to solve the general QP and is an important class of problems for research. For the convex KSQP, linear time algorithms are available. However, if some quadratic terms or even only one term is negative in KSQP, the problem is known to be NP-hard, i.e. it is notoriously difficult to solve. The main objective of this dissertation is to develop efficient algorithms to solve general KSQP. Thus, the contributions of this dissertation are five-fold. First, this dissertation includes comprehensive literature review for convex and nonconvex KSQP by considering their computational efficiencies and theoretical complexities. Second, a new algorithm with quadratic time worst-case complexity is developed to globally solve the nonconvex KSQP, having open box constraints. Third, the latter global solver is utilized to develop a new bounding algorithm for general KSQP. Fourth, another new algorithm is developed to find a bound for general KSQP in linear time complexity. Fifth, a list of comprehensive applications for convex KSQP is introduced, and direct applications of indefinite KSQP are described and tested with our newly developed methods. Experiments are conducted to compare the performance of the developed algorithms with that of local, global, and commercial solvers such as IBM CPLEX using randomly generated problems in the context of certain applications. The experimental results show that our proposed methods are superior in speed as well as in the quality of solutions

Self-tuning algorithms for the assignment of packet control units and handover parameters in GERAN

Esta tesis aborda el problema de la optimización automática de parámetros en redes de acceso radio basadas en GSM-EDGE Radio Access Network (GERAN). Dada la extensión del conjunto de parámetros que se puede optimizar, este trabajo se centra en dos de los procesos encargados de la gestión de la movilidad: el proceso de (re)selección de celda para servicios por conmutación de paquetes y el proceso de traspaso para servicios de voz por conmutación de circuitos

Ordonnancement et gestion des ressources pour un système de télécommunications haut débit : Optimisation de la bande passante satellite

Les télécommunications par satellite ont connu ces dernières années un regain d'intérêt important, du fait de leur capacité à permettre la réduction de la fracture numérique. En effet, un satellite en orbite géostationnaire peut s'appuyer sur une très grande couverture et une capacité importante pour atteindre des zones où le déploiement des réseaux terrestres n'est pas envisageable, comme les transports (bateau, avion), ou bien les zones blanches, où il serait difficilement rentable. Traditionnellement concentrés sur la diffusion de télévision numérique, les dernières générations de standards reflètent cet engouement en faisant une place de choix à la transmission de données bidirectionnelle, notamment en permettant une prise en charge simple des protocoles de l'Internet. Le problème de l'ordonnancement dans ces systèmes devient alors particulièrement important, puisqu'il doit prendre en compte deux processus évoluant de manière totalement décorrélée. D'un côté, l'évolution de la demande des utilisateurs, dépendante des applications (vidéo, voix, données). De l'autre, l'évolution de la capacité du système, celle-ci étant tributaire des conditions de transmission : les fréquences utilisées dans ces systèmes sont particulièrement sensibles à l'atténuation due à l'eau dans l'atmosphère. Cette thèse s'intéresse au problème de l'ordonnancement et de l'allocation de ressources, dans le but de fournir un service comparable aux réseaux terrestres en termes de services, en présentant les meilleures performances possibles. Si un certain nombre de propositions ont été faites sur le sujet, aucune ne prend en compte l'ensemble des contraintes d'un tel système. Outre le caractère variable de la capacité, la variabilité de la demande, conjuguée avec les contraintes de qualité de service constitue une difficulté supplémentaire. Enfin, il nous faut considérer la faisabilité de notre solution dans un contexte temps réel, nécessaire dans l'optique d'une implantation dans un système réel. Nous avons ainsi développé une architecture d'ordonnanceur pour la voie Aller, reposant sur des fonctions d'utilité, permettant ainsi une formulation simple du compromis entre demande et capacité. Nous montrons comment cet algorithme pourrait être utilisable dans un système complet, à travers une implantation détaillée, de faible complexité, ainsi que des simulations de cas réels. Nous portons ensuite notre attention sur la voie Retour, où nous proposons une méthode d'allocation de ressources prenant en compte de manière conjointe la qualité de service et la qualité du support pour délivrer une allocation à la fois conforme et performante. Les simulations montrent que notre algorithme obtient une efficacité et une meilleure gestion du trafic que des solutions de référence présentées dans la littérature