Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.

Novel double-sided linear generator for the wave energy conversion

The direct drive point absorber is a robust and efficient system for wave energy harvesting, where the linear generator represents the most complex part of the system. Therefore, its design and optimization are crucial tasks. The tubular shape of a linear generator’s magnetic circuit offers better permanent magnet flux encapsulation and reduction in radial forces on the translator due to its symmetry. A double stator topology can improve the power density of the linear tubular machine. Common designs employ a set of aligned stators on each side of a translator with radially magnetized permanent magnets. Such designs require doubling the amount of permanent magnet material and lead to an increase in the cogging force. The design presented in this thesis utilizes a translator with buried axially magnetized magnets and axially shifted positioning of the two stators such that no additional magnetic material, compared to single side machine, is required. In addition to the conservation of magnetic material, a significant improvement in the cogging force occurs in the two phase topology, while the double sided three phase system produces more power at the cost of a small increase in the cogging force. The analytical and the FEM models of the generator are described and their results compared to the experimental results. In general, the experimental results compare favourably with theoretical predictions. However, the experimentally observed permanent magnet flux leakage in the double sided machine is larger than predicted theoretically, which can be justified by the limitations in the prototype fabrication and resulting deviations from the theoretical analysis.

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Optimization of Cooling Protocols for Hearts Destined for Transplantation

Design and analysis of conceptually different cooling systems for the human heart preservation are numerically investigated. A heart cooling container with required connections was designed for a normal size human heart. A three-dimensional, high resolution human heart geometric model obtained from CT-angio data was used for simulations. Nine different cooling designs are introduced in this research. The first cooling design (Case 1) used a cooling gelatin only outside of the heart. In the second cooling design (Case 2), the internal parts of the heart were cooled via pumping a cooling liquid inside both the heart’s pulmonary and systemic circulation systems. An unsteady conjugate heat transfer analysis is performed to simulate the temperature field variations within the heart during the cooling process. Case 3 simulated the currently used cooling method in which the coolant is stagnant. Case 4 was a combination of Case 1 and Case 2. A linear thermoelasticity analysis was performed to assess the stresses applied on the heart during the cooling process. In Cases 5 through 9, the coolant solution was used for both internal and external cooling. For external circulation in Case 5 and Case 6, two inlets and two outlets were designed on the walls of the cooling container. Case 5 used laminar flows for coolant circulations inside and outside of the heart. Effects of turbulent flow on cooling of the heart were studied in Case 6. In Case 7, an additional inlet was designed on the cooling container wall to create a jet impinging the hot region of the heart’s wall. Unsteady periodic inlet velocities were applied in Case 8 and Case 9. The average temperature of the heart in Case 5 was +5.0oC after 1500 s of cooling. Multi-objective constrained optimization was performed for Case 5. Inlet velocities for two internal and one external coolant circulations were the three design variables for optimization. Minimizing the average temperature of the heart, wall shear stress and total volumetric flow rates were the three objectives. The only constraint was to keep von Mises stress below the ultimate tensile stress of the heart’s tissue.

Distributed parallelization of greedy Mobile Network Optimization algorithms

The Mobile Network Optimization (MNO) technologies have advanced at a tremendous pace in recent years. And the Dynamic Network Optimization (DNO) concept emerged years ago, aimed to continuously optimize the network in response to variations in network traffic and conditions. Yet, DNO development is still at its infancy, mainly hindered by a significant bottleneck of the lengthy optimization runtime. This paper identifies parallelism in greedy MNO algorithms and presents an advanced distributed parallel solution. The solution is designed, implemented and applied to real-life projects whose results yield a significant, highly scalable and nearly linear speedup up to 6.9 and 14.5 on distributed 8-core and 16-core systems respectively. Meanwhile, optimization outputs exhibit self-consistency and high precision compared to their sequential counterpart. This is a milestone in realizing the DNO. Further, the techniques may be applied to similar greedy optimization algorithm based applications.

Optimization and Prediction of Mechanical and Thermal Properties of Graphene/LLDPE Nanocomposites by Using Artificial Neural Networks

The focus of this work is to develop the knowledge of prediction of the physical and chemical properties of processed linear low density polyethylene (LLDPE)/graphene nanoplatelets composites. Composites made from LLDPE reinforced with 1, 2, 4, 6, 8, and 10 wt% grade C graphene nanoplatelets (C-GNP) were processed in a twin screw extruder with three different screw speeds and feeder speeds (50, 100, and 150 rpm). These applied conditions are used to optimize the following properties: thermal conductivity, crystallization temperature, degradation temperature, and tensile strength while prediction of these properties was done through artificial neural network (ANN). The three first properties increased with increase in both screw speed and C-GNP content. The tensile strength reached a maximum value at 4 wt% C-GNP and a speed of 150 rpm as this represented the optimum condition for the stress transfer through the amorphous chains of the matrix to the C-GNP. ANN can be confidently used as a tool to predict the above material properties before investing in development programs and actual manufacturing, thus significantly saving money, time, and effort.

Topology Optimization of continuum structures with epsilon-relaxed stress constraints

Topology optimization of linear elastic continuum structures is a challenging problem when considering local stress constraints. The reasons are the singular behavior of the constraint with the density design variables, combined with the large number of constraints even for small finite element meshes. This work presents an alternative formulation for the s-relaxation technique, which provides an workaround for the singularity of the stress constraint. It also presents a new global stress constraint formulation. Derivation of the sensitivities for the constraint by the adjoint method is shown. Results for single and multiple load cases show the potential of the new formulation.

Approximation limits of linear programs (beyond hierarchies)

We develop a framework for proving approximation limits of polynomial size linear programs (LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any LP as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^1/2-ε)-approximations for CLIQUE require LPs of size 2^nΩ(ε). This lower bound applies to LPs using a certain encoding of CLIQUE as a linear optimization problem. Moreover, we establish a similar result for approximations of semidefinite programs by LPs. Our main technical ingredient is a quantitative improvement of Razborov's [38] rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of shifts of the unique disjointness matrix.

Calculated ionization potentials of the linear alkanes

The equivalent orbital (EO) method is investigated and used for predicting outer and inner ionization potentials of the linear alkanes. The calculated ionization potentials are in good agreement with those observed in photoelectron spectra provided that a set of 12 parameters is used in the theory. An optimization technique is used to find the best values for thle parameters and a single transferable parameter set can be found which is applicable to all the n-alkanes. A good fit to the experimental results can only be obtained if the uppermost molecular orbital of the n-alkanes is an antisymmetrical orbital built up from CH equivalent orbitals.

Balancing Energy and Performance in Dense Linear System Solvers for Hybrid ARM+GPU platforms

The high performance computing community has traditionally focused uniquely on the reduction of execution time, though in the last years, the optimization of energy consumption has become a main issue. A reduction of energy usage without a degradation of performance requires the adoption of energy-efficient hardware platforms accompanied by the development of energy-aware algorithms and computational kernels. The solution of linear systems is a key operation for many scientific and engineering problems. Its relevance has motivated an important amount of work, and consequently, it is possible to find high performance solvers for a wide variety of hardware platforms. In this work, we aim to develop a high performance and energy-efficient linear system solver. In particular, we develop two solvers for a low-power CPU-GPU platform, the NVIDIA Jetson TK1. These solvers implement the Gauss-Huard algorithm yielding an efficient usage of the target hardware as well as an efficient memory access. The experimental evaluation shows that the novel proposal reports important savings in both time and energy-consumption when compared with the state-of-the-art solvers of the platform.

Modelo para distribuição de recursos nos municípios brasileiros baseado na lei de diretrizes orçamentárias, análise multicritério e programação linear

The municipal management in any country of the globe requires planning and allocation of resources evenly. In Brazil, the Law of Budgetary Guidelines (LDO) guides municipal managers toward that balance. This research develops a model that seeks to find the balance of the allocation of public resources in Brazilian municipalities, considering the LDO as a parameter. For this using statistical techniques and multicriteria analysis as a first step in order to define allocation strategies, based on the technical aspects arising from the municipal manager. In a second step, presented in linear programming based optimization where the objective function is derived from the preference of the results of the manager and his staff. The statistical representation is presented to support multicriteria development in the definition of replacement rates through time series. The multicriteria analysis was structured by defining the criteria, alternatives and the application of UTASTAR methods to calculate replacement rates. After these initial settings, an application of linear programming was developed to find the optimal allocation of enforcement resources of the municipal budget. Data from the budget of a municipality in southwestern Paraná were studied in the application of the model and analysis of results.

Optimization of growth and bacteriocin activity of the food bioprotective Carnobacterium divergens V41 in an animal origin protein free medium

Optimization of Carnobacterium divergens V41 growth and bacteriocin activity in a culture medium deprived of animal protein, needs for food bioprotection, was performed by using a statistical approach. In a screening experiment, twelve factors (pH, temperature, carbohydrates, NaCl, yeast extract, soy peptone, sodium acetate, ammonium citrate, magnesium sulphate, manganese sulphate, ascorbic acid and thiamine) were tested for their influence on the maximal growth and bacteriocin activity using a two-level incomplete factorial design with 192 experiments performed in microtiter plate wells. Based on results, a basic medium was developed and three variables (pH, temperature and carbohydrates concentration) were selected for a scale-up study in bioreactor. A 23 complete factorial design was performed, allowing the estimation of linear effects of factors and all the first order interactions. The best conditions for the cell production were obtained with a temperature of 15°C and a carbohydrates concentration of 20 g/l whatever the pH (in the range 6.5-8), and the best conditions for bacteriocin activity were obtained at 15°C and pH 6.5 whatever the carbohydrates concentration (in the range 2-20 g/l). The predicted final count of C. divergens V41 and the bacteriocin activity under the optimized conditions (15°C, pH 6.5, 20 g/l carbohydrates) were 2.4 x 1010 CFU/ml and 819200 AU/ml respectively. C. divergens V41 cells cultivated in the optimized conditions were able to grow in cold-smoked salmon and totally inhibited the growth of Listeria monocytogenes (< 50 CFU g-1) during five weeks of vacuum storage at 4° and 8°C.

Efficient Hill Climber for Constrained Pseudo-Boolean Optimization Problems

Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For $k$-bounded pseudo-Boolean functions where each variable appears in at most a constant number of subfunctions, it has been theoretically proven that the neighborhood of a solution can be explored in constant time. These hill climbers, combined with a high-level exploration strategy, have shown to improve state of the art methods in experimental studies and open the door to the so-called Gray Box Optimization, where part, but not all, of the details of the objective functions are used to better explore the search space. One important limitation of all the previous proposals is that they can only be applied to unconstrained pseudo-Boolean optimization problems. In this work, we address the constrained case for multi-objective $k$-bounded pseudo-Boolean optimization problems. We find that adding constraints to the pseudo-Boolean problem has a linear computational cost in the hill climber.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.