Optimization on manifolds: Methods and applications

This paper provides an introduction to the topic of optimization on manifolds. The approach taken uses the language of differential geometry, however,we choose to emphasise the intuition of the concepts and the structures that are important in generating practical numerical algorithms rather than the technical details of the formulation. There are a number of algorithms that can be applied to solve such problems and we discuss the steepest descent and Newton's method in some detail as well as referencing the more important of the other approaches.There are a wide range of potential applications that we are aware of, and we briefly discuss these applications, as well as explaining one or two in more detail. © 2010 Springer -Verlag Berlin Heidelberg.

Colony development and physiological characterization of the edible blue-green alga, Nostoc sphaeroides (Nostocaceae, Cyanophyta)

The edible blue-green alga, Nostoc sphaeroides Kutzing, is able to form microcolonies and spherical macrocolonies. It has been used as a potent herbal medicine and dietary supplement for centuries because of its nutraceutical and pharmacological benefits. However, limited information is available on the development of the spherical macrocolonies and the environmental factors that affect their structure. This report described the morphogenesis of N. sphaeroides from single trichomes to macrocolonies. During the process, most structural features of macrocolonies of various sizes were dense maculas, rings, the compact core and the formation of liquid core; and the. laments within the macrocolonies showed different lengths and arrays depending on the sizes of macrocolonies. Meanwhile temperature and light intensity also strongly affected the internal structure of macrocolonies. As microcolonies further increased in size to form 30 mm macrocolonies, the colonies differentiated into distinct outer, middle and inner layers. The. laments of the outer layer showed higher maximum photosynthetic rates, higher light saturation point, and higher photosynthetic effciency than those of the inner layer; whereas the. laments of the inner layer had a higher content of chlorophyll a and phycobiliproteins than those of the outer layer. The results obtained in this study were important for the mass cultivation of N. sphaeroides as a nutraceutical product. (c) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Multispacecraft refueling optimization considering the J2 perturbation and window constraints

The optimization of a near-circular low-Earth-orbit multispacecraft refueling problem is studied. The refueling sequence, service time, and orbital transfer time are used as design variables, whereas the mean mission completion time and mean propellant consumed by orbital maneuvers are used as design objectives. The J2 term of the Earth's nonspherical gravity perturbation and the constraints of rendezvous time windows are taken into account. A hybridencoding genetic algorithm, which uses normal fitness assignment to find the minimum mean propellant-cost solution and fitness assignment based on the concept of Pareto-optimality to find multi-objective optimal solutions, is presented. The proposed approach is demonstrated for a typical multispacecraft refueling problem. The results show that the proposed approach is effective, and that the J2 perturbation and the time-window constraints have considerable influences on the optimization results. For the problems in which the J2 perturbation is not accounted for, the optimal refueling order can be simply determined as a sequential order or as the order only based on orbitalplane differences. In contrast, for the problems that do consider the J2 perturbation, the optimal solutions obtained have a variety of refueling orders and use the drift of nodes effectively to reduce the propellant cost for eliminating orbital-plane differences. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Optimization of operational conditions in a submerged membrane bioreactor

In this study, optimization of operational conditions of a submerged membrane bioreactor treating municipal waste-water was studied. Mixed liquid suspended solid (MLSS), membrane flux (J(v)), aeration (Q), ratio of pumping, time to break time (t(p)/t(b)), and ratio of up flow area to down flow area (A Ad) were chosen as the easily manipulable parameters to study their effects on removal efficiency and membrane fouling. Totally, 16 different runs were designed to compare and select the best combination of the 5 parameters. The results showed that the optimal operational conditions were MLSS = 7g(.)L(-1), J(v) = 10L(.)m(-2.)h(-1), Q = 6 m(3.)h(-1), t(p)/t(b)= 4 min/1 min, and A(r)/A(d) = 1.7 m(2)/m(2). Under such conditions, the SMBR could achieve a double win of high removal efficiency and low membrane fouling.

Optimization algorithms and ODE's in MDO

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework's tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context. Copyright © 2013 by ASME.

GPU-accelerated optimization of fuel treatments for mitigating wildfire hazard

Fuel treatment is considered a suitable way to mitigate the hazard related to potential wildfires on a landscape. However, designing an optimal spatial layout of treatment units represents a difficult optimization problem. In fact, budget constraints, the probabilistic nature of fire spread and interactions among the different area units composing the whole treatment, give rise to challenging search spaces on typical landscapes. In this paper we formulate such optimization problem with the objective of minimizing the extension of land characterized by high fire hazard. Then, we propose a computational approach that leads to a spatially-optimized treatment layout exploiting Tabu Search and General-Purpose computing on Graphics Processing Units (GPGPU). Using an application example, we also show that the proposed methodology can provide high-quality design solutions in low computing time. © 2013 The Authors. Published by Elsevier B.V.

Efficient strategies for process design and optimization in ring rolling

Ring rolling is an incremental bulk forming process for the near-net-shape production of seamless rings. This paper shows how nowadays the process design and optimization can be efficiently supported by simulation methods. For reliable predictions of the material flow and the microstructure evolution it's necessary to include a real ring rolling mill's control algorithm into the model. Furthermore an approach for the online measurement of the profile evolution during the process is presented by means of axial profiling in ring rolling. Hence the definition of new ring rolling strategies is possible even for advanced geometries.

Gaussian processes for POMDP-based dialogue manager optimization

A partially observable Markov decision process (POMDP) has been proposed as a dialog model that enables automatic optimization of the dialog policy and provides robustness to speech understanding errors. Various approximations allow such a model to be used for building real-world dialog systems. However, they require a large number of dialogs to train the dialog policy and hence they typically rely on the availability of a user simulator. They also require significant designer effort to hand-craft the policy representation. We investigate the use of Gaussian processes (GPs) in policy modeling to overcome these problems. We show that GP policy optimization can be implemented for a real world POMDP dialog manager, and in particular: 1) we examine different formulations of a GP policy to minimize variability in the learning process; 2) we find that the use of GP increases the learning rate by an order of magnitude thereby allowing learning by direct interaction with human users; and 3) we demonstrate that designer effort can be substantially reduced by basing the policy directly on the full belief space thereby avoiding ad hoc feature space modeling. Overall, the GP approach represents an important step forward towards fully automatic dialog policy optimization in real world systems. © 2013 IEEE.

Optimization of an effective extraction procedure for the analysis of microcystins in soils and lake sediments

Microcystin analysis in sediments and soils is considered very difficult due to low recovery for extraction. This is the primary limiting factor for understanding the fate of toxins in the interface between water and sediment in both the aquatic ecosystem as well as in soils. In the present study, a wide range of extraction solvents were evaluated over a wide range of pH, extraction approaches and equilibration time to optimize an effective extraction procedure for the analysis of microcystins in soils and lake sediments. The number of extractions required and acids in extraction solutions were also studied. In this procedure, EDTA-sodium pyrophosphate solution was selected as an extraction solvent based on the adsorption mechanism study. The optimized procedure proved to be highly efficient and achieved over 90% recovery. Finally, the developed procedure was applied to field soil and sediment sample collected from Chinese lakes during bloom seasons and microcystins were determined in six of ten samples. (c) 2005 Elsevier Ltd. All rights reserved.

Optimization by orthogonal array design and humoral immunity of the bivalent vaccine against Aeromonas hydrophila and Vibrio fluvialis infection in crucian carp (Carassius auratus L.)

Aeromonas hydrophila and Vibrio fluvialis are the causative agents of a serious haemorrhagic septicaemia that affects a wide range of freshwater fish in China. In order to develop a bivalent anti-A. hydrophila and anti-V. fluvialis formalin-killed vaccine to prevent this disease, an orthogonal array design (OAD) method was used to optimize the production conditions, using three factors, each having three levels. The effects of these factors and levels on the relative per cent survival for crucian carp were quantitatively evaluated by analysis of variance. The final optimized formulation was established. The data showed that inactivation temperature had a significant effect on the potency of vaccine, but formalin concentration did not. The bivalent vaccine could elicit a strong humoral response in crucian carp (Carassius auratus L.) against both A. hydrophila and V. fluvialis simultaneously, which peaked at 3 or 5 weeks respectively. Antibody titres remained high until week 12, the end of the experiment, after a single intraperitoneal injection. The verification experiment confirmed that an optimized preparation could provide protection for fish at least against A. hydrophila infection, and did perform better than the non-optimized vaccine judged by the antibody levels and protection rate, suggesting that OAD is of value in the development of improved vaccine formulations.

Optimization of RP-HPLC analysis of low molecular weight organic acids in soil

RP-HPLC analysis for low molecular weight organic acids in soil solution has been optimized. An Atlantis (TM) C-18 column was used for the analyses. An optimal determination for eleven organic acids in soil solution was found at room temperature (25 degrees C) and 220 nm detection wavelength, with a mobile phase of 10 mM KH2PO4 -CH3OH (955, pH 2.7), a flow rate of 0.8 mL/min and 10 mu L sample size. The detection limits ranged 3.2-619 ng/mL, the coefficients of variation ranged 1.3-4.6%, and the recoveries ranged 95.6-106.3% for soil solution with standard addition on the optimal conditions proposed.

The optimization of high performance liquid chromatographic method for analysis of trace microcystins in natural water bodies

The ratio of methanol., water and trifluoroacetic acid ( TFA) was regulated to change the polarity and the pH of the rinse solution and the eluent, so as to improve the high performance liquid chromatography HPLC) detection method for trace microcystines (MCs) in natural water bodies. The results showed that 40 % similar to 45 % methanol-water solution containing 0. 1 % TFA could get good effects on the rinse of impurity, and 70% methanol-water solution containing 0. 1% TFA could elute all the MCs in solid phase extraction ( SPE) cartridge ( C-18), In this way. it is suggested that, in analysis of environmental samples with high concentration of impurity, impurity should be washed with 40% similar to 45% methanol-water solution containing 0. 1% TFA, and MCs should be eluted with 70% similar to 100% methanol-water solution containing 0. 1% TFA.

Motor control optimization of compliant one-legged locomotion in rough terrain

While underactuated robotic systems are capable of energy efficient and rapid dynamic behavior, we still do not fully understand how body dynamics can be actively used for adaptive behavior in complex unstructured environment. In particular, we can expect that the robotic systems could achieve high maneuverability by flexibly storing and releasing energy through the motor control of the physical interaction between the body and the environment. This paper presents a minimalistic optimization strategy of motor control policy for underactuated legged robotic systems. Based on a reinforcement learning algorithm, we propose an optimization scheme, with which the robot can exploit passive elasticity for hopping forward while maintaining the stability of locomotion process in the environment with a series of large changes of ground surface. We show a case study of a simple one-legged robot which consists of a servomotor and a passive elastic joint. The dynamics and learning performance of the robot model are tested in simulation, and then transferred the results to the real-world robot. ©2007 IEEE.

Predictive entropy search for efficient global optimization of black-box functions

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

Manopt, a matlab toolbox for optimization on manifolds

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design effcient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. By dealing internally with most of the differential geometry, the package aims particularly at lowering the entrance barrier. © 2014 Nicolas Boumal.