Implementation of novel methods of global and nonsmooth optimization : GANSO programming library

We discuss the implementation of a number of modern methods of global and nonsmooth continuous optimization, based on the ideas of Rubinov, in a programming library GANSO. GANSO implements the derivative-free bundle method, the extended cutting angle method, dynamical system-based optimization and their various combinations and heuristics. We outline the main ideas behind each method, and report on the interfacing with Matlab and Maple packages.

Ecology of arboreal marsupials in a network of remnant linear habitats

Linear strips of vegetation set within a less-hospitable matrix are common features of landscapes throughout the world. Depending on location, form and function, these linear landscape elements include hedgerows, fencerows, shelterbelts, roadside or streamside strips and wildlife corridors. In many anthropogenically-modified landscapes, linear strips are important components for conservation because they provide a large proportion of the remaining wooded or shrubby habitat for fauna. They may also function to provide connectivity across the landscape. In some districts, the linear strips form an interconnected network of habitat. The spatial configuration of remnant habitat (size, shape and arrangement) may influence habitat suitability, and hence survival, of many species of plant and animal in modified landscapes. Near Euroa in south-eastern Australia, the clearing and fragmentation of temperate woodlands for agriculture has been extensive and, at present, less than 5% tree cover remains, most of which (83%) occurs as linear strips along roads and streams. The remainder of the woodland occurs as relatively small patches and single isolated trees scattered across the landscape. As an assemblage, arboreal marsupials are woodland dependent and vary in their sensitivity to habitat loss and fragmentation. This thesis focusses on determining the conservation status of arboreal marsupials in the linear network and understanding how they utilise the landscape mosaic. Specifically, the topics examined in this thesis are: (1) the composition of the arboreal marsupial assemblage in linear and non-linear woodland remnants; (2) the status and habitat preferences of species of arboreal marsupial within linear remnants; and (3) the ecology of a population of the Squirrel Glider Petaurus norfolcensis in the linear network, focusing on population dynamics, spatial organisation, and use of den trees. The arboreal marsupial fauna in the linear network was diverse, and comprised seven out of eight species known to occur in the district. The species detected within the strips were P. norfolcensis, the Sugar Glider Petaurus breviceps, Common Brushtail Possum Trichosums vulpecula, Common Ringtail Possum Pseudocheirus peregrinus, Brush-tailed Phascogale Phascogale tapoatafa, Koala Phascolarctos cinereus and Yellow-footed Antechinus Antechinus flavipes. The species not detected was the Feathertail Glider Acrabates pygmaeus. Survey sites in linear remnants (strips of woodland along roads and streams) supported a similar richness and density of arboreal mammals to sites in non-linear remnants (large patches or continuous tracts of woodland nearby). Furthermore, the combined abundance of all species of arboreal marsupials was significantly greater in sites in the linear remnants than in the non-linear remnants. This initial phase of the study provided no evidence that linear woodland remnants support a degraded or impoverished arboreal marsupial fauna in comparison with the nonlinear remnants surveyed. Intensive trapping of arboreal marsupials within a 15 km linear network between February 1997 and June 1998 showed that all species of arboreal marsupial (except A. pygmaeus) were present within the linear strips. Further analyses related trap-based abundance estimates to measures of habitat quality and landscape structure. Width of the linear habitat was significantly positively correlated with the combined abundance of all arboreal marsupials, as well as with the abundance of P. norfolcensis and T. vulpecula. The abundance of T. vulpecula was also significantly positively correlated with variation in overstorey species composition, Acacia density and the number of hollow-bearing trees. The abundance of P. norfolcensis was positively correlated with Acacia density and canopy width, and negatively correlated with distance to the nearest intersection with another linear remnant. No significant variables were identified to explain the abundance of P. tapoatafa, and there were insufficient captures of the remaining species to investigate habitat preferences. Petaurus norfolcensis were resident within the linear network and their density (0.95 -1.54 ha-1) was equal to the maximum densities recorded for this species in continuous forest elsewhere in south-eastern Australia. Rates of reproduction were also similar to those in continuous forest, with births occurring between May and December, a mean natality rate of 1.9, and a mean litter size of 1.7. Sex ratios never differed significantly from parity. Overall, the population dynamics of P. norfolcensis were comparable with published results for the species in contiguous forest, clearly suggesting that the linear remnants currently support a self-sustaining, viable population. Fifty-one P. norfolcensis were fitted with radio transmitters and tracked intermittently between December 1997 and November 1998. Home ranges were small (1.3 - 2.8 ha), narrow (20 - 40 m) and elongated (322 - 839 m). Home ranges were mostly confined to the linear remnants, although 80% of gliders also utilised small clumps of adjacent woodland within farm paddocks for foraging or denning. Home range size was significantly larger at intersections between two or more linear remnants than within straight sections of linear remnants. Intersections appeared to be important sites for social interaction because the overlap of home ranges of members of adjacent social groups was significantly greater at intersections than straight sections. Intersections provided the only opportunity for members of three or more social groups to interact, while still maintaining their territories. The 51 gliders were radiotracked to 143 different hollow-bearing trees on 2081 occasions. On average, gliders used 5.3 den trees during the study (range 1-15), and changed den trees every 4.9 days. The number of den trees used by each glider is likely to be conservative because the cumulative number of den trees continued to increase over the full duration of the study. When gliders shifted between den trees, the mean distance between consecutive den sites was 247 m. Den trees were located throughout a glider's home range, thereby reducing the need to return to a central den site and potentially minimising energy expenditure. Dens were usually located in large trees (mean diameter 88.5 cm) and were selected significantly more often than expected based on their occurrence within the landscape. The overall conclusion of this thesis is that the linear network I studied provides high quality habitat for resident populations of arboreal marsupials. Important factors influencing the suitability of the linear remnants appear to be the high level of network connectivity, the location on soils of high nutrient status, the high density of large trees and an acacia understorey. In highly fragmented landscapes, linear habitats as part of the remaining woodland mosaic have the potential to be an integral component in the conservation of woodland-dependent fauna. The habitat value of linear strips of vegetation should not be underestimated.

Integrated modelling of cost-effective siting and operation of flow-control infrastructure for river ecosystem conservation

Wetland and floodplain ecosystems along many regulated rivers are highly stressed, primarily due to a lack of environmental flows of appropriate magnitude, frequency, duration, and timing to support ecological functions. In the absence of increased environmental flows, the ecological health of river ecosystems can be enhanced by the operation of existing and new flow-control infrastructure (weirs and regulators) to return more natural environmental flow regimes to specific areas. However, determining the optimal investment and operation strategies over time is a complex task due to several factors including the multiple environmental values attached to wetlands, spatial and temporal heterogeneity and dependencies, nonlinearity, and time-dependent decisions. This makes for a very large number of decision variables over a long planning horizon. The focus of this paper is the development of a nonlinear integer programming model that accommodates these complexities. The mathematical objective aims to return the natural flow regime of key components of river ecosystems in terms of flood timing, flood duration, and interflood period. We applied a 2-stage recursive heuristic using tabu search to solve the model and tested it on the entire South Australian River Murray floodplain. We conclude that modern meta-heuristics can be used to solve the very complex nonlinear problems with spatial and temporal dependencies typical of environmental flow allocation in regulated river ecosystems. The model has been used to inform the investment in, and operation of, flow-control infrastructure in the South Australian River Murray.

Direct method for optimal power management in hybrid electric vehicles

Hybrid electric vehicles are powered by an electric system and an internal combustion engine. The components of a hybrid electric vehicle need to be coordinated in an optimal manner to deliver the desired performance. This paper presents an approach based on direct method for optimal power management in hybrid electric vehicles with inequality constraints. The approach consists of reducing the optimal control problem to a set of algebraic equations by approximating the state variable which is the energy of electric storage, and the control variable which is the power of fuel consumption. This approximation uses orthogonal functions with unknown coefficients. In addition, the inequality constraints are converted to equal constraints. The advantage of the developed method is that its computational complexity is less than that of dynamic and non-linear programming approaches. Also, to use dynamic or non-linear programming, the problem should be discretized resulting in the loss of optimization accuracy. The propsed method, on the other hand, does not require the discretization of the problem producing more accurate results. An example is solved to demonstrate the accuracy of the proposed approach. The results of Haar wavelets, and Chebyshev and Legendre polynomials are presented and discussed. © 2011 The Korean Society of Automotive Engineers and Springer-Verlag Berlin Heidelberg.

Efficient subwindow search with submodular score functions

Subwindow search aims to find the optimal subimage which maximizes the score function of an object to be detected. After the development of the branch and bound (B&B) method called Efficient Subwindow Search (ESS), several algorithms (IESS [2], AESS [2], ARCS [3]) have been proposed to improve the performance of ESS. For nn images, IESS's time complexity is bounded by O(n³) which is better than ESS, but only applicable to linear score functions. Other work shows that Monge properties can hold in subwindow search and can be used to speed up the search to O(n³), but only applies to certain types of score functions. In this paper we explore the connection between submodular functions and the Monge property, and prove that sub-modular score functions can be used to achieve O(n³) time complexity for object detection. The time complexity can be further improved to be sub-cubic by applying B&B methods on row interval only, when the score function has a multivariate submodular bound function. Conditions for sub-modularity of common non-linear score functions and multivariate submodularity of their bound functions are also provided, and experiments are provided to compare the proposed approach against ESS and ARCS for object detection with some nonlinear score functions.

Prediction interval-based modelling of polymerization reactor: a new modelling strategy for chemical reactors

Precise and reliable modelling of polymerization reactor is challenging due to its complex reaction mechanism and non-linear nature. Researchers often make several assumptions when deriving theories and developing models for polymerization reactor. Therefore, traditional available models suffer from high prediction error. In contrast, data-driven modelling techniques provide a powerful framework to describe the dynamic behaviour of polymerization reactor. However, the traditional NN prediction performance is significantly dropped in the presence of polymerization process disturbances. Besides, uncertainty effects caused by disturbances present in reactor operation can be properly quantified through construction of prediction intervals (PIs) for model outputs. In this study, we propose and apply a PI-based neural network (PI-NN) model for the free radical polymerization system. This strategy avoids assumptions made in traditional modelling techniques for polymerization reactor system. Lower upper bound estimation (LUBE) method is used to develop PI-NN model for uncertainty quantification. To further improve the quality of model, a new method is proposed for aggregation of upper and lower bounds of PIs obtained from individual PI-NN models. Simulation results reveal that combined PI-NN performance is superior to those individual PI-NN models in terms of PI quality. Besides, constructed PIs are able to properly quantify effects of uncertainties in reactor operation, where these can be later used as part of the control process. © 2014 Taiwan Institute of Chemical Engineers.

Performance analysis of three advanced controllers for polymerization batch reactor: an experimental investigation

The performances of three advanced non-linear controllers are analyzed for the optimal set point tracking of styrene free radical polymerization (FRP) in batch reactors. The three controllers are the artificial neural network-based MPC (NN-MPC), the artificial fuzzy logic controller (FLC) as well as the generic model controller (GMC). A recently developed hybrid model (Hosen et al., 2011a. Asia-Pac. J. Chem. Eng. 6(2), 274) is utilized in the control study to design and tune the proposed controllers. The optimal minimum temperature profiles are determined using the Hamiltonian maximum principle. Different types of disturbances are introduced and applied to examine the stability of controller performance. The experimental studies revealed that the performance of the NN-MPC is superior to that of FLC and GMC. © 2013 The Institution of Chemical Engineers.

Primary voltage control of a single-phase inverter using linear quadratic regulator with integrator

This paper proposes a linear quadratic regulator with integral action, ensuring fast dynamic response and resisting capability of voltage deviation from instantaneous reference grid voltage, to control the inverter voltage that can also be used in a microgrid. The proposed control strategy is based on a linear quadratic regulator, minimizing the cost function of the system, with integral action used to impede voltage degradation from a reference voltage for outside disturbances of the system, such as abrupt load change. The combined integral term assists to recover the voltage difference between grid and reference grid voltage. The validity of the proposed controller has been tested with linear and non-linear loads under various conditions. In both cases, the effectiveness of the controller has been proved. The result of the proposed controller is good to track the instantaneous reference grid voltage.

Simultaneous pattern and size optimisation of rock bolts for underground excavations

Designing a rock bolt reinforcement system for underground excavation involves determining bolt pattern, spacing, and size. In this paper, a topology optimisation technique is presented and employed to simultaneously optimise these design variables. To improve rock bolt design, the proposed technique minimises a displacement based function around the opening after bolt installation. This optimisation technique is independent of the material model and can be easily applied to any material model for rock and bolts. It is also extremely flexible in that it can be applied to any mechanical analysis method. To illustrate the capabilities of this method, numerical examples with non-linear material models and discontinuities in the host rock are presented. It is shown that the complexity of systems optimised using this approach is only restricted by limitations of the method used to analyse mechanical system responses.