On increasing the developability of a trimmed NURBS surface

Developable surfaces are desired in designing products manufactured from planar sheets. Trimmed non-uniform rational B-spline (NURBS) surface patches are widely adopted to represent 3D products in CAD/CAM. This paper presents a new method to increase the developability of an arbitrarily trimmed NURBS surface patch. With this tool, designers can first create and modify the shape of a product without thinking about the developable constraint. When the design is finished, our approach is applied to increase the developability of the designed surface patches. Our method is an optimisation-based approach. After defining a function to identify the developability of a surface patch, the objective function for increasing the developability is derived. During the optimisation, the positions and weights of the free control points are adjusted. When increasing the developability of a given surface patch, its deformation is also minimised and the singular points are avoided. G⁰ continuity is reserved on the boundary curves during the optimisetion, and the method to reserve G¹ continuity across the boundaries is also discussed in this paper. Compared to other existing methods, our approach solves the problem in a novel way that is close to the design convention, and we are dealing with the developability problem of an arbitrarily trimmed NURBS patch.     

Comparison of global and local response surface techniques in reliability-based optimization of composite structures

This paper discusses the development and application of two alternative strategies, in the form of global and sequential local response surface (RS) techniques, for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS), whereas the local technique uses multiple first-order RS models, with each applied to a small subregion of the FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, the thickness and orientation angle of each ply, the diameter and length of the cylinder, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of the ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with the reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of the reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy, with the sequential local RS technique having a considerably better computational efficiency.     

Spatial and temporal variations of summer surface temperatures of wet polygonal tundra in Siberia - implications for MODIS LST based permafrost monitoring

The surface temperature of permafrost soils in remote arctic areas is accessible by satellite land surface temperature (LST) detection. However, the spatial resolution of satellite measurements such as the MODIS LST products is limited and does not detect the heterogeneities of the wet polygonal tundra landscape where surface wetness varies over distances of several meters. This paper examines the spatial and temporal variability of summer surface temperatures of a polygonal tundra site in northern Siberia using a ground based high resolution thermal imaging system. Thermal infrared images were taken of a 1000 m² polygonal tundra area in 10 min intervals from July to September 2008. Under clear sky conditions, the individual measurements indicate temperature differences of up to 6 K between dry and wet tundra surfaces and which can exceed 12 K when dry tundra and water surfaces are compared. These differences disappear when temperature averages are considered for intervals longer than the diurnal cycle; for weekly averages the spatial temperature variability decreases below 1 K. The exception is the free water surface of a shallow polygonal pond where weekly averaged temperature differences of 2.5 K are sustained compared to the tundra surface.The ground based thermal infrared images are upscaled to MODIS sized pixels and compared to available MODIS LST data for individual measurements and weekly averages. The comparisons show generally good agreement for the individual measurements under clear sky conditions, which exist during 20% of the studied time period. However, several erroneous measurements and large data gaps occur in the MODIS LST data during cloudy conditions, leading to biased weekly temperature averages inferred from the satellite observations. Based on these results the following recommendations are given for future permafrost temperature monitoring based on MODIS LST products: (i) high resolution surface water masks for the quality assessment in landscapes where lakes and ponds are frequent and (ii) reliable cloud cover detection in conjunction with a gap filling procedure for accurate temporal averages.     

Developable polynomial surface approximation to smooth surfaces for fabrication parameters of a large curved shell plate by Differential Evolution

This paper presents a simple and efficient method to approximate a developable surface to a compound design surface by a polynomial. It is required to predict a final shape of roll bending in the fabrication of a curved shell plate. The roll bending process usually makes the cylindrical or conical curvature from an initial flat plate. It means that the final shape is developable or the surface representation has zero Gaussian curvature. The fabrication shape is important in order to estimate process parameters of roller bending.An optimization problem is formulated to determine the polynomial surface which is in the closest proximity to the design surface or the given shell plate, which is subjected to developability. The results and the efficiency of this algorithm are verified and evaluated by applying it to some shell plates which are obtained from a real ship model. The predicted bending shape becomes fundamental information in determining more process parameters for the fabrication of a compound curved shell plate.     

Visualization of hypersurfaces and multivariable (objective) functions by partial global optimization

Hypersurfaces of the type z=F(x₁,...,x_n), where F are single-valued functions of n real variables, cannot be visualized directly due to our inability to perceive dimensions higher than three. However, by projecting them down to two or three dimensions many of their properties can be revealed. In this paper a method to generate such projections is proposed, requiring successive global minimizations and maximizations of the function with respect to n-1 or n-2 variables. A number of examples are given to show the usefulness of the method, particularly for optimization problems where there is a direct interest in the minimum or maximum domains of objective functions.     

Analysis and optimization of surface roughness in the ball burnishing process using response surface methodology and desirabilty function

In the present study, an optimization strategy based on desirability function approach (DFA) together with response surface methodology (RSM) has been used to optimize ball burnishing process of 7178 aluminium alloy. A quadratic regression model was developed to predict surface roughness using RSM with rotatable central composite design (CCD). In the development of predictive models, burnishing force, number of passes, feed rate and burnishing speed were considered as model variables. The results indicated that burnishing force and number of passes were the significant factors on the surface roughness. The predicted surface roughness values and the subsequent verification experiments under the optimal conditions were confirmed the validity of the predicted model. The absolute average error between the experimental and predicted values at the optimal combination of parameter settings for surface roughness was calculated as 2.82%.     

Layout and material gradation in topology optimization of functionally graded structures: a global–local approach

By means of continuous topology optimization, this paper discusses the influence of material gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including material gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering material gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular materials.     

PANMIN: sequential and parallel global optimization procedures with a variety of options for the local search strategy

We present two sequential and one parallel global optimization codes, that belong to the stochastic class, and an interface routine that enables the use of the Merlin/MCL environment as a non-interactive local optimizer. This interface proved extremely important, since it provides flexibility, effectiveness and robustness to the local search task that is in turn employed by the global procedures. We demonstrate the use of the parallel code to a molecular conformation problem.

Program summary

Title of program: PANMINCatalogue identifier: ADSUProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSUProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: PANMIN is designed for UNIX machines. The parallel code runs on either shared memory architectures or on a distributed system. The code has been tested on a SUN Microsystems ENTERPRISE 450 with four CPUs, and on a 48-node cluster under Linux, with both the GNU g77 and the Portland group compilers. The parallel implementation is based on MPI and has been tested with LAM MPI and MPICHInstallation: University of Ioannina, GreeceProgramming language used: Fortran-77Memory required to execute with typical data: Approximately O(n²) words, where n is the number of variablesNo. of bits in a word: 64No. of processors used: 1 or manyHas the code been vectorised or parallelized?: Parallelized using MPINo. of bytes in distributed program, including test data, etc.: 147163No. of lines in distributed program, including the test data, etc.: 14366Distribution format: gzipped tar fileNature of physical problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques can be trapped in any local minimum. Global Optimization is then the appropriate tool. For example, solving a non-linear system of equations via optimization, one may encounter many local minima that do not correspond to solutions, i.e. they are far from zeroMethod of solution: PANMIN is a suite of programs for Global Optimization that take advantage of the Merlin/MCL optimization environment [1,2]. We offer implementations of two algorithms that belong to the stochastic class and use local searches either as intermediate steps or as solution refinementRestrictions on the complexity of the problem: The only restriction is set by the available memory of the hardware configuration. The software can handle bound constrained problems. The Merlin Optimization environment must be installed. Availability of an MPI installation is necessary for executing the parallel codeTypical running time: Depending on the objective functionReferences: [1] D.G. Papageorgiou, I.N. Demetropoulos, I.E. Lagaris, Merlin-3.0. A multidimensional optimization environment, Comput. Phys. Commun. 109 (1998) 227-249. [2] D.G. Papageorgiou, I.N. Demetropoulos, I.E. Lagaris, The Merlin Control Language for strategic optimization, Comput. Phys. Commun. 109 (1998) 250-275.     

Topology and parameter optimization of a foaming jig reinforcement structure by the response surface method

A dilemma in the foaming of inner polyurethane (PU) pieces for household refrigerators is that of keeping the production costs down without adversely affecting the dimension precision. One way to do this is to reduce the electric power consumption spent running the polyurethane foaming line in which a number of heavy foaming jigs are continuously circulating, by optimally designing the reinforcement structure of the jig. In this paper, topology optimization and parameter optimization utilizing the response surface method (RSM) are applied for the optimum design of the jig reinforcement structure, in order to minimize the total jig weight while securing the dimension precision of the foamed urethane case. Both the reliability of the approximated response surfaces and the validity of the proposed optimization procedure are verified through illustrative optimization experiments. In addition, it is confirmed that the proposed procedure provides us with an optimum reinforcement structure which remarkably reduces the total jig weight.     

Path planning of a mobile robot by optimization and reinforcement learning

At AROB5, we proposed a solution to the path planning of a mobile robot. In our approach, we formulated the problem as a discrete optimization problem at each time step. To solve the optimization problem, we used an objective function consisting of a goal term, a smoothness term, and a collision term. While the results of our simulation showed the effectiveness of our approach, the values of the weights in the objective function were not given by any theoretical method. This article presents a theoretical method using reinforcement learning for adjusting the weight parameters. We applied Williams' learning algorithm, episodic REINFORCE, to derive a learning rule for the weight parameters. We verified the learning rule by some experiments. This work was presented, in part, at the Sixth International Symposium on Artificial Life and Robotics, Tokyo, Japan, January 15–17, 2001     

Ab initio calculation of the deformation potential and photoelastic coefficients of silicon with a non-uniform finite-difference solver based on the local density approximation

The band diagram, deformation potential and photoelastic tensor of silicon are calculated self-consistently under uniaxial and shear strain by solving for the electronic wavefunctions with a finite-difference method. Many-body effects are accounted for by the local density approximation. In order to accommodate the large number of grid points required due to the diverging electrostatic potential near the atomic nuclei in an all-electron calculation, a non-uniform meshing is adopted. Internal displacements are taken into account by adding an additional coordinate transform to the method of Bir and Pikus. Good consistency of the calculated deformation potential and photoelastic coefficients is obtained with prior experimental and theoretical results, validating the numerical methods. Furthermore, it is shown that a slight correction of the multiplicative coefficient of the Xα$X\alpha$ approximation for conduction bands results in good agreement with experiment for both the direct and indirect bandgaps.     

Integrated optimization of inventory-distribution systems by random local search and a genetic algorithm

A new model and its solution procedure for the commodity distribution system consisting of distribution centers and consumer points are discussed. Demand is assumed to be a random variable that obeys a known, stationary probability distribution. An integrated optimization model is built where both the order-up-to-R policy, which is one of the typical inventory policies for periodic review models, and the transportation problem are considered simultaneously. The assignment of consumer points to distribution centers is not fixed. The problem is to determine the target inventory and the transportation quantity in order to minimize the expectation of the sum of inventory related costs and transportation costs. Simulation and linear programming are used to calculate the expected costs, and a random local search method is developed in order to determine the optimum target inventory. A genetic algorithm is also tested and compared with the proposed random local search method. The model and effectiveness of the proposed solution procedure are clarified by computational experiments.     

Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches

Mathematical modelling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modelling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended Karush-Kuhn-Tucker (KKT) transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformation.     

On the designing principles and optimization approaches of bio-inspired self-organized network: a survey

A plethora of studies on self-organization has been carried out in broad areas including chemistry, biology, astronomy, medical science, telecommunications, etc., in both academia and industry. Following the studies on swarm intelligence observed in social species, the artificial self-organized systems are expected to exhibit some intelligent features (e.g., flexibility, robustness, decentralized control, self-evolution, etc.) that may have made social species so successful in the biosphere. In this paper, the application of swarm intelligence in communications networks will be studied, and we survey different aspects of bio-inspired mechanisms and examine various algorithms that have been proposed to improve the performance of artificial systems. Some fundamental self-organized networking (SON) mechanisms, designing principles and optimization approaches for artificial systems will then be investigated, followed by some well-known bio-inspired algorithms (e.g., cooperation, division of labor, distributed network synchronization, load balancing, etc.) as well as their applications to the maintenance/operation/optimization of artificial systems being analyzed. Besides, some new emerging technologies, such as the Self-X capabilities and cognitive machine-to-machine (M2M) optimization for the 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE)/LTE-Advanced systems, are also surveyed. Finally, the remaining challenges to be faced in designing the future heterogeneous systems will be discussed.     

Mathematical model and genetic optimization for the job shop scheduling problem in a mixed- and multi-product assembly environment: A case study based on the apparel industry

An effective job shop scheduling (JSS) in the manufacturing industry is helpful to meet the production demand and reduce the production cost, and to improve the ability to compete in the ever increasing volatile market demanding multiple products. In this paper, a universal mathematical model of the JSS problem for apparel assembly process is constructed. The objective of this model is to minimize the total penalties of earliness and tardiness by deciding when to start each order’s production and how to assign the operations to machines (operators). A genetic optimization process is then presented to solve this model, in which a new chromosome representation, a heuristic initialization process and modified crossover and mutation operators are proposed. Three experiments using industrial data are illustrated to evaluate the performance of the proposed method. The experimental results demonstrate the effectiveness of the proposed algorithm to solve the JSS problem in a mixed- and multi-product assembly environment.     

Local and global optima in decision-making: a sheaf-theoretical analysis of the difference between classical and behavioral approaches

One of the main differences between the traditional and the behavioral approaches to decision-making is that the latter has not yet been captured in a unifying framework. This hampers in a certain way the whole research program and raises the question of whether this competing approach can provide an encompassing alternative to the classical one. We analyze this issue in light of the problem of reconstructing global choices of an agent up from the solutions found for local problems. We show that a representation based on category theory of the conditions for such reconstruction is general and robust enough to represent both the case in which problems are non-contextual and local as well as that, typical in the literature on behavioral decision-making, in which such properties do not hold. In the first case, we show how a sheaf-theoretical representation provides an abstract characterization of the global solution. In the latter case, we show how locality and contextuality generate obstructions toward the reconstruction of global solutions, yielding a possible clue for the intrinsic difference between behavioral and classical decision theory.     

Characterising groundwater use by vegetation using a surface energy balance model and satellite observations of land surface temperature

This study presents a novel ‘model-data’ approach to detect groundwater-dependent vegetation (GDV), through differences in modelled and observed land surface temperatures (LST) in space and time. Vegetation groundwater use is inferred where modelled LST exceeds observed LST by more than a threshold determined from consideration of systematic and random errors in model and observations. Modelled LST was derived from a surface energy balance model and LST observations were obtained from Terra-MODIS thermal imagery. The model-data approach, applied in the Condamine River Catchment, Queensland, Australia, identified GDV coincident to existing mapping. GDV were found to use groundwater up to 48% of the time and for as many as 56 consecutive days. Under driest of conditions, groundwater was estimated to contribute up to 0.2 mm h⁻¹ to total ET for GDV. The ability to both detect the location and water-use dynamics of GDV is a significant advancement on previous remote-sensing GDV methods.