Geometry Optimization Algorithms Research Articles

Innovative analytic and experimental methods for thermal management of SMD-type LED chips

In this study, we propose innovative analytic and experimental methods for thermal management of SMD-type LED chips: a geometry optimization algorithm of natural convective heat sinks together with a novel technique for estimation of the LED surface temperature. An analytic algorithm for the optimal design of the LED heat sink is proposed. By using this algorithm, the optimal fin configuration and corresponding thermal performance of the heat sink can be readily predicted according to the inputted base plate dimensions, ambient condition, heat dissipation rate, and LED chip distributions. In addition, a novel experimental technique for an accurate measurement of the LED junction temperature is proposed based on infrared thermometry and an isothermal chamber with an observation hole. The LED junction temperature is also measured using T3ster method, and the results are compared with those from the aforementioned infrared thermometry and analytic procedure. The proposed analytic and experimental results are shown to agree with each other well. The present analytic model is well validated by experimental results, and can be widely utilized for designing the cooling system related to various LED products.

Comparison of Genetic Algorithm and Harmony Search Method for 2D Geometry Optimization.

There are many applications of Genetic Algorithm (GA) and Harmony Search (HS) Method for solving problems in civil engineering design. The question is, still, which method is better for geometry optimization of a steel structure. The purpose of this paper is to compare GA and HS performance for geometric optimization of a steel structure. This problem is solved by optimizing a steel structure using GA and HS and then comparing the structure’s weight as well as the time required for the calculation. In this study, GA produced a structural weight of 2308.00 kg to 2387.00 kg and HS scored 2193.12 kg to 2239.48 kg. The average computational time required by GA is 607 seconds and HS needed 278 seconds. It concludes that HS is faster and better than GA for geometry optimization of a steel structure.

Efficient Geometry Minimization and Transition Structure Optimization Using Interpolated Potential Energy Surfaces and Iteratively Updated Hessians.

An efficient geometry optimization algorithm based on interpolated potential energy surfaces with iteratively updated Hessians is presented in this work. At each step of geometry optimization (including both minimization and transition structure search), an interpolated potential energy surface is properly constructed by using the previously calculated information (energies, gradients, and Hessians/updated Hessians), and Hessians of the two latest geometries are updated in an iterative manner. The optimized minimum or transition structure on the interpolated surface is used for the starting geometry of the next geometry optimization step. The cost of searching the minimum or transition structure on the interpolated surface and iteratively updating Hessians is usually negligible compared with most electronic structure single gradient calculations. These interpolated potential energy surfaces are often better representations of the true potential energy surface in a broader range than a local quadratic approximation that is usually used in most geometry optimization algorithms. Tests on a series of large and floppy molecules and transition structures both in gas phase and in solutions show that the new algorithm can significantly improve the optimization efficiency by using the iteratively updated Hessians and optimizations on interpolated surfaces.

Metastable exohedrally decorated Borospherene B40

The experimental discovery of borospherene, the only non-carbon fullerene observed in nature, has generated a lot of interest in the scientific community and led to the theoretical prediction of various endohedrally and exohedrally decorated borospherene. We apply Minima Hopping Method (MHM), a global geometry optimization algorithm at the density functional level to check the stability of recently proposed exohedrally decorated borospherenes M6@B40 for (M = Li, Na, K, Rb, Be, Mg, Ca, Sr, Sc and Ti). By performing short MHM runs, we find that the proposed fullerene structures are not global minima. Our new lowest energy structures are significantly deformed and of much lower symmetry. These low energy structures spontaneously aggregate by forming chemical bonds when they are brought together. Therefore, it would be challenging to synthesize bulk materials made out of the theoretically postulated exohedrally decorated borospherenes such as B40M6 which might have technologically useful properties.

Optimal design of aerodynamic force supplementary devices for the improvement of fuel consumption and emissions

One of the primary concerns in the automotive industry is energy saving, protecting the global environment and fuel consumption reduction. The main purpose of this study is to develop optimal supplementary parts for reduction of aerodynamic force of highway tractor and trailer combinations to reduce aerodynamic drag, without negatively affecting the usefulness or profitability of the vehicles. In this article, the possibility to improve the aerodynamic performance for boosting fuel economy of trucks is studied by optimal designing of supplementary devices. That will be carried out by using integrated computational fluid dynamic and genetic algorithm for simulation and geometry optimization of applied devices. Also, simulation results are verified by experimental results in wind tunnel. For this purpose, effects of various supplementary devices and configuration are added to space between cabin and cargo compartment to stabilize the vortex and decrease the drag resistance force. Finally, the geometry of appended device with considering the installation and packing conditions is optimized by using a genetic algorithm. Through the analysis of airflow contours and optimization procedure, results indicate that using two plates at the sidewalls of the gap with optimized length and installation angle can reach the maximum reduction of drag force and fuel consumption by 20 and 10%, respectively.

Numerical and experimental analysis of a ducted propeller designed by a fully automated optimization process under open water condition

A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The developed process allows the direct integration of a RANSE solver in the design stage. A practical ducted propeller design case study is carried out for validation. Numerical simulations and open water tests are fulfilled and proved that the optimum ducted propeller improves hydrodynamic performance as predicted.

Designs of Helix Metamaterials for Broadband and High-Transmission Polarization Rotation

Artificial optical activity can be realized using chiral metamaterials, in which chirality is normally implemented with rotationally stacked planar structures. However, such geometries usually suffer from great loss and limited operation bandwidth, which may hinder their usage in many applications. In this study, by incorporating genetic algorithm for geometry optimization, we present designs of helix metamaterials that exhibit high transmission above 95% and a broad bandwidth with low ellipticity. The optical characteristics are described, and the nature behind the high transmission and broad bandwidth is discussed.

Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: Geometry optimization and spin-state energetics of a ruthenium nitrosyl complex

We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08Å for S0 and 0.11Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.

Optimization of a Compact Frequency- and Environment-Reconfigurable Antenna

This paper presents a novel ultra-compact ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$0.17\times 0.17\times 0.05$</tex></formula> wavelengths) reconfigurable antenna equipped with shunt switches at the edges of the radiating elements; in addition to wide-band frequency-reconfigurability, the antenna can also adapt to different environments. The challenging task of designing a compact antenna for multi-band and multi-environment operation is tackled by a hierarchical optimization process consisting of the genetic algorithm (GA) and local search for geometry optimization, and exhaustive search for computation of the optimum switch patterns for a fixed geometry. Both tunability and environment robustness were confirmed in simulation and measurements on a proof-of-concept prototype where switches were simulated by soldering. Numerical analysis of the impact of commercial MEMS devices is also reported, including a case study of practical interest: a compact antenna that can operate at different locations around a simplified model of a laptop PC without performance degradation.

Geometry optimization of bimetallic clusters using an efficient heuristic method

In this paper, an efficient heuristic algorithm for geometry optimization of bimetallic clusters is proposed. The algorithm is mainly composed of three ingredients: the monotonic basin-hopping method with guided perturbation (MBH-GP), surface optimization method, and iterated local search (ILS) method, where MBH-GP and surface optimization method are used to optimize the geometric structure of a cluster, and the ILS method is used to search the optimal homotop for a fixed geometric structure. The proposed method is applied to Cu(38-n)Au(n) (0 ≤ n ≤ 38), Ag(55-n)Au(n) (0 ≤ n ≤ 55), and Cu(55-n)Au(n) (0 ≤ n ≤ 55) clusters modeled by the many-body Gupta potential. Comparison with the results reported in the literature indicates that the present method is highly efficient and a number of new putative global minima missed in the previous papers are found. The present method should be a promising tool for the theoretical determination of ground-state structure of bimetallic clusters. Additionally, some key elements and properties of the present method are also analyzed.

PSO-CGO

In this paper the authors present PSO-CGO, a novel particle swarm algorithm for cluster geometry optimization. The proposed approach combines a steady-state strategy to update solutions with a structural distance measure that helps to maintain population diversity. Also, it adopts a novel rule to update particles, which applies velocity only to a subset of the variables and is therefore able to promote limited modifications in the structure of atomic clusters. Results are promising, as PSO-CGO is able to discover all putative global optima for short-ranged Morse clusters between 30 and 50 atoms. A comprehensive analysis is presented and reveals that the proposed components are essential to enhance the search effectiveness of the PSO.

Quantum algorithm for molecular properties and geometry optimization

Quantum computers, if available, could substantially accelerate quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.

A study on diversity for cluster geometry optimization

Diversity is a key issue to consider when designing evolutionary approaches for difficult optimization problems. In this paper, we address the development of an effective hybrid algorithm for cluster geometry optimization. The proposed approach combines a steady-state evolutionary algorithm and a straightforward local method that uses derivative information to guide search into the nearest local optimum. The optimization method incorporates a mechanism to ensure that the diversity of the population does not drop below a pre-specified threshold. Three alternative distance measures to estimate the dissimilarity between solutions are evaluated. Results show that diversity is crucial to increase the effectiveness of the hybrid evolutionary algorithm, as it enables it to discover all putative global optima for Morse clusters up to 80 atoms. A comprehensive analysis is presented to gain insight about the most important strengths and weaknesses of the proposed approach. The study shows why distance measures that consider structural information for estimating the dissimilarity between solutions are more suited to this problem than those that take into account fitness values. A detailed explanation for this differentiation is provided.

MOLCAS 7: The Next Generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies.

A novel optimization approach for minimum cost design of trusses

This paper describes new optimization strategies that offer significant improvements in performance over existing methods for bridge-truss design. In this study, a real-world cost function that consists of costs on the weight of the truss and the number of products in the design is considered. We propose a new sizing approach that involves two algorithms applied in sequence – (1) a novel approach to generate a “good” initial solution and (2) a local search that attempts to generate the optimal solution by starting with the final solution from the previous algorithm. A clustering technique, which identifies members that are likely to have the same product type, is used with cost functions that consider a cost on the number of products. The proposed approach gives solutions that are much lower in cost compared to those generated in a comprehensive study of the same problem using genetic algorithms (GA). Also, the number of evaluations needed to arrive at the optimal solution is an order of magnitude lower than that needed in GAs. Since existing optimization techniques use cost functions like those of minimum-weight truss problems to illustrate their performance, the proposed approach is also applied to the same examples in order to compare its relative performance. The proposed approach is shown to generate solutions of not only better quality but also much more efficiently. To highlight the use of this sizing approach in a broader optimization framework, a simple geometry optimization algorithm that uses the sizing approach is presented. This algorithm is also shown to provide solutions better than the existing results in literature.

The quasi-independent curvilinear coordinate approximation for geometry optimization.

This paper presents an efficient alternative to well established algorithms for molecular geometry optimization. This approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate system, allowing separation of the 3N-dimensional optimization problem into an O(N) set of quasi-independent one-dimensional problems. Each uncoupled optimization is developed by a weighted least squares fit of energy gradients in the internal coordinate system followed by extrapolation. In construction of the weights, only an implicit dependence on topologically connected internal coordinates is present. This new approach is competitive with the best internal coordinate geometry optimization algorithms in the literature and works well for large biological problems with complicated hydrogen bond networks and ligand binding motifs.

Methods for optimizing large molecules. Part III. An improved algorithm for geometry optimization using direct inversion in the iterative subspace (GDIIS)

The geometry optimization using direct inversion in the iterative subspace (GDIIS) has been implemented in a number of computer programs and is found to be quite efficient in the quadratic vicinity of a minimum. However, far from a minimum, the original method may fail in three typical ways: (a) convergence to a nearby critical point of higher order (e.g. transition structure), (b) oscillation around an inflection point on the potential energy surface, (c) numerical instability problems in determining the GDIIS coefficients. An improved algorithm is presented that overcomes these difficulties. The modifications include: (a) a series of tests to control the construction of an acceptable GDIIS step, (b) use of a full Hessian update rather than a fixed Hessian, (c) a more stable method for calculating the DIIS coefficients. For a set of small molecules used to test geometry optimization algorithms, the controlled GDIIS method overcomes all of the problems of the original GDIIS method, and performs as well as a quasi-Newton RFO (rational function optimization) method. For larger molecules and very tight convergence, the controlled GDIIS method shows some improvement over an RFO method. With a properly chosen Hessian update method, the present algorithm can also be used in the same form to optimize higher order critical points.

Global Geometry Optimization of Molecular Clusters: TIP4P Water

In this paper, we present an extension of our phenotype algorithm for global cluster geometry optimization from atomic clusters to the more difficult molecular clusters. A successful application to the benchmark case of TIP4P water clusters shows that the new method is at least as good as one of the best methods in the literature so far. We point out why the TIP4P water cluster system starts to become very complicated beyond twenty water molecules and follow the traces of a beginning structural transition from clusters with all water molecules at the surface to clathrate-like cages with a truly interior water molecule.

Geometry optimization in Cartesian coordinates: Constrained optimization

AbstractAn efficient algorithm for constrained geometry optimization in Cartesian coordinates is presented. It incorporates mode‐following techniques within both the classical method of Lagrange multipliers and the penalty function method. Both constrained minima and transition states can be located and, unlike the standard Z‐matrix using internal coordinates, the desired constraints do not have to be satisfied in the initial structure. The algorithm is as efficient as a Z‐matrix optimization while presenting several additional advantages.

Geometry optimization of molecules within anLCGTO local-density functional approach

We describe our implementation of geometry optimization techniques within the linear combination of Gaussian-type orbitals (LCGTO) approach to local-density functional theory. The algorithm for geometry optimization is based on the evaluation of the gradient of the total energy with respect to internal coordinates within the local-density functional scheme. We present optimization results for a range of small molecules which serve as test cases for our approach.