Two-point Scheme Research Articles

Evaluation of the genetic algorithm parameters on the optimization performance: a case study on pump-and-treat remediation design

In this study, the impacts of different crossover and encoding schemes on the performance of a genetic algorithm (GA) in finding optimal pump-and-treat (P&T) remediation designs are investigated. For this purpose, binary and Gray encodings of the decision variables are tested. Uniform and two-point crossover schemes are evaluated for two different crossover probabilities. Analysis is performed for two P&T system optimization scenarios. Results show that uniform crossover operator with Gray encoding outperforms the other alternatives for the complex problem with higher number of decision variables. On the other hand, when a simpler problem, which had a lower number of decision variables, is solved, the efficiency of GA is independent of the encoding and crossover schemes.

A 2.4-GHz Low-Power All-Digital Phase-Locked Loop

This paper presents an all-digital phase-locked loop (ADPLL) for the 2.4-GHz ISM band frequency synthesis. The ADPLL is built around a digitally controlled LC oscillator. In the feedback path, a high-speed topology is employed for the variable phase accumulator to count full cycles of the RF output. A simple technique based on a short delay line in the reference signal path allows the time-to-digital converter core to operate at a low duty cycle with about 95% reduction of its average power consumption. To allow direct frequency modulation, the ADPLL incorporates a two-point modulation scheme with an adaptive gain calibration. Fabricated in a 65-nm CMOS, the ADPLL has an active area of 0.24 mm2. Measured phase noise at 1-MHz offset is -120 dBc/Hz with a power consumption of 12 mW, and -112 dBc with power consumption lowered to 8 mW. The integrated phase noise of the ADPLL is measured to be 1.7° rms.

Two-point difference schemes of an arbitrary given order of accuracy for nonlinear BVPs

In this paper we consider difference schemes for two-point BVPs for systems of first order nonlinear ODEs. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which a priori possesses an arbitrary given order of accuracy m . Here, we demonstrate that the TDS can be reduced to the numerical solution of some IVPs defined on each segment [ x j − 1 , x j ] of the grid by an arbitrary IVP-solver of the order m . Using the difference schemes of the orders of accuracy m and m + 1 we develop an a posteriori error estimator for the numerical solution of the order m . An algorithm for the automatic generation of a grid which guarantees the prescribed accuracy is presented. It is based on embedded Runge–Kutta methods. Some numerical results confirming the efficiency of the algorithm are given.

A discrete particle swarm optimization for lot-streaming flowshop scheduling problem

We consider an n-job, m-machine lot-streaming problem in a flowshop with equal-size sublots where the objective is to minimize the total weighted earliness and tardiness. To solve this problem, we first propose a so-called net benefit of movement (NBM) algorithm, which is much more efficient than the existing linear programming model for obtaining the optimal starting and completion times of sublots for a given job sequence. A new discrete particle swarm optimization (DPSO) algorithm incorporating the NBM algorithm is then developed to search for the best sequence. The new DPSO improves the existing DPSO by introducing an inheritance scheme, inspired by a genetic algorithm, into particles construction. To verify the proposed DPSO algorithm, comparisons with the existing DPSO algorithm and a hybrid genetic algorithm (HGA) are made. Computational results show that the proposed DPSO algorithm with a two-point inheritance scheme is very competitive for the lot-streaming flowshop scheduling problem.

The optimal MR acquisition strategy for exponential decay constants estimation

Estimating the relaxation constant of an exponentially decaying signal from experimental MR data is fundamental in diffusion tensor imaging, fractional anisotropy mapping, measurements of transverse relaxation rates and contrast agent uptake. The precision of such measurements depends on the choice of acquisition parameters made at the design stage of the experiments. In this report, chi(2) fitting of multipoint data is used to demonstrate that the most efficient acquisition strategy is a two-point scheme. We also conjecture that the smallest coefficient of variation of the decay constant achievable in any N-point experiment is 3.6 times larger than that in the image intensity obtained by averaging N acquisitions with minimal exponential weighting.

Accurate extrapolation of electron correlation energies from small basis sets

A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as deltaE(X) proportional, variant(X + xi(i))(-gamma). The angular momentum offset xi(i) captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L = X-1 for hydrogen and helium and up to L = X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules (H, C, N, O, F) for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and (TQ) extrapolations are found to reproduce a small set of available R12 reference data better than even (56) extrapolations using the conventional asymptotic limit formula deltaE(X) proportional, variantX(-3). Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed.

MP2 Basis Set Limit Binding Energy Estimates of Hydrogen-bonded Complexes from Extrapolation-oriented Basis Sets

By use of a simple two-point extrapolation scheme estimating the correlation energies of the molecules along with the basis sets specifically targeted for extrapolation, we have shown that the MP2 basis set limit binding energies of large hydrogen-bonded complexes can be accurately predicted with relatively small amount of computational cost. The basis sets employed for computation and extrapolation consist of the smallest correlation consistent basis set cc-pVDZ and another basis set made of the cc-pVDZ set plus highest angular momentum polarization functions from the cc-pVTZ set, both of which were then augmented by diffuse functions centered on the heavy atoms except hydrogen in the complex. The correlation energy extrapolation formula takes the (X+1) -3 form with X corresponding to 2.0 for the cc-pVDZ set and 2.3 for the other basis set. The estimated MP2 basis set limit binding energies for water hexamer, hydrogen fluoride pentamer, alanine-water, phenol-water, and guanine-cytosine base pair complexes of nucleic acid by this method are 45.2(45.9), 36.1(37.5), 10.9(10.7), 7.1(6.9), and 27.6(27.7) kcal/mol, respectively, with the values in parentheses representing the reference basis set limit values. A comparison with the DFT results by B3LYP method clearly manifests the effectiveness and accuracy of this method in the study of large hydrogen-bonded complexes.

Discussion of Derivation of high-order advection-diffusion schemes by Pavel Tkalich, 2006 J. Hydroinf. 8(3), 149–164

The Discusser would like to congratulate the Author for rigorous development and complete treatment of numerical characteristics of finite difference schemes derived from the concept of polynomial interpolation of advected (concentration) values at the foot of backwards characteristic. It is important that such complete treatment is published nowadays because the current practice of using market-available codes without knowledge of underlying numerical problems leads not only to the blind application of “encapsulated methods” but also does not help to awaken a vocation and liking for numerical analysis in younger generations. This said, the Discusser is disappointed to see that the paper seems to imply that the only way to obtain high-order schemes is to develop them from piece-wise interpolation algebraic polynomial such as given by Eq. 2. Such procedure leads automatically, when higher order approximations are concerned, to involvement of more than two computational points in space. Thus the difference upwind formulas needed to compute the advected values at point xnþ1 i involve computational points xi, xi21, xi22, and even xi23 at times level tn. While such an approach is perfectly correct for functions that do not present large variations in space, it is awkward to apply in simulation systems for real rivers and streams. Indeed, not only boundary conditions ask for special procedures (as the Author shows in Appendix B) but it is very difficult and even tricky to include internal special conditions such as weirs, brusque variations of cross-sections, bifurcations etc. Such difficulties are well known to all developers of the schemes applied to simulate unsteady flows that include more than two space computational points (or more than one space interval). For that reason a fourth-order two-point advective transport scheme has been developed and it is disappointing that the Author neither mentioned nor included the reference to that development in his bibliography. This fourth-order two-point scheme is based on the hermitian interpolation of advected values at the foot of backwards characteristic and its originality comes from this approach: instead to follow classic algebraic polynomial procedure new finite difference scheme was developed, or should we say invented, to be coherent with a two-points unsteady flow simulation scheme. This scheme virtually eliminates numerical diffusion and thus permits modelling physical convection and physical diffusion without having to compensate for numerical inadequacy. The development of the fourth-order two-point scheme was carried out by F.M. Holly, Jr and A. Preissmann (1977). The description and details can be found in this paper and other referenced papers (Cunge et al. 1980; Holly & Usseglio-Polatera 1984; Holly and Toda 1984).

Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation

In this paper, a special lattice Boltzmann model is proposed to simulate two-dimensional unsteady Burgers’ equation. The maximum principle and the stability are proved. The model has been verified by several test examples. Excellent agreement is obtained between numerical predictions and exact solutions. The cases of steep oblique shock waves are solved and compared with the two-point compact scheme results. The study indicates that lattice Boltzmann model is highly stable and efficient even for the problems with severe gradients.

A fast correlated electronic structure method for computing interaction energies of large van der Waals complexes applied to the fullerene–porphyrin dimer

A new implementation of the scaled opposite spin Møller-Plesset (SOS-MP2) method is briefly described, which exploits the locality and sparsity of expansion coefficients and as a result has computational costs that increase approximately quadratically with molecular size. The performance of SOS-MP2 for describing stacked pi-complexes is carefully investigated using the benzene, ethylene, uracil, and naphthalene dimers as model systems. It is demonstrated that counterpoise-corrected SOS-MP2 results, extrapolated towards the complete basis set (CBS) limit using a two-point extrapolation scheme, can yield association energies that are reasonably close to the best available numbers, when the single scale factor is chosen as 1.55 for extrapolating results at the cc-pVDZ and cc-pVTZ levels. This methodology yields an interaction energy for the fullerene-tetraphenylporphyrin dimer of -31.47 kcal mol(-1) while Hartree-Fock (HF) with the cc-pVTZ basis finds the dimer at the same geometry is unbound by +10.83 kcal mol(-1). This implies that the net binding is a result of substantial correlation effects, presumably long-range London dispersions.

Design of electrically small wire antennas using a pareto genetic algorithm

We report on the use of a genetic algorithm (GA) in the design optimization of electrically small wire antennas, taking into account of bandwidth, efficiency and antenna size. For the antenna configuration, we employ a multisegment wire structure. The Numerical Electromagnetics Code (NEC) is used to predict the performance of each wire structure. To efficiently map out this multiobjective problem, we implement a Pareto GA with the concept of divided range optimization. In our GA implementation, each wire shape is encoded into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. An optimal set of designs, trading off bandwidth, efficiency, and antenna size, is generated. Several GA designs are built, measured and compared to the simulation. Physical interpretations of the GA-optimized structures are provided and the results are compared against the well-known fundamental limit for small antennas. Further improvements using other geometrical design freedoms are discussed.

Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation

This paper is devoted to the testing and comparison of numerical solutions obtained from higher-order accurate finite difference schemes for the two-dimensional Burgers' equation having moderate to severe internal gradients. The fourth-order accurate two-point compact scheme, and the fourth-order accurate Du Fort Frankel scheme are derived. The numerical stability and convergence are presented. The cases of shock waves of severe gradient are solved and checked with the fourth-order accurate Du Fort Frankel scheme solutions. The present study shows that the fourth-order two-point compact scheme is highly stable and efficient in comparison with the fourth-order accurate Du Fort Frankel scheme.

Deterministic safety study of advanced molten salt nuclear systems for prospective nuclear power

The inter-comparative analysis of the deterministic safety potential of innovative molten salt systems with critical and sub-critical cores is presented for both fast and thermal neutron spectra. The analysis includes two aspects: the choice of an initial level of sub-criticality and the study of multiple unprotected transients which have been simulated on the basis of one-point kinetics and two-point thermo-hydraulic schemes considering realistic feedback effects. Our preliminary results show that even small levels of sub-criticality (2–3 dollars) of cores can improve their safety characteristics significantly.

Shape optimization of corrugated coatings under grazing incidence using a genetic algorithm

We report on the use of a genetic algorithm (GA) to design optimal shapes for a corrugated coating under near-grazing incidence. A full-wave electromagnetic solver based on the boundary integral formulation is employed to predict the performance of the coating shape. In our GA implementation, we encode each shape of the coating into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. A standard magnetic radar absorbing material (MAGRAM) is used for the absorber coating. We present the optimized coating shapes depending on different polarizations. A physical interpretation for the optimized structure is discussed and the resulting shape is compared to conventional planar and triangular shaped designs. Next, we extend this problem from single to multiobjective optimization by using a Pareto GA. The optimization results with two different objectives, viz. height (or weight) of the coating versus absorbing performance, are presented.

Composite structures optimization using sequential convex programming

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described. Several modifications of these approximations are presented. They are now based on gradient information at two successive iterations, avoiding the use of the expensive second-order derivatives. A two-point fitting scheme is also described, where the function value at the preceding design point is used to improve the approximation. Numerical examples compare these new purely non-monotonous schemes to the existing ones for the selection of optimal fibers orientations in laminates. It is shown how these two-point based approximations are well adapted to the problem and can improve the optimization task, leading to reasonable computational efforts. A procedure is also derived for considering simultaneously monotonous and non-monotonous structural behaviors. The resulting generalized approximation scheme is well suited for the optimization of composite structures when both plies thickness and fibers orientations are considered as design variables. It is concluded that the newly developed approximation schemes of the MMA family are reliable for composite structures optimization. All the studied approximations are convex and separable: the optimization problem can then be solved using a dual approach.

Simulation of Liquid Composite Molding Based on Control-Volume Finite Element Method

The control-volume finite element method (CVFEM) is a widely used numerical tool for modeling the polymer molding process because it is more user friendly and more robust than the conventional finite element or finite difference methods. This work compares the accuracy and stability of five upwind schemes of CVFEM for simulating the non-isothermal flow in the reactive liquid composite molding (LCM) processes. The results show that the mass weighted skew upwind (MAW) and the one-point upwind schemes are the most robust for simulating non-isothermal reactive flow in complicated flow domains and mesh shape. The streamline upwind control-volume (SUCV) scheme provides better numerical accuracy for simulating isothermal reactive flow. However, it tends to give unrealistic solutions at nodes close to the inlet region when simulating non-isothermal reactive flow in complicated geometry with obtuse triangular mesh. The two-point upwind scheme is inferior to MAW, the one-point upwind, and the SUCV schemes. The exponential and linear shape functions are not suitable for simulating the reactive LCM processes.

Rembrandt and the Church Interiors of the Delft School

The new Delft-type of church interiors appeared in Dutch painting of the Golden Age exactly at mid-century. It is characterized by an original two-point scheme designed to form a corner at the nearest, assymetrically placed column. No convincing explanation has been provided for this dramatic turn around 1650 (Giltaij), especially in view of the fact that Gerard Houckgeest - the inventor of the scheme - painted still in 1648 church interiors of the traditional type. I would like to suggest here a source of possible inspiration, namely Rembrandt's Medea-etching of 1648, which on closer analysis shows a similar spatial arrangement. A further link might be provided by the use of curtains both in Rembrandt's works (Holy Family, 1646) and in the church interiors of the Delft-type.

Output regulation of nonisothermal plug-flow reactors with inlet perturbations

This work addresses the output regulation of flow systems described by a class of nonlinear partial differential equation (NPDE) systems with either one or two manipulated inputs. The main design procedures involves two steps, the first is to determine the feasible steady-state operation through the numerical computation, the second is to use the ‘boundary’ controls whose number and position can be directly planned. The developed control strategy can be treated as a typical linearization design, so that the outlet state of flow systems can be approximately linearized and maintain a certain degree of output tracking performance. Since the inlet perturbations may cause the hot spot phenomenon or open-loop instability of nonisothermal processes, the special two-point control scheme can suppress the effect of inlet disturbances and alleviate the control action. Finally, several issues are evaluated through simulations and implemented on an exothermic plug-flow reactor (PFR).

A new two-point approximation approach for structural optimization

The objective of this work is to build up a high-quality approximation scheme to realize computational savings for the solution of structural optimization problems. To this end, a newly developed two-point approximation scheme is proposed. This scheme is constructed by the linear combination of Taylor expansions in terms of both original and reciprocal variables. The coefficients of the combination are determined by utilizing both the function and gradient information of two different design points obtained during the process of optimization. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of previously published work.

Two-point control of a reactive distillation column for composition and conversion

Reactive distillation is a hybrid process with dual process objectives: reactant conversion and product composition. Control schemes for reactive distillation frequently neglect the effect of the principal operating parameters on the reactant conversion, and this has a detrimental effect on the overall process profitability. An ETBE reactive distillation column has been used as a case study to show how a two-point control configuration, which recognises the importance of both composition and conversion, can be developed and implemented for a reactive distillation process. The combined composition and conversion control configuration was tested using SpeedUp dynamic simulations and proved to be effective in maintaining a high isobutylene conversion despite process disturbances. The two-point control scheme also had superior disturbance rejection capability, especially for feed rate changes, and composition set-point sensitivity compared with a one-point control scheme.