DIviding RECTangles Algorithm Research Articles

Discrete sizing optimization method based on dividing rectangles algorithm and local response surface for steel frame structures

It has always been the goal of structural engineers to construct safe and stable buildings using the least amount of materials. Utilizing a quick and effective way to optimize the cross-section size is crucial because conventional building design methods are impacted by the designers' knowledge, and it is challenging to prevent material waste. Due to its implicit optimization function, discrete design variables, and expensive individual evaluation, sizing optimization of high-rise buildings is very challenging to achieve. In order to effectively handle this optimization problem, a two-stage discrete sizing optimization method for high-rise buildings based on the DIviding RECTangles (DIRECT) algorithm and local response surface is proposed in this paper. The optimization method suggested in this research consists of two key stages: the global search stage and the local search stage. In the global search stage, the entire design domain is divided using a modified DIRECT algorithm to swiftly identify potentially optimal subregions that may contain the best points. In the local search stage, the local response surface model is constructed to approximate the objective and constraint functions using the sampling points from the previous stage, and the discrete optimal solution is rapidly found through mathematical iterative solving. A sizing optimization calculation program for high-rise buildings was developed in Microsoft Visual Studio 2015 on the basis of C++ to achieve automatic optimization. The new method was applied to optimize three high-rise steel frame buildings with different heights and plan shapes. The results showed that the material cost could be successfully saved compared with the conventional design, and the over-limit constraints could be adjusted automatically, which demonstrated the viability and efficacy of the two-stage optimization method.

Structure search method for atomic clusters based on the dividing rectangles algorithm.

The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.

Managing merging from a CAV lane to a human-driven vehicle lane considering the uncertainty of human driving

This paper proposes a control strategy for a freeway merging bottleneck consisting of a Connected and Automated Vehicle (CAV) exclusive lane and a human-driven vehicle (HDV) lane, aiming to achieve fuel economy and increase traffic efficiency. The trajectories of CAVs are optimized to enable them to smoothly merge into the gaps in the HDV lane. We utilize a stochastic car-following model to incorporate the uncertainty of HDVs and adopt the concept of α-percentile trajectory proposed in our earlier work (Xiong and Jiang, 2021) to estimate the trajectories of HDVs. Based on these, an optimization model is constructed to optimize the merging sequence and the merging trajectories of CAVs simultaneously. We use dynamic programming to solve the optimization model. Dividing RECTangles algorithm and Hamiltonian analysis are imbedded as a subroutine to obtain the energy efficient merging trajectory of each CAV. Simulation results show that the proposed control strategy is capable of reducing average fuel consumption and travel time under a wide range of inflow rates. The benefits depend on the inflow rate and the trajectory percentile α. When the total inflow rate is low, the impact of α is insignificant. If the total inflow rate increases to a high level, the impact of α becomes remarkable and the maximum benefits would be achieved at an intermediate range of α. Moreover, the computation efficiency of the proposed system is fast enough and can be implemented in real-time in the near future.

Automated Registration of 3-D Knee Implant Models to Fluoroscopic Images Using Lipschitzian Optimization.

This paper describes an automated method for registering 3-D models of metallic knee implants to single-plane radiographic images. We develop a multistage approach that identifies the correct pose by matching altered dilations of an edge-detected image with the silhouette of an implant model. The location of the similarity function's minimum is found using a novel optimization routine that combines the Dividing Rectangles algorithm with properties of the registration metric. Depending on the implant type (tibial or femoral), this technique reliably converges under maximum displacements of approximately 25 to 55 millimeters for translation components and 25° to 55° for Euler angles. The method proves to be robust to noise from bones and soft tissue. After an initial guess for the first image in the sequence, subsequent frames can be automatically registered from the optimum pose in the previous image.

A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics

We present a modification of the DIRECT (DIviding RECTangles) algorithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem, since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema and unavailable derivatives. DIRECT performs a sampling of the feasible domain over a set of points that becomes dense in the limit, thus ensuring the everywhere dense convergence; however, it becomes ineffective on significant instances of the problem under consideration, because it tends to produce a uniform coverage of the feasible domain, by oversampling regions that are far from the optimal solution. DIRECT has been modified by embodying information provided by a suitable discretization of the feasible domain, based on the signal theory, which takes into account the variability of the objective function. Numerical experiments show that DIRECT-G largely outperforms DIRECT and the grid search, the latter being the reference algorithm in the astrophysics community. Furthermore, DIRECT-G is comparable with a genetic algorithm specifically developed for the problem. However, DIRECT-G inherits the convergence properties of DIRECT, whereas the genetic algorithm has no guarantee of convergence.

A Global Maximum Power Point Tracking Scheme Employing DIRECT Search Algorithm for Photovoltaic Systems

This paper presents a maximum power point tracking approach for a photovoltaic system using the dividing rectangles algorithm. The new approach overcomes some weaknesses of the existing methods such as the perturb and observe method as it is capable of searching for global maximum. This is particularly important for a system that is partially shaded. To validate the performance of the proposed scheme, experimental studies have been conducted. The results have shown that the proposed approach is robust and possesses a fast tracking speed.

Phase Distortion Estimation by DIRECT and Spline Interpolation Algorithms

An important cause of performance loss in source localization in underwater acoustics is that towed flexible antennas deviate from the assumed rectilinear shape. In this work, the localization of sources in presence of phase errors is studied. Cancellation of phase errors is necessary to solve the source-localization problem. A previous work led to interesting results for antennas composed of a few sensors. We propose here a novel algorithm which is adapted to the antennas composed of a large number of sensors, keeping a small computational load. Our method is based on an orthogonality property between signal and noise subspaces and a novel optimization method: the robust dividing rectangles algorithm accelerated by spline interpolation. The performances of the proposed method are illustrated by applying it to the characterization of three sources.