Dimension Of Search Space Research Articles

Linear Algebraic Beamforming Design for Multiuser MISO Interference Channels: A Reduction in Search Space Dimension.

Near-optimal transmit beamformers are designed for multiuser multiple-input single-output interference channels with slowly time-varying block fading. The main contribution of this article is to provide a method for deriving closed-form solutions to effective beamforming in both low and high signal-to-noise ratio regimes. The proposed method basically leverages side information obtained from the channel correlation between adjacent coding blocks. More specifically, our methodology is based on a linear algebraic approach, which is more efficient than the optimal scheme based on the Gaussian input in the sense of reducing the average number of search space dimensions for designing the near-optimal transmit beamformers. The proposed method is shown to exhibit near-optimal performance via computer simulations in terms of the average sum-rate.

GalaxyGPCRloop: Template-Based and Ab Initio Structure Sampling of the Extracellular Loops of G-Protein-Coupled Receptors.

The second extracellular loops (ECL2s) of G-protein-coupled receptors (GPCRs) are often involved in GPCR functions, and their structures have important implications in drug discovery. However, structure prediction of ECL2 is difficult because of its long length and the structural diversity among different GPCRs. In this study, a new ECL2 conformational sampling method involving both template-based and ab initio sampling was developed. Inspired by the observation of similar ECL2 structures of closely related GPCRs, a template-based sampling method employing loop structure templates selected from the structure database was developed. A new metric for evaluating similarity of the target loop to templates was introduced for template selection. An ab initio loop sampling method was also developed to treat cases without highly similar templates. The ab initio method is based on the previously developed fragment assembly and loop closure method. A new sampling component that takes advantage of secondary structure prediction was added. In addition, a conserved disulfide bridge restraining ECL2 conformation was predicted and analytically incorporated into sampling, reducing the effective dimension of the conformational search space. The sampling method was combined with an existing energy function for comparison with previously reported loop structure prediction methods, and the benchmark test demonstrated outstanding performance.

Ensemble Kalman filter inference of spatially-varying Manning’s n coefficients in the coastal ocean

Ensemble Kalman (EnKF) filtering is an established framework for large scale state estimation problems. EnKFs can also be used for state-parameter estimation, using the so-called “Joint-EnKF” approach. The idea is simply to augment the state vector with the parameters to be estimated and assign invariant dynamics for the time evolution of the parameters. In this contribution, we investigate the efficiency of the Joint-EnKF for estimating spatially-varying Manning’s n coefficients used to define the bottom roughness in the Shallow Water Equations (SWEs) of a coastal ocean model.Observation System Simulation Experiments (OSSEs) are conducted using the ADvanced CIRCulation (ADCIRC) model, which solves a modified form of the Shallow Water Equations. A deterministic EnKF, the Singular Evolutive Interpolated Kalman (SEIK) filter, is used to estimate a vector of Manning’s n coefficients defined at the model nodal points by assimilating synthetic water elevation data. It is found that with reasonable ensemble size (O(10)), the filter’s estimate converges to the reference Manning’s field. To enhance performance, we have further reduced the dimension of the parameter search space through a Karhunen-Loéve (KL) expansion. We have also iterated on the filter update step to better account for the nonlinearity of the parameter estimation problem. We study the sensitivity of the system to the ensemble size, localization scale, dimension of retained KL modes, and number of iterations. The performance of the proposed framework in term of estimation accuracy suggests that a well-tuned Joint-EnKF provides a promising robust approach to infer spatially varying seabed roughness parameters in the context of coastal ocean modeling.

An efficient aerodynamic shape optimization of blended wing body UAV using multi-fidelity models

This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation models. The wing aerodynamic shape optimization problem is solved by dividing optimization into three steps—modeling 3D (high-fidelity) and 2D (low-fidelity) models, building global meta-models from prominent instead of all variables, and determining robust optimizing shape associated with tuning local meta-models. The adaptive robust design optimization aims to modify the shape optimization process. The sufficient infilling strategy—known as adaptive uniform infilling strategy—determines search space dimensions based on the last optimization results or initial point. Following this, 3D model simulations are used to tune local meta-models. Finally, the global optimization gradient-based method—Adaptive Filter Sequential Quadratic Programing (AFSQP) is utilized to search the neighborhood for a probable optimum point. The effectiveness of the proposed method is investigated by applying it, along with conventional optimization approach-based meta-models, to a Blended Wing Body (BWB) Unmanned Aerial Vehicle (UAV). The drag coefficient is defined as the objective function, which is subjected to minimum lift coefficient bounds and stability constraints. The simulation results indicate improvement in meta-model accuracy and reduction in computational time of the method introduced in this paper.

Economic optimization of Organic Rankine cycle with pure fluids and mixtures for waste heat and solar applications using particle swarm optimization method

The optimization criterion for designing the thermodynamic layout of an organic Rankine cycle is often based on either achieving maximum thermodynamic efficiency or incurring minimum initial specific investment costs. Such designs, however, need not lead to the maximum utilization of waste heat potential or an optimal investment. For full potential utilization of a waste heat source, its temperature should be brought down to near ambient temperatures via transfer of enthalpy to the organic Rankine cycle working fluid. In the limit, however, pursuit of complete source utilization may lead to capital intensive organic Rankine cycle layouts that demand infinitesimal temperature gradients in heat exchangers leading to massive heat transfer areas. This paper defines a new objective function that reveals the tradeoffs between specific investment cost and the extent to which waste heat is utilized. A particle swarm optimization algorithm is used to optimize 7 and 8 dimensional search space for pure and mixture based working fluids, respectively, for case studies involving power capacities of 5, 50 and 500 kWe, waste heat source temperatures ranging from 75 to 275 °C and a number of working fluids. As a practical aid to designers, a methodology for generating high isentropic efficiency scroll geometries corresponding to optimized cycles is presented, and the optimization analysis is further extended to solar thermal applications.

Neural network and fuzzy system for the tuning of Gravitational Search Algorithm parameters

A good trade-off between exploration and exploitation to find optimal values in search algorithms is very hard to achieve. On the other hand, the combination of search methods may cause computational complexity increase problems. The Gravitational Search Algorithm (GSA) is a swarm optimization algorithm based on the law of gravity, where the solution search process depends on the velocity of particles. The application of intelligent techniques can improve the search performances of GSA. This paper proposes the design of a Neuro and Fuzzy Gravitational Search Algorithm (NFGSA) to achieve better results than GSA in terms of global optimum search capability and convergence speed, without increasing the computational complexity. Both the algorithms have the same computational complexity O(nd), where n is the number of agents and d is the search space dimension. The main task of the designed intelligent system is to adjust a GSA parameter on a revised version of GSA. NFGSA is compared with GSA, a Plane Surface Gravitational Search Algorithm (PSGSA) and a Modified Gravitational Search Algorithm (MGSA). The results show that NFGSA improves the optimization performances of GSA and PSGSA, without adding computational costs. Moreover, the proposed algorithm is better than MGSA for a benchmark function and achieves similar results for two test functions. The analysis on the computational complexity shows that NFGSA has a better computational complexity than MGSA, because NFGSA has complexity O(nd), whereas MGSA has complexity O((nd)2).

Generalized Grover’s Algorithm for Multiple Phase Inversion States

Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator inverts the sign on only one state. Here we provide an exact solution to the problem of performing Grover's search where the Grover operator inverts the sign on N states. We show the underlying structure in terms of the eigenspectrum of the generalized Hamiltonian, and derive an appropriate initial state to perform the Grover evolution. This allows us to use the quantum phase estimation algorithm to solve the search problem in this generalized case, completely bypassing the Grover algorithm altogether. We obtain a time complexity of this case of sqrt[D/M^{α}], where D is the search space dimension, M is the number of target states, and α≈1, which is close to the optimal scaling.

A comparative study of the A* heuristic search algorithm used to solve efficiently a puzzle game

The puzzle game presented in this paper consists in polyhedra (prisms, pyramids or pyramidal frustums) which can be moved using the free available spaces. The problem requires to be found the minimum number of movements in order the game reaches to a goal configuration starting from an initial configuration. Because the problem is enough complex, the principal difficulty in solving it is given by dimension of search space, that leads to necessity of a heuristic search. The improving of the search method consists into determination of a strong estimation by the heuristic function which will guide the search process to the most promising side of the search tree. The comparative study is realized among Manhattan heuristic and the Hamming heuristic using A* search algorithm implemented in Java. This paper also presents the necessary stages in object oriented development of a software used to solve efficiently this puzzle game. The modelling of the software is achieved through specific UML diagrams representing the phases of analysis, design and implementation, the system thus being described in a clear and practical manner. With the purpose to confirm the theoretical results which demonstrates that Manhattan heuristic is more efficient was used space complexity criterion. The space complexity was measured by the number of generated nodes from the search tree, by the number of the expanded nodes and by the effective branching factor. From the experimental results obtained by using the Manhattan heuristic, improvements were observed regarding space complexity of A* algorithm versus Hamming heuristic.

A highly accurate differential evolution–particle swarm optimization algorithm for the construction of initial value problem solvers

ABSTRACTIn this work a new evolutionary computation technique is introduced for the construction of initial value solvers based on Runge–Kutta (RK) pairs. The derivation of RK pairs corresponds to solving a nonlinear optimization problem with a multimodal objective function in a high dimensional search space; additional difficulty stems from the fact that only solutions with accuracy at least equal to machine epsilon are acceptable. The proposed approach involves hybridizing a Differential Evolution (DE) strategy with elements from Particle Swarm Optimization (PSO) in order to produce a method for solving optimization problems with high accuracy. The resulting methodology is applied to two different problems of RK pair derivation of orders 5 and 4 and compared with standard DE techniques. Numerical experiments show that the proposed hybrid DE-PSO satisfies the strict accuracy requirements imposed by the particular problem, while outperforming its rivals.

Capacity of finite secondary cognitive radio networks: Bounds and optimizations

Though there are works that show the asymptotic capacity bounds in a wireless network considering interference constraints from all transmitting nodes, there are no such evaluation of capacity bounds for finite secondary cognitive radio networks where the primaries pose additional constraints. In this paper, we find the bounds for the maximum achievable capacity of a randomly deployed secondary cognitive radio network with finite number of nodes in the presence of primary users, i.e., in the underlay mode. Since solving the functional constrained optimization problem of maximizing the secondary network’s capacity subject to other radio constraints is computationally complex, we derive analytical bounds for the solution. That is achieved by deriving a pre-engineered deployment with the best possible pairings of transmitters and receivers, from the random deployment. The capacity of the former is used to upper bound the capacity of the latter. The bounds are based on the maximum signal to interference and noise ratio (SINR) of all transmitter-receiver pairs and their geometrical placement. The derived bounds provide an insight about the network’s maximum and minimum achievable capacities since solving the optimization problem shows in-scalability both in time and search space dimensionality. To this end, we reduce the optimizer’s search space by eliminating transmitters and receivers that do not contribute positively to the system capacity. Such reduction depends on primary transmit power, primary’s interference tolerance, and mutual distances between primaries and secondaries. Further, we propose a metric that gives the relative goodness of node pairs for being potential winners for power allocation from the global power optimizer. The metric also facilitates certain trade-offs such as achieving optimal capacity using all nodes or better execution time using a partial set of nodes (expected winners). We show how the metric along with the elimination schemes can be used for pre-processing (search space dimension reduction) the input power vector before it is fed to any power optimizer. Through simulation results we show the theoretical bounds and the capacity obtained via the proposed optimizations. We also show the gains obtained due to search space reduction.

Efficient number of calibrated cross sections bottom levels on a hydrodynamic model using the SCE-UA algorithm. Case study: Madeira River

ABSTRACT Hydrodynamic models are important tools for simulating river water level and flow. A considerable fraction of the hydrodynamic model errors are related to parameters uncertainties. As cross sections bottom levels considerably affect water level simulation, this parameter has to be well estimated for flood studies. Automatic calibration performance and processing time depend on the search space dimension, which is related to the number of calibrated parameters. This paper shows the application of the Shuffled Complex Evolution (SCE-UA) optimization algorithm to assess the number of cross sections bottom levels used in calibration. Also was evaluated the extent of algorithm exploration regarding computational processing time and accuracy. It was tested the calibration of 2, 4, 7 and 10 cross sections bottom levels (2PAR, 4PAR, 7PAR and 10PAR calibration configurations) of a 1,100 km reach of the Madeira River. 7PAR and 10PAR representation had better fitness (lower objective function value) on cross sections used for calibration; however, the error on other cross sections (2 validation gauging stations) was higher than 2PAR and 4PAR calibration. The short number (5) of gauging stations used in calibration has limited the number of calibrated parameters to represent adequately the river level profile. Finally, this paper shows a contribution for the parsimonious selection of parameters regarding the spatial distribution of observation sites used in calibration.

A two stage grading approach for feature selection and classification of microarray data using Pareto based feature ranking techniques: A case study

High dimensional search space in microarray data with large number of genes and few dozen of samples increases the complexity of analysis of such databases. All the genes are not significant and hence informative genes are required to be extracted. So dimension reduction is necessary for this process. It is often found in literature that the ranking approaches are used for feature selection. Different ranking techniques may assign different rank to the same gene and the selection made based on these ranks may not be suitable for different problems. So use of one ranking technique may lead to rejection of some important genes and possibly selection of some insignificant genes. Such selection may degrade the performance of the classifier. To overcome this problem, here abi-objective ranked based Pareto front technique is proposed. In this technique using two ranked based technique the Pareto optimal solution is generated with a set of features. For the experimental work, 21 models based on 7 feature ranking strategies are considered. Eight different microarray data are taken to find the suitable ranking combination for the work. A grading method is used to rank the models and statistical test is performed to validate the findings.

A population-based fast algorithm for a billion-dimensional resource allocation problem with integer variables

Among various complexities affecting the performance of an optimization algorithm, the search space dimension is a major factor. Another key complexity is the discreteness of the search space. When these two complexities are present in a single problem, optimization algorithms have been demonstrated to be inefficient, even in linear programming (LP) problems. In this paper, we consider a specific resource allocation problem constituting to an integer linear programming (ILP) problem which, although comes from a specific industry, is similar to other practical resource allocation and assignment problems. Based on a population based optimization approach, we present a computationally fast method to arrive at a near-optimal solution. Compared to two popular softwares (glpk,Makhorin, 2012 and CPLEX,Gay, 2015), which are not able to handle around 300 and 2000 integer variables while continuing to run for hours, respectively, our proposed method is able to find a near-optimal solution in less than second on the same computer. Moreover, the main highlight of this study is to propose a customized population based optimization algorithm that scales in almost a linear computational complexity in handling 50,000 to one billion (109) variables. We believe that this is the first time such a large-sized real-world constrained problem is ever handled using any optimization algorithm. We perform sensitivity studies of our method for different problem parameters and these studies clearly demonstrate the reasons for such a fast and scale-up application of the proposed method.

Truss structure damage identification using residual force vector and genetic algorithm

In this paper, damage detection has been introduced as an optimization problem and a two-step method has been proposed that can detect the location and severity of damage in truss structures precisely and reduce the volume of computations considerably. In the first step, using the residual force vector concept, the suspected damaged members are detected which will result in a reduction in the number of variables and hence a decrease in the search space dimensions. In the second step, the precise location and severity of damage in the members are identified using the genetic algorithm and the results of the first step. Considering the reduced search space, the algorithm can find the optimal points (i.e. the solution for the damage detection problem) with less computation cost. In this step, the Efficient Correlation Based Index (ECBI), that considers the structure\'s first few frequencies in both damaged and healthy states, is used as the objective function and some examples have been provided to check the efficiency of the proposed method; results have shown that the method is innovatively capable of detecting damage in truss structures.

Mutated IWO Optimized 4-D Array for Femtocell Cognitive Radio

This letter presents the design and optimization of a four-dimensional (4-D) time-modulated linear array to be used in harmonic beamforming-based femtocell cognitive radio network. A novel mutated invasive weed optimization (MIWO) algorithm, where remarkable performance enhancement is achieved especially in the case of problems involving higher dimensional search space through attainment of simultaneous exploration and exploitation, is introduced in this purpose. Moreover, a subarrayed approach is adopted to gain control over beam direction of the main band as well as all the harmonics being used. The reduced search range for each subarray is analytically determined to make the MIWO search faster and more effective.

A novel teaching-learning based optimization approach for design of broad-band anti-reflection coatings

Abstract The design of thin-film multilayered anti-reflection (AR) coating is quite an intricate task due to highly nonlinear and complex dimensional search space, which includes many local minima. In this paper, a novel teaching-learning based optimization (TLBO) approach is employed to design ultra-low reflective coating over a broad wavelength-band using multilayer thin-film structures for optoelectronic devices. The algorithm is implemented using LabVIEW as a programming tool. Various design specific input parameters such as scanning range of wavelengths, step-size, angle of incidence, number of layers, the name and sequence of coating materials etc. are required to be fed by the user on the graphical user interface. The algorithm minimizes the average reflectivity computed over given wavelength range by tuning the thickness of layers in the multilayer stack. The reliability and evolution of design solution with iterations have been systematically investigated for different learner-sizes. Finally, using the optimized learner size and desired number of iterations, the optimum AR design is obtained in terms of the thickness of each layer for the multilayer AR coating. The effectiveness of the TLBO approach has been compared with that of an established algorithm, i.e. genetic algorithm (GA), by means of Wilcoxon singed ranked test. It is concluded that the TLBO can be a very efficient, simpler and relatively faster approach to address complex optimization problems such as broad-band AR coating designs.

Gradual and Cumulative Improvements to the Classical Differential Evolution Scheme through Experiments

Abstract The paper presents the experimental results of some tests conducted with the purpose to gradually and cumulatively improve the classical DE scheme in both efficiency and success rate. The modifications consisted in the randomization of the scaling factor (a simple jitter scheme), a more efficient Random Greedy Selection scheme, an adaptive scheme for the crossover probability and a resetting mechanism for the agents. After each modification step, experiments have been conducted on a set of 11 scalable, multimodal, continuous optimization functions in order to analyze the improvements and decide the new improvement direction. Finally, only the initial classical scheme and the constructed Fast Self-Adaptive DE (FSA-DE) variant were compared with the purpose of testing their performance degradation with the increase of the search space dimension. The experimental results demonstrated the superiority of the proposed FSA-DE variant.

An improved dynamic discrete firefly algorithm for blind image steganalysis

This paper presents an improved firefly algorithm (DyFA) for feature selection that improves the convergence rate and reduces computational complexity through dynamic adaptation in blind image steganalysis. The alpha and gamma parameters of the Firefly algorithm are made to vary dynamically with each generation for faster convergence. If firefly algorithm’s performance does not improve for certain numbers of iterations then the particles with the worst fitness function values are replaced with new particles in the search space and particle dimensions are reduced by eliminating redundant features. This approach is effective in reducing computational complexity and improving detection capability of the classifier. To further reduce the computational complexity a hybrid DyFA is designed by ensemble of a filter approach (t test + regression) and wrapper approach (DyFA) incrementally. In this study, support vector machine classifier with radial basis function kernel and ten fold cross validation is used to evaluate the effectiveness of the proposed Firefly algorithm. DyFA is compared with well-known wrapper feature selection algorithms. Experimental results are performed on datasets constructed from four steganography algorithms nsF5, Perturbed Quantization, Outguess and Steghide with subtractive pixel adjacency matrix (SPAM) feature vector from spatial domain and Cartesian Calibrated features extracted by Pevnýfeature vector from transform domain. Experimental results demonstrate that DyFA reduces computation time and improves classification accuracy as compared to other feature selection algorithms. Hybrid DyFA shows an improvement in classification accuracy and in eliminating redundant features in more than 85 % of cases with respect to hybrid GLBPSO.

Subpermutation-Based Evolutionary Multiobjective Algorithm for Load Restoration in Power Distribution Networks

This paper proposes a new multiobjective evolutionary algorithm for handling the problem of distribution network restoration after failures. The problem is formulated as a bi-objective optimization problem considering the total load restored and the time required for restoration. A new encoding scheme is proposed, in which the variables that encode the switch operation are separated into six groups, according to their roles in the faulty system configuration. Employing the idea of defining subspaces of a combinatorial space, those groups are used in order to define subpermutations within which the crossover and mutation operations are performed. In this way, the dimensionality of the search space becomes reduced, allowing a much more efficient search. The proposed encoding scheme also makes a single individual to encode several different solutions, leading to a further reduction of the search space dimensionality. Due to this peculiar feature of the encoding scheme, it becomes convenient to use an adaptation of the Strength Pareto Evolutionary Algorithm 2 , in which the raw fitness is modified in order to allow the assignment of fitness to individuals that simultaneously encode several different solutions. The proposed algorithm was implemented such that good solutions are delivered within low processing times, of the order of some minutes for large real systems.

Early Mission Design of Transfers to Halo Orbits via Particle Swarm Optimization

Particle Swarm Optimization (PSO) is used to prune the search space of a low-thrust trajectory transfer from a high-altitude, Earth orbit to a Lagrange point orbit in the Earth-Moon system. Unlike a gradient based approach, this evolutionary PSO algorithm is capable of avoiding undesirable local minima. The PSO method is extended to a “local” version and uses a two dimensional search space that is capable of reducing the computation run-time by an order of magnitude when compared with published work. A technique for choosing appropriate PSO parameters is demonstrated and an example of an optimized trajectory is discussed.