Multi-directional Search Algorithm Research Articles

Multi-Directional Search

In the Multi-Agent Meeting (MAM) problem, the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding optimal meeting locations for multiple agents. A number of admissible heuristics are proposed and experiments demonstrate the benefits of MM*.

An Artificial Neural Network Genetic Algorithm with Shuffled Frog Leap Algorithm for Software Defect Prediction

Defect prediction performances are significant to attain quality of the software and to understand previous errors. In this work, for assessing the classification accuracy, precision, and recall and F measure for various classifiers are used. The artificial neural network optimizations make the assumption that more than two algorithms for one optimization have been implemented. The optimization makes use of a heuristic for choosing the best of the algorithms for being applied in a particular situation. An approach of hybrid optimization for designing of the linkages method and is used for the dimensional synthesis of the mechanism. The ANN models are assisted in their convergence towards a global minimum by the multi-directional search algorithm that is incorporated in the GA. The results have shown an accuracy of classification of the NN-hybrid shuffled from algorithm to perform better by about 5.94% than that of the fuzzy classifiers and by about 3.59% of the NN-Lm training and by about 1.42% of the NN-shuffled frog algorithm..

An Artificial Neural Network Genetic Algorithm with Shuffled Frog Leap Algorithm for Software Defect Prediction

Defect prediction performances are significant to attain quality of the software and to understand previous errors. In this work, for assessing the classification accuracy, precision, and recall and F measure for various classifiers are used. The artificial neural network optimizations make the assumption that more than two algorithms for one optimization have been implemented. The optimization makes use of a heuristic for choosing the best of the algorithms for being applied in a particular situation. An approach of hybrid optimization for designing of the linkages method and is used for the dimensional synthesis of the mechanism. The ANN models are assisted in their convergence towards a global minimum by the multi-directional search algorithm that is incorporated in the GA. The results have shown an accuracy of classification of the NN-hybrid shuffled from algorithm to perform better by about 5.94% than that of the fuzzy classifiers and by about 3.59% of the NN-Lm training and by about 1.42% of the NN-shuffled frog algorithm..

Compressor Design optimization for a High speed Jet engine

This is a study that is focused on developing an individual design methodology for a centrifugal jet and generating a mixed flow jet for a small turbojet engine by using this methodology. The structure of the methodology is based on the design, modelling and the optimization processes, which are operated sequentially. The design process consists of engine design and compressor design codes operated together with a commercial design code. Design of Experiment methods and an in-house Neural Network code is used for the modelling phase. The optimization is based on an in-house code which is generated based on multidirectional search algorithm. The optimization problem is constructed by using the in house parametric design codes of the engine and the compressor. The goal of the optimization problem is to reach an optimum design which gives the best possible combination of the thrust and the fuel consumption for a small turbojet engine. The final combination of the design parameters obtained from the optimization study are used in order to generate the final design with the commercial design code. On the last part of the thesis a comparison of the final design and a standard radial flow jet is made in order to clarify the benefit of the study. The results have been showed that a mixed flow compressor design is superior to a standard radial flow compressor in a small turbojet application.

Electromagnetic Imaging of Dielectric Objects Using a Multi-Directional Search-Based Simulated Annealing.

In this paper, we introduce a global optimization method that is a novel combination of the simulated annealing method and the multi-directional search algorithm. We demonstrate the use of the algorithm for a microwave-imaging system to obtain the electrical properties of objects. The proposed global optimizer significantly improves the performance and speed of the simulated annealing method by utilizing a nonlinear simplex search, starting from an initial guess, and taking effective steps in obtaining the global solution of the minimization problem. Due to the efficient performance of the proposed global optimization method, we are able to obtain the shape, location, and material properties of the target without considering any a priori information about them. The accuracy and applicability of the proposed imaging method is demonstrated with some numerical results in which two-dimensional images of multiple objects are successfully reconstructed.

Multi-directional bat algorithm for solving unconstrained optimization problems

In this paper, we propose a new hybrid algorithm for solving unconstrained global optimization problems by hybridizing the bat algorithm with multi-directional search algorithm (MDS). We call the proposed algorithm by multi-directional bat algorithm (MDBAT). In MDBAT algorithm, we try to overcome the slow convergence of the bat algorithm as a metaheuristic algorithm by invoking one of the promising direct search algorithm which is called MDS algorithm. The bat algorithm has a good ability to make exploration and exploitation search while the MDS has a good ability for accelerating convergence on the region of optimal response. In the beginning, the standard bat algorithm starts the search for number of iterations then the MDS algorithm starts its search from bat algorithm found so far. The combination between the standard bat algorithm and the MDS algorithm helps the MDS algorithm to start the search from a good solution instead of the random initial solution. The MDS algorithm can accelerate the search of the proposed algorithm instead of letting the algorithm running for more iterations without any improvement. We investigate the general performance of the MDBAT algorithm by applying it on 16 unconstrained global optimization problems and comparing it against 8 benchmark algorithms. The experimental results indicate that MDBAT is a promising algorithm and outperforms the other algorithms in most cases.

RSCS: A Parallel Simplex Algorithm for the Nimrod/O Optimization Toolset

This paper describes a method of parallelisation of the popular Nelder-Mead simplex optimization algorithms that can lead to enhanced performance on parallel and distributed computing resources. A reducing set of simplex vertices are used to derive search directions generally closely aligned with the local gradient. When tested on a range of problems drawn from real-world applications in science and engineering, this reducing set concurrent simplex (RSCS) variant of the Nelder-Mead algorithm compared favourably with the original algorithm, and also with the inherently parallel multidirectional search algorithm (MDS). All algorithms were implemented and tested in a general-purpose, grid-enabled optimization toolset.

Sparse Radiographic Tomography and System Identification Imaging from Single View, Multiple Time Sample Density Plots

Abstract Tomography is a classic inverse problem in which multiple density projections of an object are processed to infer some approximation of the original. We consider the highly sparse inverse problem of single angle projection, but seek to reduce the ambiguity through multiple time observations in a dynamic system of known or partially known dynamics. In this work we solve the planar problem by optimization techniques based on a gradient-free multi-directional search algorithm to minimize our nonlinear functional. We demonstrate convincingly successful numerical examples to support our relatively simple technique.

Parameter estimation in thermalhydraulic models using the multidirectional search method

Some uncertainty is introduced in the simulation of the behavior of a nuclear power plant because some of the parameters of the models used for the simulation are undefined or unknown. The values of these parameters are usually determined by the analyst using their own judgement and thus a user effect is introduced into the simulation process. The uncertainty caused by user effects may be mitigated by the utilization of an automatic and systematic search and optimization method to estimate parameters for the simulation model of a particular plant. The multidirectional search algorithm is proposed as an optimization technique. Two different applications have been studied which successfully show the applicability of the optimization methodology. First, the methodology is applied using the RELAP5 code to determine the best boundary conditions to simulate an experiment performed at the facility of the Royal Institute of Technology. The second application consists of the development of a two loop reduced PWR reactor model and the determination of some of its effective parameters to adjust the reduced model behavior to a given reference associated with particular operational transients.

Implementation of the multidirectional search algorithm on an automated chemistry workstation. A parallel yet adaptive approach for reaction optimization

We have developed an experiment-planning module for applying a powerful new pattern search algorithm toward the problems of reaction investigation and optimization. The experiment planner works in conjunction with a closed-loop automated chemistry workstation equipped for parallel experimentation. The new algorithm, developed by Torczon for parallel computation of mathematical functions, achieves a focused yet parallel approach to finding regions of improved response. Like a full factorial design, the search space involves a regular grid of points. Like the Simplex algorithm, the multidirectional search (MDS) algorithm uses the movement of a simplex through a search space. However, with each movement all points except the single best are discarded, whereas the Simplex algorithm discards only the one worst point. Thus, in an n-dimensional space, the MDS algorithm projects n mandatory points at every cycle (beyond the initial). In addition, a larger number of exploratory points are identified by look-ahead projection of possible future simplices. Such exploratory points lie on multiple independent lines of search. The responses for the mandatory and exploratory points are acquired via parallel experimentation, with the latter points examined to the extent that the workstation has available capacity during the same schedule. The data from such exploratory points can be used in later cycles of experimentation, accelerating convergence on the region of optimal response. In the case of unlimited parallel experimentation capacity, all possible points in the space are projected, as in a full factorial design. The MDS algorithm thus adapts to the available parallel capacity of the workstation. The MDS planning module includes options for specifying initial points, stop criteria, and early-termination processes. Provisions are included for parallel scheduling of batches of experiments, convergence of the search, and movement at the boundaries of the search space. An MDS investigation can thus be implemented with global decision-making concerning movements through a search space, and local decision-making concerning termination of individual experiments. The MDS algorithm enables directed evolutionary searches in a parallel mode and is ideally suited for rapid optimization of chemical reactions using a microscale automated chemistry workstation.

On the Convergence of the Multidirectional Search Algorithm

This paper presents the convergence analysis for the multidirectional search algorithm, a direct search method for unconstrained minimization. The analysis follows the classic lines of proofs of convergence for gradient-related methods. The novelty of the argument lies in the fact that explicit calculation of the gradient is unnecessary, although it is assumed that the function is continuously differentiable over some subset of the domain. The proof can be extended to treat most nonsmooth cases of interest; the argument breaks down only at points where the derivative exists but is not continuous. Finally, it is shown how a general convergence theory can be developed for an entire class of direct search methods—which includes such methods as the factorial design algorithm and the pattern search algorithm—that share a key feature of the multidirectional search algorithm.