B. H. V. Topping

Improved genetic operators for structural engineering optimization

Abstract The initial motivation for the development of algorithms inspired by biological principles of evolution was the design and implementation of robust adaptive systems. Among the most utilized of these techniques are the Genetic Algorithms (GAs) which combine principles of population genetics and natural selection. Their growing popularity may be attributed to the ability of GAs as powerful function optimizers of general application to combinatorial problems that have been traditionally difficult to optimize. [1, 2] (De Jong, K. A. and Spears, W. M., Using genetic algorithms to solve NP-complete problems. In Proceedings of the Third International Conference on Genetic Algorithms , June 1989, pp. 124–132; Hurley, S., Using Genetic Algorithms Based Search in Optimization. The Institute of Mathematics and its Applications, Vol. 29, March/April 1993, pp. 43–46.) Considerable progress has been made in identifying the limitations of the GAs resulting in a range of approaches and modifications which attempt to improve the efficiency of the GAs as function optimizers. These adaptive approaches in such GA-based optimizers are in general tailored to classes of functions. The engineering optimization problems may be governed by different classes of functions which result in very complex design spaces. In this paper a general purpose optimization technique is investigated, the best of the traditional methods may perform well but only in a narrow class of problems. Revised genetic operators and a new recombination scheme are presented in this paper. These features respectively increase the exploratory power of the GA while simultaneously introducing additional selection pressure to increase the speed of convergence. These features are designed to ensure the balance between effective exploration and selective pressure to exploit the better solutions which are the main power behind the GAs. The gain of exploratory power not only extends the applicability of the method and improves the quality of the results but also helps prevent premature convergence. On the other hand, selective pressure applied locally may speed up the convergence while still refining the results. Finally, in order to map GAs onto engineering optimization problems, this paper draws some guidelines for handling the constraints using transformation methods.

Parallel adaptive mesh generation

Abstract Unstructured meshes have proved to be a powerful tool for adaptive remeshing of finite element idealizations. This paper presents a transputer-based parallel algorithm for two dimensional unstructured mesh generation. A conventional mesh generation algorithm for unstructured meshes is reviewed by the authors, and some program modules of sequential C source code are given. The concept of adaptivity in the finite element method is discussed to establish the connection between unstructured mesh generation and adaptive remeshing. After these primary concepts of unstructured mesh generation and adaptivity have been presented, the scope of the paper is widened to include parallel processing for un-structured mesh generation. The hardware and software used is described and the parallel algorithms are discussed. The Parallel C environment for processor farming is described with reference to the mesh generation problem. The existence of inherent parallelism within the sequential algorithm is identified and a parallel scheme for unstructured mesh generation is formulated. The key parts of the source code for the parallel mesh generation algorithm are given and discussed. Numerical examples giving run times and the consequent “speed-ups” for the parallel code when executed on various numbers of transputers are given. Comparisons between sequential and parallel codes are also given. The “speed-ups” achieved when compared with the sequential code are significant. The “speed-ups” achieved when networking further transputers is not always sustained. It is demonstrated that the consequent “speed-up” depends on parameters relating to the size of the problem.

Computer methods for the generation of membrane cutting patterns

Abstract Computer techniques for the generation of cutting patterns for membrane structures are reviewed. The two types of design systems under review are based on the dynamic relaxation and force density methods. With the dynamic relaxation system a geometric unfolding method is used to generate cutting patterns, whereas with the force density system a least squares minimization procedure is used to generate the cutting pattern. A new procedure for generating cutting patterns, using a two-dimensional dynamic relaxation analysis for each cloth, is proposed. Comparisons are undertaken for a standard test case and reassembled cloth strips are re-analysed and variations in stress compared.

Parallel processing neural networks and genetic algorithms

Abstract In an earlier paper [1] some recent developments in computational technology to structural engineering were described. The developments included: parallel and distributed computing; neural networks; and genetic algorithms. In this paper, the authors concentrate on parallel implementations of neural networks and genetic algorithms. In the final section of the paper the authors show how a parallel finite element analysis may be undertaken in an efficient manner by preprocessing of the finite element model using a genetic algorithm utilizing a neural network predictor. This preprocessing is the partitioning of the finite element mesh into sub-domains to ensure load balancing and minimum interprocessor communication during the parallel finite element analysis on a MIMD distributed memory computer.

Parallel computation schemes for dynamic relaxation

This paper describes a parallel algorithm for the dynamic relaxation (DR) method. The basic theory of the dynamic relaxation is briefly reviewed to prepare the reader for the parallel implementation of the algorithm. Some fundamental parallel processing schemes have been explored for the implementation of the algorithm. Geometric Parallelism was found suitable for the DR method when using transputer‐based systems. The evolution of the parallel algorithm is given by identifying the steps which may be executed in parallel. The structure of the parallel code is discussed and then described algorithmically. Two geometrically non‐linear parallel finite element analyses have been performed using different mesh densities. The number of processors was varied to investigate algorithm efficiency and speed ups. Using the results obtained it is shown that the computational efficiency increases when the computational load per processor is increased.

Parallel training of neural networks for finite element mesh decomposition

Abstract This paper describes a parallel processing implementation for neural computing and its application to finite element mesh decomposition. The parallelized neural network software developed is based on the public domain NASA developed program NETS 2.01, which is based on the back propagation algorithm of Rumelhart et al . [Learning internal representation by error propagation. In: Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Edited by D. E. Rummelhart and J. L. McClelland), Vol. 1: Foundations . MIT Press, MA (1986)]. The principal focus of this research concerns the parallel implementation. Comparisons between sequential and parallel versions are given. Finally a structural design problem concerned with finite element mesh generation is solved using the parallel neural network software.

Finite element mesh partitioning using neural networks

This paper examines the application of neural networks to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite element analysis. The use of the mean field annealing (MFA) technique, which is based on the mean field theory (MFT), for finding approximate solutions to the partitioning of the finite element meshes is investigated. The partitioning is based on the recursive bisection approach. The method of mapping the mesh bisection problem onto the neural network, the solution quality and the convergence times are presented. All computational studies were carried out using a single T800 transputer.

Parallel finite element analysis using Jacobi-conditioned conjugate gradient algorithm

In this paper a modified parallel Jacobi-conditioned conjugate gradient (CG) method is proposed for solving linear elastic finite element system of equations. The conventional element-by-element and diagonally conditioned approaches are discussed with respect to parallel implementation on distributed memory MIMD architectures. The effects of communication overheads on the efficiency of the parallel CG solver are considered and it is shown that for the efficient performance of a parallel CG solver, the interprocessor communication has to be carried out concurrently. A concurrent communication scheme is proposed by relating the semi-bandwidth of the stiffness matrix with the number of independent degrees of freedom and the number of processors and inducing directionalization of communication within the processor pipeline. With the aid of two examples the effectiveness of the proposed method is demonstrated showing that the cost of communication remains low and relatively insensitive to the increase in the number of processors.

Subdomain generation for parallel finite element analysis

Abstract This paper describes an optimization and artificial intelligence-based approach for solving the mesh partitioning problem in parallel finite element analysis. The problem of domain decomposition with reference to the mesh partitioning approach is described. Some current mesh partitioning approaches are discussed with respect to their limitations. The formulation of the optimization problem is presented. The theory for the mesh partitioning approach using an optimization and a predictive module is also described. It is shown that a genetic algorithm linked to a neural network predictive module may be used successfully to limit the computational load and the number of design variables for the decomposition problem. This approach does not suffer from the limitations of some current domain decomposition approaches, where an overall mesh is first generated and then partitioned. It is shown that by partitioning the coarse initial background mesh, near optimal partitions for finer graded (adaptive) meshes may be obtained economically. The use of the genetic algorithm for the optimization module and neural networks as the predictive module is described. Finally, a comparison between some current mesh partitioning algorithms and the proposed method is made with the aid of three examples, thus illustrating the feasibility of the method.

Parallel and distributed adaptive quadrilateral mesh generation

Abstract A parallel quadrilateral mesh generation using advanced front technology is presented in this paper. An improved quadrilateral mesh generation technology which uses the advancing front technology was introduced by the authors previously. This new quadrilateral mesh generation technique has been developed for use with parallel computing environments. The parallel code has been created by adapting the sequential code using each coarse quadrilateral as a sub-domain for remeshing. A transputer-based parallel system and a heterogeneous network of workstations using the parallel virtual machine system were employed. The use of these parallel environments to improve the efficiency of the proposed mesh generator was investigated. Some pre-processes have been introduced to ensure load balancing during the parallel mesh generation. A post processor has been developed to assist in the assembly of the distributed portions of the mesh. Four examples are presented to demonstrate the robustness and efficiency of this parallel mesh generator. Some nearly linear speed-up curves have been achieved for some large meshes by using up to 11 transputers.