Albert A. Groenwold

A Study of Global Optimization Using Particle Swarms

Abstract.A number of recently proposed variants of the particle swarm optimization algorithm (PSOA) are applied to an extended Dixon-Szeg und constrained test set in global optimization. Of the variants considered, it is shown that constriction as proposed by Clerc, and dynamic inertia and maximum velocity reduction as proposed by Fourie and Groenwold, represent the main contenders from a cost efficiency point of view. A parameter sensitivity analysis is then performed for these two variants in the interests of finding a reliable general purpose off-the-shelf PSOA for global optimization. In doing so, it is shown that inclusion of dynamic inertia renders the PSOA relatively insensitive to the values of the cognitive and social scaling factors.

Global search for critical failure surface in slope stability analysis

Soil slope stability problems in engineering works are often analyzed using limiting equilibrium methods. A number of methods are based on the method of vertical slices in which assumptions about the geometry of the failure surface are made. For homogeneous soils the assumed failure surface is often of a regular shape, but for a layered profile the shape of the failure surface is more complex, making it difficult to find the critical failure surface. This paper describes the use of a global optimization algorithm for determining the critical failure surface in slope stability analyses. An important feature of this new method it that no assumptions are required with regards to the geometry of the failure surface and no restrictions are placed on the positions of the initiation and termination point. As a result the solution is completely general. Janbus simplified method and Spencers method are used to demonstrate the new approach of formulating this programming problem.

An efficient 4‐node 24 D.O.F. thick shell finite element with 5‐point quadrature

A 4‐node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D‐SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin. The part of the stiffness matrix associated with in—plane displacements and rotations is integrated over the element domain by a modified 5‐point reduced integration scheme, resulting in greater efficiency without the sacrifice of rank sufficiency. The scheme produces a soft higher order deformation mode which increases numerical accuracy. A large number of standard benchmark problems are analyzed. Some examples show that the effectiveness of a previously proposed “membrane locking correction” technique is significantly reduced when employing distorted elements. However, the element is shown to be generally accurate and in many cases superior to existing elements.

A pseudo-discrete rounding method for structural optimization

A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denotedselective dynamic rounding, is presented. The method is based on the sequential rounding of a continuous solution and is in its current form used for the optimal discrete sizing design of truss structures. A simple criterion based on discrete variable proximity is proposed for selecting the sequence in which variables are to be rounded, and allowance is made for both upward and downward rounding. While efficient in terms of the required number of function evaluations, the method is also effective in obtaining a low discrete approximation to the global optimum. Numerical results are presented to illustrate the effectiveness and efficiency of the method.

Global Optimization using Dynamic Search Trajectories

Two global optimization algorithms are presented. Both algorithms attempt to minimize an unconstrained objective function through the modeling of dynamic search trajectories. The first, namely the Snyman–Fatti algorithm, originated in the 1980s and still appears an effective global optimization algorithm. The second algorithm is currently under development, and is denoted the modified bouncing ball algorithm. For both algorithms, the search trajectories are modified to increase the likelihood of convergence to a low local minimum. Numerical results illustrate the effectiveness of both algorithms.

Optimal discrete sizing of truss structures subject to buckling constraints

The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckling constraints. The algorithm begins with a continuous optimum followed by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predicted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for those variables fixed on discrete values in each intermediate mixed-discrete nonlinear problem. It is shown that a continuous design based on the regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A range of examples is used to illustrate that with “conservative” regression, discrete designs can be achieved which are significantly lighter than those in which the variables have been rounded up.

OPTIMAL SIZING DESIGN OF TRUSS STRUCTURES USING THE PARTICLE SWARM OPTIMIZATION ALGORITHM

The optimal sizing design of truss structures is studied using the recently proposed particle swarm optimization algorithm (PSOA), in which the social behavior of birds is mimicked. Individual birds in a flock exchange information about their position, velocity and fitness, and the behavior of the flock is then influenced to increase the probability of migration to regions of high fitness. A simple approach is presented to accommodate the stress and displacement constraints during initial stages of the swarm searches. In this approach, increased social pressure, at the cost of cognitive learning, is exerted on infeasible birds to increase their rate of migration to feasible regions. Numerical results are presented for a number of well known test functions, with dimensionality of up to 21.

Optimal structural design of a planar parallel platform for machining

Abstract Parallel manipulators have many advantages over traditional serial manipulators. These advantages include high accuracy, high stiffness and high load-to-weight ratio, which make parallel manipulators ideal for machining operations where high accuracy is required to meet the requirements that modern standards demand. Recently, the finite element method has been used by some workers to determine the stiffness of spatial manipulators. These models are mainly used to verify stiffness predicted using kinematic equations, and are restricted to relatively simple truss-like models. In this study, state-of-the-art finite elements are used to determine the out of plane stiffness for parallel manipulators. Euler–Bernoulli beam elements and flat shell elements with drilling degrees of freedom are used to model the platform assembly. The main objective of this study is to quantify the stiffness, particularly the out of plane stiffness, of a planar parallel platform to be used for machining operations. The aim is to obtain a design that is able to carry out machining operations to an accuracy of 10 μm for a given tool force. Reducing the weight of a parallel manipulator used in machining applications has many advantages, e.g. increased maneuverability, resulting in faster material removal rates. Therefore the resulting proposed design is optimized with respect to weight, subject to displacement and stress constraints to ensure feasible stiffness and structural integrity. The optimization is carried out by means of two gradient-based methods, namely LFOPC and Dynamic-Q.

A 24 d.o.f. four‐node flat shell finite element for general unsymmetric orthotropic layered composites

The constitutive relationship of a four‐node flat shell finite element with six degrees of freedom per node and a modified five‐point quadrature, previously presented by the authors, is extended to include symmetric and unsymmetric orthotropy. Through manipulation of the kinematic assumptions, provision is made for out‐of‐plane warp. A wide range of membrane and thin to moderately thick plate and shell examples are used to demonstrate the accuracy and robustness of the resulting element.

Multiple Parallel Local Searches in Global Optimization

The unconstrained global programming problem is addressed using an efficient multi-start algorithm, in which parallel local searches contribute towards a Bayesian global stopping criterion. n nThe stopping criterion, denoted the unified Bayesian global stopping criterion, is based on the mild assumption that the probability of convergence to the global optimum x* is comparable to the probability of convergence to any local minimum xj. n nThe combination of the simple multi-start local search strategy and the unified Bayesian global stopping criterion outperforms a number of leading global optimization algorithms, for both serial and parallel implementations. Results for parallel clusters of up to 128 machines are presented.