A hybrid topology optimization algorithm for structural design

A hybrid algorithm for solving structural topology optimization problems is presented. This hybrid algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This hybrid algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value during the optimization. This hybrid algorithm has improved calculation efficiency and accelerated convergence when compared with the MMA or MGCMMA algorithm, which is demonstrated with three examples.     

Wave field reconstruction from multiple plane intensity-only data: augmented lagrangian algorithm

A complex-valued wave field is reconstructed from intensity-only measurements given at multiple observation planes parallel to the object plane. The phase-retrieval algorithm is obtained from the constrained maximum likelihood approach provided that the additive noise is gaussian. The forward propagation from the object plane to the measurement plane is treated as a constraint in the proposed variational setting of reconstruction. The developed iterative algorithm is based on an augmented lagrangian technique. An advanced performance of the algorithm is demonstrated by numerical simulations.     

A unified parametric design approach to structural shape optimization

This paper presents a general parametric design approach for 2-D shape optimization problems. This approach has been achieved by integrating practical design methodologies into numerical procedures. It is characterized by three features: (i) automatic selection of a minimum number of shape design variables based on the CAD geometric model; (ii) integration of sequential convex programming algorithms to solve equality constrained optimization problems; (iii) efficient sensitivity analysis by means of the improved semi-analytical method. It is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities. Numerical solutions are performed to demonstrate the applicability of the proposed approach. A discussion of the results is also given:     

An augmented lagrangian approach to material discontinuities in meshless methods

The purely nodal discretization, typical of meshless methods, turns out in the necessity of properly defining both the external boundary and the material interfaces which may be present in the analysis of mechanical problems. Each material domain is dicretized independently, and interface conditions are imposed into the variational formulation by the augmented Lagrangian method. This allows for a numerically efficient formulation where the number of approximation variables is unchanged by the presence of any number of interface constraints.     

A direct application of higher-order parametric programming techniques to structural optimization

Computational methods based on a sequence of parametric programming problems are presented for solving constrained optimization problems (COP) without any parameter. An auxiliary parametric programming problem (APPP) is formulated in order to solve COP. The procedure is started with an arbitrary initial solution which is the trivial solution of APPP corresponding to the initial value of the parameter. Then the optimal solution for the final value of the parameter, which is the optimal solution of COP, is estimated by Taylor's expansion with respect to the parameter where higher-order terms are incorporated. It is shown that the incorporation of the higher-order terms indeed leads to a faster convergence of the solution. As an extension of the method, a general algorithm is presented for optimum design problems with state variable constraints which are implicit functions of the design variables. Logarithmic penalty functions are incorporated and the weight coefficients for the penalty terms are updated continuously. The derivatives of the state variables with respect to the parameter and their sensitivity coefficients are expressed explicitly in terms of those of the design variables. Finally, a method of simultaneous analysis and optimization is developed for trusses with geometrical non-linearity.     

A surrogate assisted evolutionary optimization method with application to the transonic airfoil design

A multi-layer perceptron neural network (NN) method is used for efficient estimation of the expensive objective functions in the evolutionary optimization with the genetic algorithm (GA). The estimation capability of the NN is improved by dynamic retraining using the data from successive generations. In addition, the normal distribution of the training data variables is used to determine well-trained parts of the design space for the NN approximation. The efficiency of the method is demonstrated by two transonic airfoil design problems considering inviscid and viscous flow solvers. Results are compared with those of the simple GA and an alternative surrogate method. The total number of flow solver calls is reduced by about 40% using this fitness approximation technique, which in turn reduces the total computational time without influencing the convergence rate of the optimization algorithm. The accuracy of the NN estimation is considerably improved using the normal distribution approach compared with the alternative method.     

A new optimization algorithm for solving complex constrained design optimization problems

This article presents the performance of a very recently proposed Jaya algorithm on a class of constrained design optimization problems. The distinct feature of this algorithm is that it does not have any algorithm-specific control parameters and hence the burden of tuning the control parameters is minimized. The performance of the proposed Jaya algorithm is tested on 21 benchmark problems related to constrained design optimization. In addition to the 21 benchmark problems, the performance of the algorithm is investigated on four constrained mechanical design problems, i.e. robot gripper, multiple disc clutch brake, hydrostatic thrust bearing and rolling element bearing. The computational results reveal that the Jaya algorithm is superior to or competitive with other optimization algorithms for the problems considered.     

A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co-operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient-based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.     

A hybrid artificial neural network method with uniform design for structural optimization

This paper presents a new hybrid artificial neural network (ANN) method for structural optimization. The method involves the selection of training datasets for establishing an ANN model by uniform design method, approximation of the objective or constraint functions by the trained ANN model and yields solutions of structural optimization problems using the sequential quadratic programming method (SQP). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the objective or constraint functions and then provides an accurate estimation of the optimum solution. It is shown through three numerical examples that the proposed method provides accurate and computationally efficient estimates of the solutions of structural optimization problems.     

Minimax multiobjective optimization in structural design

The use of multiobjective optimization techniques, which may be regarded as a systematic sensitivity analysis, for the selection and modification of system parameters is presented. A minimax multiobjective optimization model for structural optimization is proposed. Three typical multiobjective optimization techniques—goal programming, compromise programming and the surrogate worth trade-off method—are used to solve such a problem. The application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper.     

A parallel triangular decomposition algorithm on a workstation network with application to structural vibration analysis

This paper presents a parallel triangular decomposition algorithm for banded symmetric matrices and its application to structural vibration analysis, which gives high rates of parallel efficiency on a workstation network. In case of decomposition of a matrix with halfbandwidth 822, the working efficiency rate was 84% using a network of six workstations (SUN SparcStation 20s). The algorithm provides a high rate of working efficiency in parallel environment with local memory, even if the communication time is considerably longer than the operation time. As an application of the algorithm, a finite element (FE) system for structural vibration analysis with the parallel decomposition algorithm was developed on the above workstation network and a model with more than 100,000 degrees of freedom (DOFs) was successfully analyzed by the system. The computation time for the model with 10,752 DOFs and halfbandwidth 822 was 3,661 sec by the present parallel system, whereas the computation time by a single workstation was 14,335 sec.     

Monte Carlo structural optimization in discrete variables with annealing algorithm

The paper describes the basic ideas of Monte Carlo annealing algorithms for structural optimization with discrete design parameters. The algorithm generates randomly a set of design parameters, with probability depending on the objective function and given by the Boltzmann–Gibbs distribution. In this model the search for the global minimum is simulated by a relaxation process of the statistical mechanical system with the Hamiltonian proportional to the objective function. The rate of the convergence of the method and its dependence upon the annealing probability are discussed. Numerical implementation of the method for the weight optimization of the ten-bar planar cantilever truss is presented. The results of numerical simulation are compared with those obtained by the dual methods. The principal conjecture is that the method is fairly efficient and has great potential for applicaton in engineering design.     

An algorithm for engineering design optimization

In this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one-dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general-purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.     

A generic framework for handling constraints with agent-based optimization algorithms and application to aerodynamic design

A generic constraint handling framework for use with any swarm-based optimization algorithm is presented. For swarm optimizers to solve constrained optimization problems effectively modifications have to be made to the optimizers to handle the constraints, however, these constraint handling frameworks are often not universally applicable to all swarm algorithms. A constraint handling framework is therefore presented in this paper that is compatible with any swarm optimizer, such that a user can wrap it around a chosen swarm algorithm and perform constrained optimization. The method, called separation-sub-swarm, works by dividing the population based on the feasibility of individual agents. This allows all feasible agents to move by existing swarm optimizer algorithms, hence promoting good performance and convergence characteristics of individual swarm algorithms. The framework is tested on a suite of analytical test function and a number of engineering benchmark problems, and compared to other generic constraint handling frameworks using four different swarm optimizers; particle swarm, gravitational search, a hybrid algorithm and differential evolution. It is shown that the new framework produces superior results compared to the established frameworks for all four swarm algorithms tested. Finally, the framework is applied to an aerodynamic shape optimization design problem where a shock-free solution is obtained.     

Optimum design of large-scale truss towers using cascade optimization

High number of design variables, large size of the search space, and control of a great number of design constraints are major preventive factors in performing optimum design of real-world structures in a reasonable time. The present study intends to examine the computational performance of cascading in design optimization of truss towers with large numbers of design variables. The cascade optimization procedure utilized in this paper reduces the objective function value over a number of optimization stages by initially operating on a small number of design variables, which is gradually increased stage after stage. In fact, the early stages of optimization in the cascade procedure make use of the coarsest configurations with small numbers of design variables and the later stages exploit finer configurations with larger numbers of design variables. The optimization algorithm utilized in each stage of a cascade process is enhanced colliding bodies optimization. High solution accuracy and convergence speed of the proposed method are shown through three test examples.     

舰艇武器布置问题的一种协同优化算法

针对舰艇武器布置问题的特点，提出了一种基于粒子群优化和分类器系统的协同优化算法，以粒子群优化进行优化计算，用分类器系统消除约束．计算实例表明，该算法能较好地实现优化计算，并能节省大量的计算时间．     

A fitness differential adaptive parameter controlled evolutionary algorithm with application to the design structure matrix

This paper investigates a methodology for adaptation of the mutation factor within an evolutionary algorithm by means of measuring the improvement differential between successive generations. When no improvement is obtained in an evolutionary algorithm and it has not located the global optimum, it is an indication that the algorithm may have become trapped within a local minimum or maximum. Mutation is a tool within the algorithm that is designed to assist in escaping from these local extremes. It is therefore the premise of this paper that if the preset value for mutation probability is proving insufficient to release the algorithm from entrapment in a local minima or maxima, then a temporary increase in this mutation probability may assist in freeing the algorithm and therefore increasing its chances of ultimately converging on a global optimum. In order to determine when to implement the increase in mutation probability our algorithm measures the fitness improvement between successive generations in the algorithm. When no improvement is detected for a number of successive generations the probability is increased. The design structure matrix (DSM), a scheduling tool that has previously been optimized via the application of evolutionary algorithms, has been used as a practical implementation of differential adaptation to investigate its effectiveness in solving real world problems. Solutions provided by Todd, D. (Multiple criteria genetic algorithms in engineering design and operation, PhD thesis, Department of Marine Technology, University of Newcastle, 1997), are used to benchmark the algorithm's effectiveness.     

Constraint handling in genetic algorithm integrated structural optimization

Summary This paper is concerned with constraint handling techniques in GA integrated structural optimization. A modified version of Joines and Houck's [18] penalty function method is introduced and studied with respect to discrete optimization of truss structures. Three test cases are designed and numerically examined to reflect three distinct situations of loading and constraints. Certain recommendations are reached for penalty parameter values. Furthermore, the considered penalty function is reformulated to eliminate its shortcomings. The reformulated penalty function is also applied to the three test cases and the results are compared and fully discussed.     

Cost and safety optimization of structural design specifications

The design of buildings, bridges, offshore platforms and other civil infrastructure systems is controlled by specifications whose purpose is to provide the engineering principles and procedures required for evaluating the safety of structural systems. The calibration of these codes and specifications is a continuous process necessary to maintain a safe national and global infrastructure system while keeping abreast of new developments in engineering principles, and data on new materials, and applied loads. The common approach to specification calibration is to use probabilistic tools to deal with the random behavior of materials and to account for the uncertainties associated with determining environmental and other load effects. This paper presents a procedure to calibrate load factors for a structural design specification based on cost and safety optimization. The procedure is illustrated by determining load factors that may be applicable for incorporation in a bridge design specification. Traditional code calibration procedures require a set of pre-determined safety levels that should be used as target values that each load combination case should satisfy. The procedure in this paper deduces the failure cost implied in present designs, and provides consistent safety levels for all load combination cases. For greater accuracy, load effects showing variance in time have been modeled by separating them into two random variables; time dependent r.v. (wind speed, vehicular loads, etc.) and time independent r.v. (modeling uncertainties). The total expected lifetime cost is used in the optimization to account for both initial construction cost and future equivalent failure costs.     

A transient topology optimization with time-varying deformation restriction via augmented Lagrange method

International Journal of Mechanics and Materials in Design - The extreme deformation control under transient excitation typically takes the forms of bounds in the time domain. These maximum...