Enhancing particle swarm optimization algorithm using two new strategies for optimizing design of truss structures

This work develops an augmented particle swarm optimization (AugPSO) algorithm using two new strategies,: boundary-shifting and particle-position-resetting. The purpose of the algorithm is to optimize the design of truss structures. Inspired by a heuristic, the boundary-shifting approach forces particles to move to the boundary between feasible and infeasible regions in order to increase the convergence rate in searching. The purpose of the particle-position-resetting approach, motivated by mutation scheme in genetic algorithms (GAs), is to increase the diversity of particles and to prevent the solution of particles from falling into local minima. The performance of the AugPSO algorithm was tested on four benchmark truss design problems involving 10, 25, 72 and 120 bars. The convergence rates and final solutions achieved were compared among the simple PSO, the PSO with passive congregation (PSOPC) and the AugPSO algorithms. The numerical results indicate that the new AugPSO algorithm outperforms the simple PSO and PSOPC algorithms. The AugPSO achieved a new and superior optimal solution to the 120-bar truss design problem. Numerical analyses showed that the AugPSO algorithm is more robust than the PSO and PSOPC algorithms.     

A regional genetic algorithm for the discrete optimal design of truss structures

A regional genetic algorithm (R‐GA) is used for the discrete optimal design of truss structures. The chromosomes are selected from a sub‐region centred on the continuous optimum. This approach replaces genetic rebirth as previously proposed by other authors, thereby significantly reducing computational costs. As a pure discrete method, the R‐GA method does not require heuristic arguments or approximations. This makes the algorithm highly effective when buckling and slenderness constraints with scatter in the data are introduced. A large set of numerical test examples is used to illustrate the capabilities of the method. The algorithm is shown to be effective and robust, making it suitable for the optimal design of very large truss structures. Copyright © 1999 John Wiley & Sons, Ltd.     

Sensitivity analysis and optimal design of non-linear structures

Sensitivity analysis for non-linear elastic structures in regular and critical states is first discussed including design parameters and initial imperfections. Next, the optimal design problem is formulated by considering imperfect structures and setting constraints on deflections and stresses. For structures with unstable post-critical response the limit load constraint is introduced in the optimization procedure. Several examples of truss optimization are provided. The level of initial imperfections can be regarded as design parameter and specified from the optimal solution. © 1998 John Wiley & Sons, Ltd.     

Cyclical parthenogenesis algorithm for layout optimization of truss structures with frequency constraints

Structural optimization with frequency constraints is seen as a challenging problem because it is associated with highly nonlinear, discontinuous and non-convex search spaces consisting of several local optima. Therefore, competent optimization algorithms are essential for addressing these problems. In this article, a newly developed metaheuristic method called the cyclical parthenogenesis algorithm (CPA) is used for layout optimization of truss structures subjected to frequency constraints. CPA is a nature-inspired, population-based metaheuristic algorithm, which imitates the reproductive and social behaviour of some animal species such as aphids, which alternate between sexual and asexual reproduction. The efficiency of the CPA is validated using four numerical examples.     

Use of modified hybrid PSOGSA for optimum design of RC frame

A realistic and optimum design of reinforced concrete structural frame, by hybridizing enhanced versions of standard particle swarm optimization (PSO) and standard gravitational search algorithm (GSA) is presented in this paper. PSO has been democratized by considering all good and bad experiences of the particles, whereas GSA has been made self-adaptive by considering a specific range for certain parameters like ‘gravitational constant’ and ‘set of agents with best fitness value.’ Optimal size and reinforcement of the members have been found by employing the technique in a computer-aided environment. Use of self-adaptive GSA together with democratic PSO technique has been found to provide two distinct advantages over standard PSO and GSA, namely better capability to escape from local optima and faster convergence rate. The entire formulation for optimal cost design of frame includes the cost of beams and columns. In this approach, variables of each element of structural frame have been considered as continuous functions and rounded off appropriately to imbibe practical relevance to the study. An example has been considered to emphasize the validity of this optimum design procedure and results have been compared with earlier studies.     

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

A single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.     

Genetic approach to optimal topology/controller design of adaptive structures

Integrated optimization of structural topology and control system is considered. The problem is formulated as mixed discrete-continuous multi-objective programming with a linear quadratic regulator cost index, and measures of robustness and controllability as objectives. The Genetic Algorithm (GA), a guided random search technique, is adopted for the problem-solving. A member elimination strategy that allows deleted members to be recovered is suggested in the search procedure. As verification for the proposed method, optimum layout and actuator placement for a 45-bar truss is illustrated. Numerical results indicate that the genetic algorithm can converge to optimum solutions by searching only a minor fraction of the solution space. Discussions on the algorithm are presented. © 1998 John Wiley & Sons, Ltd.     

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.     

Genetic algorithm for discrete‐sizing optimal design of trusses using the force method

In the process of discrete‐sizing optimal design of truss structures by Genetic Algorithm (GA), analysis should be performed several times. In this article, the force method is employed for the analysis. The advantage of using this method lies in the fact that the matrices corresponding to particular and complementary solutions are formed independently of the mechanical properties of members. These matrices are used several times in the process of the sequential analyses, increasing the speed of optimization. The second feature of the present method is the automatic nature of the prediction of the useful range of sections for a member from a list of profiles with a large number of cross‐sections. The third feature consists of a contraction process developed to increase the efficiency of the GA by which an optimal design for the first sub‐string associated with member cross‐sections is obtained. Improved designs are achieved in subsequent cycles by reducing the length of sub‐strings. Copyright © 2002 John Wiley & Sons, Ltd.     

Simultaneous geometrical and material optimal design of hybrid elastomer/composite sandwich plates

The paper presents the complete optimization of a hybrid elastomer/composite sandwich plate structure: design variables consist in the total number of layers of the structure, their respective thicknesses, their fiber orientations, the position(s) of the viscoelastic core(s) and the stacking sentence. The damping of the hybrid structure is calculated by the Method of Strain Energy (MSE). The constrained optimization maximizes the damping loss factor using the linear search algorithm. As an example, the method is applied to a simple structure and the results demonstrate the capabilities of our tool.     

A robust dual algorithm for topology design of structures in discrete variables

Dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since, in topology design problems, the number of constraints is small in comparison to the number of design variables. Good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint. However, when the perimeter constraint is relaxed, the dual algorithm tends to give bad results, even with the use of higher‐order finite element models as we demonstrate in this work. Since, a priori, one does not know what a good value of the perimeter to be specified is, it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint. We show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint. In particular, we show that the problem of checkerboarding which is frequently observed with the use of lower‐order finite elements is eliminated. Copyright © 2001 John Wiley & Sons, Ltd.     

A reduced SAND method for optimal design of non-linear structures

An SQP-based reduced Hessian method for simultaneous analysis and design (SAND) of non-linearly behaving structures is presented and compared with conventional nested analysis and design (NAND) methods. It is shown that it is possible to decompose the SAND formulation to take advantage of the particular structure of the problem at hand. The resulting reduced SAND method is of the same size as the conventional NAND method but it is computationally more efficient. The presentation here builds on previous research on SAND methods generalizing the solution approach to cases with both equality and inequality constraints. The new version of the reduced SAND method is tested in the context of weight minimization of 3-D truss structures with geometrically non-linear behaviour. © 1997 John Wiley & Sons, Ltd.     

A biogeography-based optimization for optimum discrete design of skeletal structures

This article presents a modified biogeography-based optimization (MBBO) algorithm for optimum design of skeletal structures with discrete variables. The main idea of the biogeography-based optimization (BBO) algorithm is based on the science of biogeography, in which each habitat is a possible solution for the optimization problem in the search space. This algorithm consists of two main operators: migration and mutation. The migration operator helps the habitats to exploit the search space, while the mutation operator guides habitats to escape from the local optimum. To enhance the performance of the standard algorithm, some modifications are made and an MBBO algorithm is presented. The performance of the MBBO algorithm is evaluated by optimizing five benchmark design examples, and the obtained results are compared with other methods in the literature. The numerical results demonstrate that the MBBO algorithm is able to show very competitive results and has merits in finding optimum designs.     

A novel surrogate-based approach for optimal design of electromagnetic-based circuits

A new geometric design centring approach for optimal design of central processing unit-intensive electromagnetic (EM)-based circuits is introduced. The approach uses norms related to the probability distribution of the circuit parameters to find distances from a point to the feasible region boundaries by solving nonlinear optimization problems. Based on these normed distances, the design centring problem is formulated as a max–min optimization problem. A convergent iterative boundary search technique is exploited to find the normed distances. To alleviate the computation cost associated with the EM-based circuits design cycle, space-mapping (SM) surrogates are used to create a sequence of iteratively updated feasible region approximations. In each SM feasible region approximation, the centring process using normed distances is implemented, leading to a better centre point. The process is repeated until a final design centre is attained. Practical examples are given to show the effectiveness of the new design centring method for EM-based circuits.     

Optimization of large‐scale truss structures using sparse SAND formulations

Sparsity features of simultaneous analysis and design (SAND) formulations are studied and exploited for optimization of large‐scale truss structures. Three formulations are described and implemented with an existing analysis code. SAND formulations have large number of variables; however, gradients of the functions and Hessian of the Lagrangian are quite sparsely populated. Therefore, this structure of the problem is exploited and an optimization algorithm with sparse matrix capability is used to solve large‐scale problems. An existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming (SQP) algorithm to solve sample problems. The formulations and algorithms work quite well for the sample problems, and their performances are compared and discussed. For all the cases considered, the SAND formulations out perform the conventional formulation except one case. Further research is suggested to fully study and utilize sparse features of the alternative SAND formulations and to develop more efficient sparse solvers for large‐scale and more complex applications. Copyright © 2006 John Wiley & Sons, Ltd.     

Ply level uncertainty effects on failure curves and optimal design of laminated composites using directional bat algorithm

The present study investigates the effect of both ply level material uncertainty and ply angle uncertainty on the failure envelope, strength characteristics and design of laminated composite. Multiple failure envelopes and distributions of the strength parameters are obtained for Tsai-Wu and maximum stress criteria using Monte Carlo simulation. A newly developed directional bat algorithm (dBA) is then used to perform the constrained design optimization of laminated composite for the first time while considering uncertainty effects. The effect of ply level uncertainty on failure envelopes and the corresponding optimal design of laminated composite structures is thus quantified.     

Fast simulation-driven design of microwave structures using improved variable-fidelity optimization technique

An improved variable-fidelity optimization algorithm for the simulation-driven design of microwave structures is presented. It exploits a set of electromagnetic-based models of increasing discretization density. These models are sequentially optimized with the optimum of the ‘coarser’ model being the initial design for the ‘finer’ one. The found optimum is further refined using a response surface approximation model constructed from the coarse-discretization simulation data. In this work, the computational efficiency of the variable-fidelity algorithm is enhanced by employing a novel algorithm for optimizing the coarse-discretization models. This allows reduction of the overall design time by up to 50% compared to the previous version. The presented technique is particularly suitable for problems where simulation-driven design is the only option, for example, ultra wideband and dielectric resonator antennas. Operation of the presented approach is demonstrated using two examples of antennas and a microstrip filter. In all cases, the optimal design is obtained at a low computational cost corresponding to a few high-fidelity simulations of the structure.     

A new numerical algorithm for sub‐optimal control of earthquake excited linear structures

Exact optimal classical closed–open‐loop control is not achievable for the buildings under seismic excitations since it requires the whole knowledge of earthquake in the control interval. In this study, a new numerical algorithm for the sub‐optimal solution of the optimal closed–open‐loop control is proposed based on the prediction of near‐future earthquake excitation using the Taylor series method and the Kalman filtering technique. It is shown numerically that how the solution is related to the predicted earthquake acceleration values. Simulation results show that the proposed numerical algorithm are better than the closed‐loop control and the instantaneous optimal control and proposed numerical solution will approach the exact optimal solution if the more distant future values of the earthquake excitation can be predicted more precisely. Effectiveness of the Kalman filtering technique is also confirmed by comparing the predicted and the observed time history of NS component of the 1940 El Centro earthquake. Copyright © 2001 John Wiley & Sons, Ltd.     

A hybrid optimization method of harmony search and opposition-based learning

The harmony search (HS) method is an emerging meta-heuristic optimization algorithm. However, like most of the evolutionary computation techniques, it sometimes suffers from a rather slow search speed, and fails to find the global optimum in an efficient way. In this article, a hybrid optimization approach is proposed and studied, in which the HS is merged together with the opposition-based learning (OBL). The modified HS, namely HS-OBL, has an improved convergence property. Optimization of 24 typical benchmark functions and an optimal wind generator design case study demonstrate that the HS-OBL can indeed yield a superior optimization performance over the regular HS method.