Iterative reliable design space approach for efficient reliability-based design optimization

Engineering with Computers - Reliability-based design optimization has gained much attention in many engineering design problems with the consideration of uncertainties. Nevertheless, the...     

An efficient structural optimization approach for the modular automotive body conceptual design

Structural and Multidisciplinary Optimization - Appropriate structural analysis and optimization methods are of great significance for automotive body in conceptual design stage. This paper...     

An efficient hybrid approach based on Harris Hawks optimization and imperialist competitive algorithm for structural optimization

In this paper, a new hybrid algorithm is introduced, combining two Harris Hawks Optimizer (HHO) and the Imperialist Competitive Algorithm (ICA) to achieve a better search strategy. HHO is a new population-based, nature-inspired optimization algorithm that mimics Harris Hawks cooperative behavior and chasing style in nature called surprise pounce HHO. It is a robust algorithm in exploitation, but has an unfavorable performance in exploring the search space, while ICA has a better performance in exploration; thus, combining these two algorithms produces an effective hybrid algorithm. The hybrid algorithm is called Imperialist Competitive Harris Hawks Optimization (ICHHO). The proposed hybrid algorithm's effectiveness is examined by comparing other nature-inspired techniques, 23 mathematical benchmark problems, and several well-known structural engineering problems. The results successfully indicate the proposed hybrid algorithm's competitive performance compared to HHO, ICA, and some other well-established algorithms.

     

Contact shape optimization: a bilevel programming approach

We consider the problem of shape optimization of nonlinear elastic solids in contact. The equilibrium of the solid is defined by a constrained minimization problem, where the body energy functional is the objective and the constraints impose the nonpenetration condition. Then the optimization problem can be formulated in terms of a bilevel mathematical program. We describe new optimality conditions for bilevel programming and construct an algorithm to solve these conditions based on Herskovits’ feasible direction interior point method. With this approach we simultaneously carry out shape optimization and nonlinear contact analysis. That is, the present method is a “one shot” technique. We describe some numerical examples solved in a very efficient way. Received July 27, 1999     

Semi-Lagrange method for level-set-based structural topology and shape optimization

In this paper, we introduce a semi-Lagrange scheme to solve the level-set equation in structural topology optimization. The level-set formulation of the problem expresses the optimization process as a solution to a Hamilton–Jacobi partial differential equation. It allows for the use of shape sensitivity to derive a speed function for a descent solution. However, numerical stability condition in the explicit upwind scheme for discrete level-set equation severely restricts the time step, requiring a large number of time steps for a numerical solution. To improve the numerical efficiency, we propose to employ a semi-Lagrange scheme to solve level-set equation. Therefore, a much larger time step can be obtained and a much smaller number of time steps are required. Numerical experiments comparing the semi-Lagrange method with the classical explicit upwind scheme are presented for the problem of mean compliance optimization in two dimensions.     

Integration of design and manufacturing for structural shape optimization

This paper presents an integrated design and manufacturing approach that supports shape optimization of structural components. The approach starts from a primitive concept stage, where boundary and loading conditions of the structural component are given to the designer. Topology optimization is conducted for an initial structural layout. The discretized structural layout is smoothed using parametric B-Spline surfaces. The B-Spline surfaces are imported into a CAD system to construct parametric solid models for shape optimization. Virtual manufacturing (VM) techniques are employed to ensure that the optimized shape can be manufactured at a reasonable cost. The solid freeform fabrication (SFF) system fabricates physical prototypes of the structure for design verification. Finally, a computer numerical control (CNC) machine is employed to fabricate functional parts as well as mold or die for mass production of the structural component. The main contribution of the paper is incorporating manufacturing into the design process, where manufacturing cost is considered for design. In addition, the overall design process starts from a primitive stage and ends with functional parts. A 3D tracked vehicle roadarm is employed throughout this paper to illustrate the overall design process and various techniques involved.     

A programming approach for nonsmooth structural optimization

A two-level programming algorithm for some nonsmooth structural optimization problems is presented. When an optimization problem has both stress and unilateral displacement constraints, we combine the structural optimization with unilateral analysis to formulate a two-level model. Quadratic programming (QP) is used in analysis level, which is solved with dual interior-point method, and linear programming (LP) is used in optimization level. Several examples with unilateral or bilateral constraints are provided to verify the proposed algorithm.     

Particle swarm approach for structural design optimization

This paper presents in detail the background and implementation of a particle swarm optimization algorithm suitable for constraint structural optimization tasks. Improvements, effect of the different setting parameters, and functionality of the algorithm are shown in the scope of classical structural optimization problems. The effectiveness of the approach is illustrated by three benchmark structural optimization tasks. Results show the ability of the proposed methodology to find better optimal solutions for structural optimization tasks than other optimization algorithms.     

An efficient second-order SQP method for structural topology optimization

This article presents a Sequential Quadratic Programming (SQP) solver for structural topology optimization problems named TopSQP. The implementation is based on the general SQP method proposed in Morales et al. J Numer Anal 32(2):553–579 (2010) called SQP+. The topology optimization problem is modelled using a density approach and thus, is classified as a nonconvex problem. More specifically, the SQP method is designed for the classical minimum compliance problem with a constraint on the volume of the structure. The sub-problems are defined using second-order information. They are reformulated using the specific mathematical properties of the problem to significantly improve the efficiency of the solver. The performance of the TopSQP solver is compared to the special-purpose structural optimization method, the Globally Convergent Method of Moving Asymptotes (GCMMA) and the two general nonlinear solvers IPOPT and SNOPT. Numerical experiments on a large set of benchmark problems show good performance of TopSQP in terms of number of function evaluations. In addition, the use of second-order information helps to decrease the objective function value.     

An efficient procedure for structural reliability-based robust design optimization

This paper focuses on the development of an optimization tool with the aim to obtain robust and reliable designs in short computational time. The robustness measures considered here are the expected value and standard deviation of the performance function involved in the optimization problem. When using these robustness measures combined, the search of optimal design appears as a robust multiobjective optimization (RMO) problem. Reliable design addresses uncertainties to restrict the structural probability of failure. The mathematical formulation for the reliability based robust design optimization (RBRDO) problem is obtained by adding a reliability based constraint into the RMO problem. As both, statistics calculations and the reliability analysis could be very costly, approximation technique based on reduced-order modeling (ROM) is also incorporated in our procedure. The selected ROM is the proper orthogonal decomposition (POD) method, with the aim to produce fast outputs considering structural non-linear behavior. Moreover, to obtain RBRDO designs with reduced CPU time we propose others developments to be added in the integrated tool. They are: Probabilistic Collocation Method (PCM) to evaluate the statistics of the structural responses and, also, an approximated reliability constraints procedure based on the Performance Measure Approach (PMA) for reliability constraint assessment. Finally, Normal-Boundary Intersection (NBI) or Normalized Normal-Constraint (NNC) multiobjective optimization techniques are employed to obtain fast and even spread Pareto robust designs. To illustrate the application of the proposed tool, optimization studies are conducted for a linear (benchmark) and nonlinear trusses problems. The nonlinear example consider different loads level, exploring the material plasticity. The integrated tool prove to be very effective reducing the computational time by up to five orders of magnitude, when compared to the solutions obtained via classical standard approaches.     

Simulation approach to structural optimization

A unified approach to various problems of structural optimization is presented. It is based on a combination of mathematical models of different complexity. The models describe the behaviour of a designed structure. From the computational point of view, it is connected with the sequential approximation of design problem constraints and/or an objective function. In each step, a subregion of the initial search region in the space of design variables is chosen. In this subregion, various points (designs) are selected, for which response analyses are carried out using a numerical method (mostly FEM). Using the least-squares method, analytical expressions are formulated, which then replace the initial problem functions. They are used as functions of a particular mathematical programming problem. The size and location of sequential subregions may be changed according to the result of the search. The choice of one particular form of the analytical expressions is described. The application of the approach is shown by means of test examples and comparison with other optimization techniques is presented.Visiting scientist in the Department of Solid Mechanics, The Technical University of Denmark, Lyngby, Denmark, September 1987 – August 1988.     

Probabilistic approach for shape optimization problems in contact mechanics

Shape optimization problem for rigid stamp interacted with elastic medium is investigated. Additional forces applied to the elastic medium are supposed to be random in considered problem formulation. Probabilistic approach is applied as for formulation as for solution of the optimization problem. As a result the optimal designs of the stamps with circular base are obtained and presented in the paper.     

A new two-point approximation approach for structural optimization

The objective of this work is to build up a high-quality approximation scheme to realize computational savings for the solution of structural optimization problems. To this end, a newly developed two-point approximation scheme is proposed. This scheme is constructed by the linear combination of Taylor expansions in terms of both original and reciprocal variables. The coefficients of the combination are determined by utilizing both the function and gradient information of two different design points obtained during the process of optimization. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of previously published work. Received April 2, 1999     

A preference aggregation rule approach for structural optimization

In this paper, preference aggregation rules are used to define overall design evaluation measures in optimal design problems. A methodology for the efficient solution of the corresponding design optimization problems is presented. Each design criterion as well as the constraints imposed on the design variables and problem parameters are characterized by preference functions. The nondifferentiable nature of the optimization problems which arise in this formulation is coped with using a first-order algorithm combined with approximation concepts. High-quality approximations for the system response functions are constructed using the concepts of intermediate response quantities and intermediate variables. These approximations are used to replace the original problem by a sequence of approximate problems. Example problems are presented to study the performance of the proposed optimization technique as well as the methodology based on approximation concepts.     

Fuzzy tolerance multilevel approach for structural topology optimization

This paper presents a novel methodology, fuzzy tolerance multilevel programming approach, for applying fuzzy set theory and sequence multilevel method to multi-objective topology optimization problems of continuum structures undergoing multiple loading cases. Ridge-type nonlinear membership functions in fuzzy set theory are applied to embody fuzzy and uncertain characteristics essentially involved by the objective and constraint functions. Sequence multilevel method is used to characterize the different priorities of loading cases at different levels making contribution to the final optimum solution, which is practically beneficial to reduce the subjective influence transferred by using weighted approaches. The solid isotropic material with penalization (SIMP) is adopted as the density-stiffness interpolation scheme to relax the original optimization problem and indicate the dependence of material properties with element pseudo-densities. Sequential linear programming (SLP) is used as the optimizer to solve the multi-objective optimization problem formulated using fuzzy tolerance multilevel programming scheme. Numerical instabilities, such as checkerboards and mesh dependencies are summarized and a duplicate sensitivity filtering method, in favor of contributing to the mesh-dependent optimum designs, is subsequently proposed to regularize the singularity of the optimization problem. The validation of the methodologies presented in this work has been demonstrated by detailed examples of numerical applications.     

A computationally efficient approach for watershed scale spatial optimization

A multi-level spatial optimization (MLSOPT) approach is developed for solving complex watershed scale optimization problems. The method works at two levels: a watershed is divided into small sub-watersheds and optimum solutions for each sub-watershed are identified individually. Subsequently sub-watershed optimum solutions are used for watershed scale optimization. The approach is tested with complex spatial optimization case studies designed to maximize crop residue (corn stover) harvest with minimum environmental impacts in a 2000 km² watershed. Results from case studies indicated that the MLSOPT approach is robust in convergence and computationally efficient compared to the traditional single-level optimization frameworks. The MLSOPT was 20 times computationally efficient in solving source area based optimization problem while it was 3 times computationally efficient for watershed outlet based optimization problem compared to a corresponding single-level optimizations. The MLSOPT optimization approach can be used in solving complex watershed scale spatial optimization problems effectively.