Optimization of retaining wall design using evolutionary algorithms

This paper explores the performance of three evolutionary optimization methods, differential evolution (DE), evolutionary strategy (ES) and biogeography based optimization algorithm (BBO), for nonlinear constrained optimum design of a cantilever retaining wall. These algorithms are based on biological contests for survival and reproduction. The retaining wall optimization problem consists of two criteria, geotechnical stability and structural strength, while the final design minimizes an objective function. The objective function is defined in terms of both cost and weight. Constraints are applied using the penalty function method. The efficiency of the proposed method is examined by means of two numerical retaining wall design examples, one with a base shear key and one without a base shear key. The final designs are compared to the ones determined by genetic algorithms as classical metaheuristic optimization methods. The design results and convergence rate of the BBO algorithm show a significantly better performance than the other algorithms in both design cases.     

A meta-level evolutionary strategy for many-criteria design: Application to improving tracking filters

We present a novel meta-level heuristic algorithm for multi-criteria search. It focuses on dynamically adapting the optimization criteria through the set of active objectives instead of using the evolutionary strategy (ES) parameters as other meta-level approaches do. The meta-level ES dynamically searches for the subset of objectives that achieves the best global performance. It assumes that the active subset can represent the real structure of the trade-off surface and consider all objectives at the same time as a pure multi-objective evolutionary approach (MOEA) would do.We have successfully applied this heuristic to improve the efficiency of tracking filters design, a real-world problem requiring effective and fast optimization techniques. Our approach yields competitive results and drastically reduces the computational cost. The results show an important advantage in efficiency with respect to previous conventional approaches for applying evolutionary algorithms (EA) to the same design problem. The proposed technique can be applied to real-world problems with a high number of active dependent objectives, a frequent occurrence in engineering design.     

Max-min surrogate-assisted evolutionary algorithm for robust design

Solving design optimization problems using evolutionary algorithms has always been perceived as finding the optimal solution over the entire search space. However, the global optima may not always be the most desirable solution in many real-world engineering design problems. In practice, if the global optimal solution is very sensitive to uncertainties, for example, small changes in design variables or operating conditions, then it may not be appropriate to use this highly sensitive solution. In this paper, we focus on combining evolutionary algorithms with function approximation techniques for robust design. In particular, we investigate the application of robust genetic algorithms to problems with high dimensions. Subsequently, we present a novel evolutionary algorithm based on the combination of a max-min optimization strategy with a Baldwinian trust-region framework employing local surrogate models for reducing the computational cost associated with robust design problems. Empirical results are presented for synthetic test functions and aerodynamic shape design problems to demonstrate that the proposed algorithm converges to robust optimum designs on a limited computational budget.     

Dynamic substructuring and reanalysis methods in a surrogate-based design optimization environment

In light weight structure design, vibration control is necessary to meet strict stability requirements and to improve the fatigue life of structural components. Due to ever-increasing demands on products, it is generally more convenient to include vibration prerequisites in a design process instead of using vibration control devices on fixed designs. One of the main difficulties associated to design optimization of complex and/or large structures is the numerous computationally demanding Finite Element (FE) calculations. The objective of this research is to present a novel strategy for efficient and accurate optimization of vibration characteristics of structures. In the proposed strategy, a sub-structuring method is utilized. The FE model of the complete structure is partitioned, reduced and then reassembled. This increases the computational efficiency of dynamic analyses. Moreover, this method is coupled with a novel reanalysis technique to speed up the repeated structural analyses. These methods are finally embedded in a surrogate-based design optimization procedure. An academic test problem is used for the validation of this novel approach.     

Aerodynamic shape optimization using efficient evolutionary algorithms and unstructured CFD solver

An efficient evolutionary algorithm is presented for shape optimization of transonic airfoils. Several techniques have been used to improve the efficiency and convergence rate of the optimization Genetic Algorithm (GA). A new airfoil shape parameterization method is used which is capable of producing more efficient shapes at viscous flow conditions. A Real-Coded Population Dispersion (PD) Genetic Algorithm is developed in order to increase the robustness and convergence rate of the Genetic Algorithm. A Multi-Layer Perceptron Neural Network (NN) is utilized to reduce the huge computational cost of the objective function evaluation. Further improvement in the performance of NN is obtained by using dynamic retraining and normal distribution of the training data to determine well trained parts of the design space to NN. Using the above techniques, the total computational time of optimization algorithm is reduced up to 60% compared with the conventional GA.     

Hybrid neural network and genetic algorithm based machining feature recognition

In this research, neural networks (NNs) and genetic algorithms (GAs) are used together in a hybrid approach to reduce the computational complexity of feature recognition problem. The proposed approach combines the characteristics of evolutionary technique and NN to overcome the shortcomings of feature recognition problem. Consideration is given to reduce the computational complexity of network with specific interest to design the optimum network architecture using GA input selection approach. In order to evaluate the performance of the proposed system, experimental results are compared with previous NN based feature recognition research.     

Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint

Two Ant Colony Optimization algorithms are proposed to tackle multiobjective structural optimization problems with an additional constraint. A cardinality constraint is introduced in order to limit the number of distinct values of the design variables appearing in any candidate solution. Such constraint is directly enforced when an ant builds a candidate solution, while the other mechanical constraints are handled by means of an adaptive penalty method (APM). The test-problems are composed by structural optimization problems with discrete design variables, and the objectives are to minimize both the structure’s weight and its maximum nodal displacement. The Pareto sets generated in the computational experiments are evaluated by means of performance metrics, and the obtained designs are also compared with solutions available from single-objective studies in the literature.     

Multi-physics bi-directional evolutionary topology optimization on GPU-architecture

Topology optimization has proven to be viable for use in the preliminary phases of real world design problems. Ultimately, the restricting factor is the computational expense since a multitude of designs need to be considered. This is especially imperative in such fields as aerospace, automotive and biomedical, where the problems involve multiple physical models, typically fluids and structures, requiring excessive computational calculations. One possible solution to this is to implement codes on massively parallel computer architectures, such as graphics processing units (GPUs). The present work investigates the feasibility of a GPU-implemented lattice Boltzmann method for multi-physics topology optimization for the first time. Noticeable differences between the GPU implementation and a central processing unit (CPU) version of the code are observed and the challenges associated with finding feasible solutions in a computational efficient manner are discussed and solved here, for the first time on a multi-physics topology optimization problem. The main goal of this paper is to speed up the topology optimization process for multi-physics problems without restricting the design domain, or sacrificing considerable performance in the objectives. Examples are compared with both standard CPU and various levels of numerical precision GPU codes to better illustrate the advantages and disadvantages of this implementation. A structural and fluid objective topology optimization problem is solved to vary the dependence of the algorithm on the GPU, extending on the previous literature that has only considered structural objectives of non-design dependent load problems. The results of this work indicate some discrepancies between GPU and CPU implementations that have not been seen before in the literature and are imperative to the speed-up of multi-physics topology optimization algorithms using GPUs.

     

Large scale structural optimization: Computational methods and optimization algorithms

Summary The objective of this paper is to investigate the efficiency of various optimization methods based on mathematical programming and evolutionary algorithms for solving structural optimization problems under static and seismic loading conditions. Particular emphasis is given on modified versions of the basic evolutionary algorithms aiming at improving the performance of the optimization procedure. Modified versions of both genetic algorithms and evolution strategies combined with mathematical programming methods to form hybrid methodologies are also tested and compared and proved particularly promising. Furthermore, the structural analysis phase is replaced by a neural network prediction for the computation of the necessary data required by the evolutionary algorithms. Advanced domain decomposition techniques particularly tailored for parallel solution of large-scale sensitivity analysis problems are also implemented. The efficiency of a rigorous approach for treating seismic loading is investigated and compared with a simplified dynamic analysis adopted by seismic codes in the framework of finding the optimum design of structures with minimum weight. In this context a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.     

Computationally efficient analysis of cable-stayed bridge for GA-based optimization

Optimum design of a cable-stayed bridge structure is very complicated because of large number of design variables. Use of genetic algorithms (GAs) in optimizing such structure consumes significant computational time. Due to nonlinearity, structural analysis itself takes considerable computational time and the genetic algorithm has to perform a large number of iterations in order to obtain global minima. A new approach combining GA and support vector machine (SVM) has been adopted. This drastically reduces the computation time of optimization. The genetic algorithm is employed to obtain the minimum cost of the cable-stayed bridge. Constraint evaluation is done using SVM which is trained by a data base generated through FEM analysis. System level optimization is carried out considering configuration and cross-sectional parameters as design variables. In the present study, optimization was carried out for bridge lengths ranging from 100 to 500 m. Final optimum designs were reanalyzed to check the adequacy of the developed approach.     

PSO-Based Multiobjective Optimization With Dynamic Population Size and Adaptive Local Archives

Recently, various multiobjective particle swarm optimization (MOPSO) algorithms have been developed to efficiently and effectively solve multiobjective optimization problems. However, the existing MOPSO designs generally adopt a notion to “estimate” a fixed population size sufficiently to explore the search space without incurring excessive computational complexity. To address the issue, this paper proposes the integration of a dynamic population strategy within the multiple-swarm MOPSO. The proposed algorithm is named dynamic population multiple-swarm MOPSO. An additional feature, adaptive local archives, is designed to improve the diversity within each swarm. Performance metrics and benchmark test functions are used to examine the performance of the proposed algorithm compared with that of five selected MOPSOs and two selected multiobjective evolutionary algorithms. In addition, the computational cost of the proposed algorithm is quantified and compared with that of the selected MOPSOs. The proposed algorithm shows competitive results with improved diversity and convergence and demands less computational cost.      

Optimum design of aerospace structural components using neural networks

The application of artificial neural networks to capture structural design expertise is demonstrated. The principal advantage of a trained neural network is that it requires a trivial computational effort to produce an acceptable new design. For the class of problems addressed, the development of a conventional expert system would be extremely difficult. In the present effort, a structural optimization code with multiple nonlinear programming algorithms and an artificial neural network code NETS were used. A set of optimum designs for a ring and two aircraft wings for static and dynamic constraints were generated using the optimization codes. The optimum design data were processed to obtain input and output pairs, which were used to develop a trained artificial neural network using the code NETS. Optimum designs for new design conditions were predicted using the trained network. Neural net prediction of optimum designs was found to be satisfactory for the majority of the output design parameters. However, results from the present study indicate that caution must be exercised to ensure that all design variables are within selected error bounds.     

Analysis and optimal design of plates and shells under dynamic loads – I: finite element and sensitivity analysis

In this paper we consider the development, integration, and application of reliable and efficient computational tools for the geometry modeling, mesh generation, structural analysis, and sensitivity analysis of variable-thickness plates and free-form shells under dynamic loads. A flexible shape-definition tool for surface modeling using Coons patches is considered to represent the shape and the thickness distribution of the structure, followed by an automatic mesh generator for structured meshes on the shell surface. Nine-node quadrilateral Mindlin–Reissner shell elements degenerated from 3D elements and with an assumed strain field, the so-called Huang–Hinton elements, are used for the FE discretization of the structure. The Newmark direct integration algorithm is used for the time discretization of the dynamic equilibrium equations for both the structural analysis and the semi-analytical (SA) sensitivity analysis. Alternatively, the sensitivities are computed by using the global finite difference (FD) method. Several examples are considered. In a companion paper, the tools presented here are combined with mathematical programming algorithms to form a robust and reliable structural optimization process to achieve better dynamic performance on the shell designs.     

Large-scale structural optimization using metaheuristic algorithms with elitism and a filter strategy

Large-scale structural optimization often requires numerous finite element analyses to assess the feasibility of the derived solutions during the optimization process, which consume most of the computational cost. To enhance the computational efficiency, this study introduces a filter strategy aiming to eliminate the redundant constraint violation evaluations in large-scale structural optimization using metaheuristic algorithms. Based on the solution selection rule, this study separates the metaheuristic algorithms into two categories: replacement and elitism. The filter mechanism founds on elitism of the metaheuristic algorithms and reduces substantially the number of structural analyses without compromising the effectiveness of the optimization algorithms and the constraint handling techniques. This study also defines a parameter, R, to assess the enhancement performance of the computational efficiency improved by the proposed method. Results from both mathematical simulations and two large-scale structural optimization examples using various metaheuristic algorithms demonstrate that the harmony search (HS) leads always to the lowest R value. The R value is less than 0.4 and is even as small as 0.09 for the 942-bar example, which means over 90% of time savings compared with the penalty method and the Deb rule and the quality of the final optimum also does not depend on the value of R.     

An artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for cardinality constrained portfolio optimization

One of the most studied variant of portfolio optimization problems is with cardinality constraints that transform classical mean–variance model from a convex quadratic programming problem into a mixed integer quadratic programming problem which brings the problem to the class of NP-Complete problems. Therefore, the computational complexity is significantly increased since cardinality constraints have a direct influence on the portfolio size. In order to overcome arising computational difficulties, for solving this problem, researchers have focused on investigating efficient solution algorithms such as metaheuristic algorithms since exact techniques may be inadequate to find an optimal solution in a reasonable time and are computationally ineffective when applied to large-scale problems. In this paper, our purpose is to present an efficient solution approach based on an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for solving cardinality constrained portfolio optimization problem. Computational results confirm the effectiveness of the solution methodology.     

Hybrid evolutionary method for capacitated location-allocation problem

Location-allocation model is widely applied for facility location design in practice. In this paper, we discuss an extension of location-allocation model which has capacity constraints and propose a hybrid evolutionary method to solve it which absorbs ideas from both genetic algorithms (GAs) and evolutionary strategy (ES) as well as combined with efficient traditional optimization techniques. It is shown that the proposed method is effective in finding global or near global solutions by numerical simulations.     

Multi-objective design optimization using cascade evolutionary computations

The consideration of uncertainties in conjunction with the probability of violation of the constraints imposed by the design codes is examined in the framework of structural optimization. The optimum design achieved based on a deterministic formulation is compared, in terms of the optimum weight, the probability of violation of the constraints and the probability of failure, with the optimum designs achieved through a robust design formulation where the variance of the response is considered as an additional criterion. The stochastic finite element problem is solved using the Monte Carlo Simulation method, combined with the Latin Hypercube Sampling technique for improving its computational efficiency. A non-dominant cascade evolutionary algorithm-based methodology is adopted for the solution of the multi-objective optimization problem encountered, in order to obtain the global Pareto front curve.     

列队竞争算法求解多产品间歇生产过程排序问题

由于组合爆炸特性,多产品厂的排序问题很难求解大规模甚至中等规模的问题,本文采用一种新的随机型进化搜索算法——列队竞争算法来对该问题进行求解,引入新的选择策略和变异方法。计算表明同已有的方法相比,该方法求解效率高、收敛速度快、使用简单方便,是一种求解多产品间歇过程排序问题的有效算法,为多目的厂间歇过程排序研究提供了新思路。     

School-based optimization for performance-based optimum seismic design of steel frames

The performance-based optimum seismic design of steel frames is one of the most complicated and computationally demanding structural optimization problems. Metaheuristic optimization methods have been successfully used for solving engineering design problems over the last three decades. A very recently developed metaheuristic method called school-based optimization (SBO) will be utilized in the performance-based optimum seismic design of steel frames for the first time in this study. The SBO actually is an improved/enhanced version of teaching–learning-based optimization (TLBO), which mimics the teaching and learning process in a class where learners interact with the teacher and between themselves. Ad hoc strategies are adopted in order to minimize the computational cost of SBO results. The objective of the optimization problem is to minimize the weight of steel frames under interstory drift and strength constraints. Three steel frames previously designed by different metaheuristic methods including particle swarm optimization, improved quantum particle swarm optimization, firefly and modified firefly algorithms, teaching–learning-based optimization, and JAYA algorithm are used as benchmark optimization examples to verify the efficiency and robustness of the present SBO algorithm. Optimization results are compared with those of other state-of-the-art metaheuristic algorithms in terms of minimum structural weight, convergence speed, and several statistical parameters. Remarkably, in all test problems, SBO finds lighter designs with less computational effort than the TLBO and other methods available in metaheuristic optimization literature.

     

Geometric analysis of collaborative optimization

Instead of the past mathematical analyses, an intuitive geometric analysis of the collaborative optimization (CO) algorithm is presented in this paper, which reveals some geometric properties of CO and gives a direct geometric interpretation of the reason for the reported computational difficulties in CO. The analysis shows that if the system-level optimum point at one iteration is outside the feasible region of the original optimization problem, at the next iteration, the system-level optimization problem may be infeasible due to the system-level consistency equality constraints. One way to solve the problem of the infeasibility is to relax the system-level consistency equality constraints using inequality constraints. However it is a delicate job to determine a rational relaxed tolerance because feasibility and consistency have conflicting requirements for the tolerance, that is, the more relaxed the better for feasibility while the stricter the better for consistency. Based on the geometric analysis, a method of variable relaxed tolerance is put forward to solve this problem. In this method, an adaptive adjustment of the tolerance is made at each iteration according to the quantified inconsistency between two subsystems. In the last section, the capabilities and limitations of the proposed method are illustrated by three examples.