Sizing and layout design of truss structures under dynamic and static constraints with an integrated particle swarm optimization algorithm

Natural frequencies offer useful knowledge on the dynamic response of the structures. It is possible to avoid from the destructive effects of dynamic loads on the structures by optimizing layout and size of their subject to constraints on natural frequencies. Since optimization problems including frequency constraints are highly nonlinear, this kind of problems forms a challenging area to test the performance of the different optimization techniques. This study tests the performance of an integrated particle swarm optimization algorithm (iPSO), a new particle swarm optimizer integrated with the improved fly-back mechanism and the weighted particle concept, in four weight minimization of truss structures with sizing and layout variables under multiple frequency constraints. Optimization results demonstrate that the new algorithm is competitive with other state-of-the-art metaheuristic algorithms in dynamic and static structural optimization problems.     

Discrete sizing/layout/topology optimization of truss structures with an advanced Jaya algorithm

Discrete optimization of truss structures is a hard computing problem with many local minima. Metaheuristic algorithms are naturally suited for discrete optimization problems as they do not require gradient information. A recently developed method called Jaya algorithm (JA) has proven itself very efficient in continuous engineering problems. Remarkably, JA has a very simple formulation and does not utilize algorithm-specific parameters. This study presents a novel JA formulation for discrete optimization of truss structures under stress and displacement constraints. The new algorithm, denoted as discrete advanced JA (DAJA), implements efficient search mechanisms for generating new trial designs including discrete sizing, layout and topology optimization variables. Besides the JA’s basic concept of moving towards the best design of the population and moving away from the worst design, DAJA tries to form a set of descent directions in the neighborhood of each candidate designs thus generating high quality trial designs that are very likely to improve current population. Results collected in seven benchmark problems clearly demonstrate the superiority of DAJA over other state-of-the-art metaheuristic algorithms and multi-stage continuous–discrete optimization formulations.     

Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints

The optimal design of a truss structure with dynamic frequency constraints is a highly nonlinear optimization problem with several local optimums in its search space. In this type of structural optimization problems, the optimization methods should have a high capability to escape from the traps of the local optimums in the search space. This paper presents hybrid electromagnetism-like mechanism algorithm and migration strategy (EM–MS) for layout and size optimization of truss structures with multiple frequency constraints. The electromagnetism-like mechanism (EM) algorithm simulates the attraction and repulsion mechanism between the charged particles in the field of the electromagnetism to find optimal solutions, in which each particle is a solution candidate for the optimization problem. In the proposed EM–MS algorithm, two mechanisms are utilized to update the position of particles: modified EM algorithm and a new migration strategy. The modified EM algorithm is proposed to effectively guide the particles toward the region of the global optimum in the search space, and a new migration strategy is used to provide efficient exploitation between the particles. In order to test the performance of the proposed algorithm, this study utilizes five benchmark truss design examples with frequency constraints. The numerical results show that the EM–MS algorithm is an alternative and competitive optimizer for size and layout optimization of truss structures with frequency constraints.     

Diversity-adaptive parallel memetic algorithm for solving large scale combinatorial optimization problems

Parallel memetic algorithms (PMAs) are a class of modern parallel meta-heuristics that combine evolutionary algorithms, local search, parallel and distributed computing technologies for global optimization. Recent studies on PMAs for large-scale complex combinatorial optimization problems have shown that they converge to high quality solutions significantly faster than canonical GAs and MAs. However, the use of local learning for every individual throughout the PMA search can be a very computationally intensive and inefficient process. This paper presents a study on two diversity-adaptive strategies, i.e., (1) diversity-based static adaptive strategy (PMA-SLS) and (2) diversity-based dynamic adaptive strategy (PMA-DLS) for controlling the local search frequency in the PMA search. Empirical study on a class of NP-hard combinatorial optimization problem, particularly large-scale quadratic assignment problems (QAPs) shows that the diversity-adaptive PMA converges to competitive solutions at significantly lower computational cost when compared to the canonical MA and PMA. Furthermore, it is found that the diversity-based dynamic adaptation strategy displays better robustness in terms of solution quality across the class of QAP problems considered. Static adaptation strategy on the other hand requires extra effort in selecting suitable parameters to suit the problems in hand.     

Modified symbiotic organisms search for structural optimization

The structural dynamic response predominantly depends upon natural frequencies which fabricate these as a controlling parameter for dynamic response of the truss. However, truss optimization problems subjected to multiple fundamental frequency constraints with shape and size variables are more arduous due to its characteristics like non-convexity, non-linearity, and implicit with respect to design variables. In addition, mass minimization with frequency constraints are conflicting in nature which intricate optimization problem. Using meta-heuristic for such kind of problem requires harmony between exploration and exploitation to regulate the performance of the algorithm. This paper proposes a modification of a nature inspired Symbiotic Organisms Search (SOS) algorithm called a Modified SOS (MSOS) algorithm to enhance its efficacy of accuracy in search (exploitation) together with exploration by introducing an adaptive benefit factor and modified parasitism vector. These modifications improved search efficiency of the algorithm with a good balance between exploration and exploitation, which has been partially investigated so far. The feasibility and effectiveness of proposed algorithm is studied with six truss design problems. The results of benchmark planar/space trusses are compared with other meta-heuristics. Complementarily the feasibility and effectiveness of the proposed algorithms are investigated by three unimodal functions, thirteen multimodal functions, and six hybrid functions of the CEC2014 test suit. The experimental results show that MSOS is more reliable and efficient as compared to the basis SOS algorithm and other state-of-the-art algorithms. Moreover, the MSOS algorithm provides competitive results compared to the existing meta-heuristics in the literature.

     

Randomized line search techniques in combined GA for discrete sizing optimization of truss structures

This paper presents two randomized line search techniques, each combined with a genetic algorithm (GA), to improve the convergence and the accuracy ratio for discrete sizing optimization of truss structures. The first technique is a simple one-dimensional line search in which design variable axes are selected randomly as search directions. The second is a line search technique whose search direction is determined randomly by fitness function values and differences in the genotypes of individuals. To apply the above-mentioned line search techniques without difficulty, real coding is adopted for discrete problems. The line search techniques are applied to discrete optimization problems of minimum-weight truss structures subjected to stress and displacement constraints. The proposed techniques provide convergence to better solutions than a conventional GA.     

分布式并行计算环境下混合遗传算法的研究

为提高混合遗传算法的计算效率和求解质量,提出一个并行混合遗传算法框架。该框架主要由遗传算法、小生境操作和单纯形3部分组成,遗传算法和小生境操作采用串行执行方式,单纯形采用分布式并行执行方式。分布式并行计算环境由4台计算机通过交换机连接构成,并设计了一个动态任务调度方案。一个典型工程算例验证了新算法的有效性,并且在分布式并行环境下取得了较好的加速比和并行效率。     

A parallel genetic algorithm to solve the set-covering problem

This work presents a parallel genetic algorithm (PGA) model to solve the set-covering problem (SCP). Experimental results obtained with a binary representation of the SCP, show that—in terms of the number of generations (computational time) needed to achieve solutions of an acceptable quality—PGA performs better than the sequential model. This comportment can be explained principally because, the PGA of p nodes—each one with its corresponding local population P_L—behaves like a sequential GA with a global population, P_G, of the same size, which it—the sequential GA—has the great disadvantage of having to completely evaluate in each generation. Not so the PGA, which only evaluates a pth part of the P_G.Scope and purposeSince classical optimization techniques are inefficient to solve NP-complete problems—in terms of computational complexity—new methods have been developed. The genetic algorithm (GA), is one of such methods proposed to solve combinatorial optimization. Although Genetic Algorithms (GAs) are efficient to solve these kinds of hard problems, during recent years, models of parallel genetic algorithms (PGAs) have been used to improve both quality of solutions and computing time. The aim of using PGAs, is to discover how the interchange of genetic information of separate populations, affects or influences the final solution. The exploration of different solution spaces could optimize the search in terms of both computational time and quality of solution.     

A hybrid OC–GA approach for fast and global truss optimization with frequency constraints

The truss optimization constrained with vibration frequencies is a highly nonlinear and more computational cost problem. To speed up the convergence and obtain the global solution of this problem, a hybrid optimality criterion (OC) and genetic algorithm (GA) method for truss optimization is presented in this paper. Firstly, the OC method is developed for multiple frequency constraints. Then, the most efficient variables are identified by sensitivity analysis and modified as iteration scheme. Finally, OC method, serving as a local search operator, is integrated with GA. The numerical results verify that the hybrid method provides powerful ability in searching for more optimal solution and reducing computational effort.     

Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints

Structural optimization with frequency constraints is a challenging class of optimization problems characterized by highly non-linear and non-convex search spaces. When using a meta-heuristic algorithm to solve a problem of this kind, exploration/exploitation balance is a key feature to control the performance of the algorithm. An excessively exploitative algorithm might focus on certain areas of the search space ignoring the others. On the other hand, an algorithm that is too explorative overlooks high quality solutions as a result of not performing adequate local search.This paper compares nine multi-agent meta-heuristic algorithms for sizing and layout optimization of truss structures with frequency constraints. The variation of the diversity index during the optimization history is analyzed in order to inspect exploration/exploitation properties of each algorithm. It appears that there is a significant relationship between the algorithm efficiency and the evolution of the diversity index.     

An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints

Structural optimization with frequency constraints is well known as a highly nonlinear and complex optimization problem with many local optimum solutions. Therefore, to solve such problems effectively, designers need to use adequate optimization methods which can make a good balance between the computational cost and the quality of solutions. In this work, a novel differential evolution (DE) is proposed to solve the shape and size optimization problems for truss structures with frequency constraints. The proposed method, called ReDE, is a new version of the DE algorithm with two improvements. Firstly, the roulette wheel selection is employed to choose members for the mutation phase instead of random selection as in the conventional DE. Secondly, an elitist selection technique is applied to the selection phase instead of basic selection to improve the convergence speed of the method. The efficiency and reliability of the proposed method are demonstrated through five numerical examples. Numerical results reveal that the proposed algorithm outperforms many optimization methods in the literature.

     

Truss optimization with multiple frequency constraints and automatic member grouping

This paper deals with sizing and shape structural optimization problems with respect to the minimization of the masses of truss structures considering multiple natural frequencies as the constraints of the problems. The sizing and shape design variables are discrete and continuous, respectively. It can be attractive to use a reduced number of distinct cross-sectional areas minimizing costs of fabrication, transportation, storing, checking, welding, and so on. Also, it is expected a labor-saving when the structure is welded, checked and so on. On the other hand, one can observe that the task of discovering the optimum member grouping is not trivial and leads to an exhaustive trial-and-error process. Cardinality constraints are adopted in order to obtain an automatic variable linking searching for the best member grouping of the bars of the trusses analyzed in this paper. A CRPSO (Craziness based Particle Swarm Optimization) is the search algorithm adopted in this paper. This algorithm uses a modified velocity expression and an operator called “craziness velocity” in order to avoid premature convergence. An Adaptive Penalty Method is adopted to handle the constraints. Six truss structures are analyzed, presenting very interesting results providing curves of tradeoff between the optimized weights versus the number of distinct cross-sectional areas used in these solutions.     

基于改进遗传算法的电力系统无功优化的研究

电力系统无功优化问题是一个多变量、多约束的混合非线性规划问题,其操作变量既有连续变量又有离散变量,其优化过程比较复杂。遗传算法是模拟生物在自然环境中的遗传和进化过程而形成的一种自适应的全局优化搜索算法,可用于解决含有离散变量的复杂优化问题。本文选用遗传算法求解电力系统无功优化问题,并对基本遗传算法的编码、初始种群、适应度函数和交叉、变异策略等进行改进,使用本文提出的改进算法对IEEE1 4节点进行无功优化计算,结果证明本文模型和算法的实用性、可靠性和优越性。     

Improved genetic algorithm with two-level approximation using shape sensitivities for truss layout optimization

Truss layout optimization is a procedure for optimizing truss structures under the combined influence of size, shape and topology variables. This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA) that uses continuous shape variables and shape sensitivities to minimize the weight of trusses under static or dynamic constraints. A uniform optimization model including continuous size/shape variables and discrete topology variables is established. With the introduction of shape sensitivities, the first-level approximations of constraint functions are constructed with respect to shape/topology/size variables. This explicit problem is solved by implementation of a real-coded GA for continuous shape variables and binary-coded GA for 0/1 topology variables. Acceleration techniques are used to overcome the convergence difficulty of the mixed-coded GA. When calculating the fitness value of each member in the current generation, a second-level approximation method is embedded to optimize the continuous size variables effectively. The results of numerical examples show that the usage of continuous shape variables and shape sensitivities improves the algorithm performance significantly.     

软件系统可靠性优化的一种改进方法研究

基于并行遗传算法将软件系统的可靠性优化问题表达为一类带约束条件的组合优化问题,并采用并行遗传算法中的岛屿模型和迁移策略,较好地改善了搜索性能。模拟实验表明:并行遗传算法有效地提高了运行速度和求解质量。     

并行遗传算法在软件可靠性优化中的应用

基于并行遗传算法将软件系统的可靠性优化问题表达为一类带约束条件的组合优化问题，并采用并行遗传算法中的岛屿模型和迁移策略，较好地改善了搜索性能。模拟实验表明：并行遗传算法有效地提高了运行速度和求解质量。     

A novel optimization approach for minimum cost design of trusses

This paper describes new optimization strategies that offer significant improvements in performance over existing methods for bridge-truss design. In this study, a real-world cost function that consists of costs on the weight of the truss and the number of products in the design is considered. We propose a new sizing approach that involves two algorithms applied in sequence – (1) a novel approach to generate a “good” initial solution and (2) a local search that attempts to generate the optimal solution by starting with the final solution from the previous algorithm. A clustering technique, which identifies members that are likely to have the same product type, is used with cost functions that consider a cost on the number of products. The proposed approach gives solutions that are much lower in cost compared to those generated in a comprehensive study of the same problem using genetic algorithms (GA). Also, the number of evaluations needed to arrive at the optimal solution is an order of magnitude lower than that needed in GAs. Since existing optimization techniques use cost functions like those of minimum-weight truss problems to illustrate their performance, the proposed approach is also applied to the same examples in order to compare its relative performance. The proposed approach is shown to generate solutions of not only better quality but also much more efficiently. To highlight the use of this sizing approach in a broader optimization framework, a simple geometry optimization algorithm that uses the sizing approach is presented. This algorithm is also shown to provide solutions better than the existing results in literature.     

Fast structural optimization with frequency constraints by genetic algorithm using adaptive eigenvalue reanalysis methods

Structural optimization with frequency constraints is highly nonlinear dynamic optimization problems. Genetic algorithm (GA) has greater advantage in global optimization for nonlinear problem than optimality criteria and mathematical programming methods, but it needs more computational time and numerous eigenvalue reanalysis. To speed up the design process, an adaptive eigenvalue reanalysis method for GA-based structural optimization is presented. This reanalysis technique is derived primarily on the Kirsch’s combined approximations method, which is also highly accurate for case of repeated eigenvalues problem. The required number of basis vectors at every generation is adaptively determined and the rules for selecting initial number of basis vectors are given. Numerical examples of truss design are presented to validate the reanalysis-based frequency optimization. The results demonstrate that the adaptive eigenvalue reanalysis affects very slightly the accuracy of the optimal solutions and significantly reduces the computational time involved in the design process of large-scale structures.     

Enhanced hybrid metaheuristic algorithms for optimal sizing of steel truss structures with numerous discrete variables

The advent of modern computing technologies paved the way for development of numerous efficient structural design optimization tools in the recent decades. In the present study sizing optimization problem of steel truss structures having numerous discrete variables is tackled using combined forms of recently proposed metaheuristic techniques. Three guided, and three guided hybrid metaheuristic algorithms are developed by integrating a design oriented strategy to the stochastic search properties of three recently proposed metaheuristic optimization techniques, namely adaptive dimensional search, modified big bang-big crunch, and exponential big bang-big crunch algorithms. The performances of the proposed guided, and guided hybrid metaheuristic algorithms are compared to those of standard variants through optimum design of real-size steel truss structures with up to 728 design variables according to AISC-LRFD specification. The numerical results reveal that the hybrid form of adaptive dimensional search and exponential big bang-big crunch algorithm is the most promising algorithm amongst the other investigated techniques.     

基于约束条件的软件可靠性优化问题的研究

基于遗传算法,将软件系统的可靠性优化问题表达为一类带约束条件的组合优化问题,较好地改善了搜索性能。模拟实验表明：遗传算法有效地提高了运行速度和求解质量。