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.     

Optimal design of truss structures for size and shape with frequency constraints using a collaborative optimization strategy

A new metaheuristic strategy is proposed for size and shape optimization problems with frequency constraints. These optimization problems are considered to be highly non-linear and non-convex. The proposed strategy extends the idea of using a single optimization process to a series of collaborative optimization processes. In this study, a modified teaching-learning-based optimization (TLBO), which is a relatively simple algorithm with no intrinsic parameters controlling its performance, is utilized in a collaborative framework and introduced as a higher-level TLBO algorithm called school-based optimization (SBO). SBO considers a school with multiple independent classrooms and multiple teachers with inter-classroom collaboration where teachers are reassigned to classrooms based on their fitness. SBO significantly improves the both exploration and exploitation capabilities of TLBO without increasing the algorithm's complexity. In addition, since the SBO algorithm uses multiple independent classrooms with interchanging teachers, the algorithm is less likely to be influenced by local optima. A parametric study is conducted to investigate the effects of the number of classes and the class size, which are the only parameters of SBO. The SBO algorithm is applied to five benchmark truss optimization problems with frequency constraints and the statistical results are compared to other optimization techniques in the literature. The quality and robustness of the results indicate the efficiency of the proposed SBO algorithm.     

Hypotrochoid spiral optimization approach for sizing and layout optimization of truss structures with multiple frequency constraints

Engineering with Computers - The primary aim of this article is to present a new improved version of the spiral optimization algorithm (SPO) for shape and size optimization of truss structures...     

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.

     

基于退火算法的生产效能最优化

实际生产中有大量工艺过程与加工路线有关,在工件上寻求最短的加工路线能极大地提高生产效能。试图求解印刷线路板(PCB)多类型孔加工过程的生产效能最优解。通过建立生产效能函数并进行分析,认为在生产条件一定的情况下换刀时间和加工路线是影响生产效能的两个主要因素。换刀时间与刀具的加工顺序有关,而加工路线本质是旅行商问题(TSP),用退火算法求其最优解,最终使生产成本最低。然后通过实例模型证明生产效能函数的可行性。该方法可广泛用于生产实践,尤其对与加工路线有关的生产过程来说,有助于提高生产效率、节约成本。     

Integrated size and topology optimization of skeletal structures with exact frequency constraints

The present paper studies the integrated size and topology optimization of skeletal structures under natural frequency constraints. It is found that, unlike the conventional compliance-oriented topology optimization problems, the considered problem may be strongly singular in the sense that the corresponding feasible domain may be disconnected and the global optimal solutions are often located at the tips of some separated low dimensional sub-domains when the cross-sectional areas of the structural components are used as design variables. As in the case of stress-constrained topology optimization, this unpleasant behavior may prevent the gradient-based numerical optimization algorithms from finding the true optimal topologies. To overcome the difficulties posed by the strongly singular optima, some particular forms of area/moment of inertia-density interpolation schemes, which can restore the connectedness of the feasible domain, are proposed. Based on the proposed optimization model, the probability of finding the strongly singular optimum with gradient-based algorithms can be increased. Numerical examples demonstrate the effectiveness of the proposed approach.     

求解旅行商问题的模拟退火蚁群算法

根据蚁群算法与模拟退火算法的特性,提出了求解旅行商问题的混合算法.由模拟退火算法生成信息素分布,然后由蚁群算法根据累计更新的信息素找出若干组解,再经过模拟退火算法在邻域内找另外一个解的操作,得到更有效的解.与模拟退火算法、标准遗传算法、蚁群算法和随机初始化的蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.     

A modified simulated annealing algorithm and an excessive area model for floorplanning using fixed-outline constraints

Outline-free floorplanning focuses on area and wirelength reductions, which are usually meaningless, since they can hardly satisfy modern design requirements. We concentrate on a more difficult and useful issue, fixed-outline floorplanning. This issue imposes fixed-outline constraints on the outline-free floorplanning, making the physical design more interesting and challenging. The contributions of this paper are primarily twofold. First, a modified simulated annealing (MSA) algorithm is proposed. In the beginning of the evolutionary process, a new attenuation formula is used to decrease the temperature slowly, to enhance MSA’s global searching capacity. After a period of time, the traditional attenuation formula is employed to decrease the temperature rapidly, to maintain MSA’s local searching capacity. Second, an excessive area model is designed to guide MSA to find feasible solutions readily. This can save much time for refining feasible solutions. Additionally, B*-tree representation is known as a very useful method for characterizing floorplanning. Therefore, it is employed to perform a perturbing operation for MSA. Finally, six groups of benchmark instances with different dead spaces and aspect ratios—circuits n10, n30, n50, n100, n200, and n300—are chosen to demonstrate the efficiency of our proposed method on fixed-outline floorplanning. Compared to several existing methods, the proposed method is more efficient in obtaining desirable objective function values associated with the chip area, wirelength, and fixed-outline constraints.     

求解约束优化的一个自适应杂交差分演化算法

结合基于可行性规则的约束处理技术,构造了一个求解约束优化问题的自适应杂交差分演化模拟退火算法。该算法以差分演化算法为基础,用模拟退火策略来增强种群的多样性,用一个基于可行性规则的约束处理技术来处理不等式约束,且自适应化关键控制参数,避开人为控制参数的困难。在标准测试集上的实验结果表明该算法的有效性,与同类算法的比较表明了该算法的优越性。     

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.     

Discrete optimization of geometrically nonlinear truss structures under stability constraints

The paper deals with discrete optimization of elastic trusses with geometrical nonlinear behaviour and constraints on stability. The problem consists of minimizing the weight and determining the optimal member distribution so that the external load does not cause a loss of stability of the structure. Member cross-sections are selected from a catalogue of available sections. Element stresses, elment stability and global structural stability constraints are considered. A controlled enumeration method according to the increasing value of the objective function is applied. Shallow space trusses are numerically analysed.     

Truss optimization with natural frequency constraints using generalized normal distribution optimization

The newly proposed Generalized Normal Distribution Optimization (GNDO) algorithm is used to design the truss structures with optimal weight. All trusses optimized have frequency constraints, which make them very challenging optimization problems. A large number of locally optimal solutions and non-convexity of search space make them difficult to solve, therefore, they are suitable for testing the performance of optimization algorithm. This work investigates whether the proposed algorithm is capable of coping with such problems. To evaluate the GNDO algorithm, three benchmark truss optimization problems are considered with frequency constraints. Numerical data show GNDO’s reliability, stability, and efficiency for structural optimization problems than other meta-heuristic algorithms. We thoroughly analyse and investigate the performance of GNDO in this engineering area for the first time in the literature.

     

一种基于改进模拟退火算法的程序性能优化参数搜索算法

高级程序变换是提高程序性能的重要手段,很多涉及到优化参数的选择问题,如为循环分块选择适当的分块因子。由于优化参数搜索问题本身是NP难问题,目前尚没有确定性的算法可以有效解决该问题,针对于此,将该问题转化为一个非线性全局最优化问题,提出一种基于改进模拟退火算法的程序性能优化参数搜索算法,实验结果验证了算法的有效性。     

函数优化问题的一种异步并行模拟退火算法

针对工程中的多极值点复杂函数的优化问题,提出一种完全异步的粗粒度并行模拟退火算法.在一定时间内将一条Markov链分裂成多条Markov链,并结合其他多种改进方法,获得了可扩展的并行效果,提高了算法应用的灵活性.数值计算表明,该方法可显著提高算法的收敛速度.     

Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming

The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimization problems to capitalize on this new design freedom. In response to this, an iterative approach in which Sequential Linear Programming (SLP) is used to simultaneously solve a size and shape optimization sub-problem subject to local stress and Euler buckling constraints is proposed in this work. To accomplish this, a first order Taylor expansion for the nodal movement and the buckling constraint is derived to conform to the SLP problem formulation. At each iteration a post-processing step is initiated to map a design vector to the exact buckling constraint boundary in order to facilitate the overall efficiency. The method is verified against an exact non-linear optimization problem formulation on a range of benchmark examples obtained from the literature. The results show that the proposed method produces optimized designs that are either close or identical to the solutions obtained by the non-linear problem formulation while significantly decreasing the computational time. This enables more efficient size and shape optimization of truss structures considering practical engineering constraints.     

Sizing optimization of truss structures using flower pollination algorithm

The recently developed flower pollination algorithm is used to minimize the weight of truss structures, including sizing design variables. The new algorithm can efficiently combine local and global searches, inspired by cross-pollination and self-pollination of flowering plants, respectively. Furthermore, it implements an iterative constraint handling strategy where trial designs are accepted or rejected based on the allowed amount of constraint violation that is progressively reduced as the search process approaches the optimum. This strategy aims to obtain always feasible optimized designs. The new algorithm is tested using three classical sizing optimization problems of 2D and 3D truss structures. Optimization results show that the proposed method is competitive with other state-of-the-art metaheuristic algorithms presented in the literature.     

求解旅行商问题的波动温控模拟退火算法

针对传统模拟退火算法在求解旅行商问题时运行时间长,易陷入局部最优,且随着问题规模的增大缺陷愈发明显的问题,对传统算法的内循环过程和退火机制进行改进,使得内循环的搜索强度根据温度的变化自适应调整,同时提出波动温度控制机制,使得算法在保持温度幅值递减的总趋势下实现多次升温过程,增强求解效果,缩短求解时间,并通过TSPLIB数据库提供的大量实例得以验证.     

A hybrid CBO–PSO algorithm for optimal design of truss structures with dynamic constraints

The vibration domain of structures can be reduced by imposing some constraints on their natural frequencies. For this purpose optimal design of structures under frequency constraints is required which involves highly non-linear and non-convex problems. In this paper an efficient hybrid algorithm is developed for solving such optimization problems. This algorithm utilizes the recently developed colliding bodies optimization (CBO) algorithm as the main engine and uses the positive properties of the particle swarm optimization (PSO) algorithm to increase the efficiency of the CBO. The distinct feature of the present hybrid algorithm is that it requires no parameter tuning. The CBO is known for being parameter independent, and avoiding the use of the traditional penalty method to handle the constraints upholds this property. Two mathematical constrained functions taken from the literature are studied to verify the performance of the algorithm. The algorithm is then applied to optimize truss structures with frequency limitations. The numerical results demonstrate the efficiency of the presented algorithm for this class of problems.     

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.