Layout Optimization Of Truss Structures Research Articles

Development of a non-uniform cellular automata framework for sizing, topology and layout optimization of truss structures

This article presents a bi-level non-uniform cellular automata (CA) algorithm for the solution of sizing, topology and layout optimization of truss structures. The non-uniform CA was successfully used in a previous study to solve the weight optimization problem of truss structures for topology and sizing (El Bouzouiki, Sedaghati, and Stiharu 2021. Computers & Structures 242: 106394). In this article, an extended version of the non-uniform CA algorithm is proposed, based on the fully stressed design approach and the distribution of strain energy within the structure, to find the optimal position of the cell’s (joint’s) coordinates. The proposed non-uniform CA algorithm can solve the minimum weight optimization problem of truss structures subjected to both stress and displacement constraints. Several benchmark problems are presented to demonstrate the efficiency and accuracy of the proposed methodology.

Sizing and layout optimization of truss structures with artificial bee colony algorithm

In this paper, a swarm intelligence-based optimization technique called Artificial Bee Colony algorithm (ABC) is employed in combined optimization of truss structures. The objective is to optimize the layout and members size of truss structures with displacement, stress and buckling constraints. The ABC is based on simulating the intelligent foraging behavior of honey bees. The nodal coordinates of the joints and the cross-sectional areas of the members for the truss structure system are the design variables of shape and size optimization, respectively. Allowable stress, Euler buckling stress, and displacement are considered as the problem constraints. The efficiency of the ABC is tested in four benchmark structural optimization problems. The results clearly reveal the superiority of ABC over other algorithms in terms of optimized weight, standard deviation and number of structural analyses. The ABC demonstrates a robust performance with a 100% success rate.

Size/Layout Optimization of Truss Structures Using Shuffled Shepherd Optimization Method

The main purpose of this paper is to investigate the ability of the recently developed multi-community meta-heuristic optimization algorithm, shuffled shepherd optimization algorithm (SSOA), in layout optimization of truss structures. The SSOA is inspired by mimicking the behavior of shepherd in nature. In this algorithm, agents are first divided into communities which are called herd and then optimization process, inspired by the shepherd’s behavior in nature, is operated on each community. The new position of agents is obtained using elitism technique. Then communities are merged for sharing the information. The results of SSOA in layout optimization show that SSOA is competitive with other considered meta-heuristic algorithms.

Size and layout optimization of truss structures with dynamic constraints using the interactive fuzzy search algorithm

Optimizing truss structures considering natural frequency constraints can fundamentally enhance their dynamic behaviour under transient loadings. In this regard, the current investigation assesses the search capability of the interactive fuzzy search algorithm (IFSA) in solving this class of problem. Since the natural frequencies are very sensitive to configuration changes in the system, throughout the optimization process the algorithm should be able to adaptively shift its search behaviour. To meet this aim, the IFSA utilizes two nine-rule fuzzy modules which permanently monitor the optimization process and try to balance the exploration and exploitation search behaviours of the algorithm. Then, the search capability of the proposed method is tested on five structural benchmark problems. The numeric results reveal that the IFSA, by systematically reducing the number of ineffective iterations, considerably decreases the required computational cost. In addition, considering solution accuracy and process stability, IFSA provides promising results in solving structural optimization problems.

Multimaterial layout optimization of truss structures via an improved particle swarm optimization algorithm

This paper presents an extension of the basic truss layout optimization, in which the use of various materials is considered. A novel improved version of the particle swarm optimization algorithm, namely, GEMPSO, is developed for solving this problem. The enhancement is realized by introducing two core strategies: gradient estimation and multiple subpopulation division. The efficiency and reliability of the proposed improvements are demonstrated on a set of six test problems and three truss structures. Two multimaterial layout optimizations of truss structures are performed. The numerical results reveal that the appropriate partial use of expensive stronger materials can reduce the overall cost of multimaterial structures.

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

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 under multiple frequency constraints. In the proposed method, which is named as hypotrochoid spiral optimization algorithm (HSPO), the movement operation of search points is redesigned, and mechanisms are utilized to boost the potency of the method in escaping from local optima and improving the accuracy of the results. Furthermore, a meta-optimization approach is developed by hybridizing the particle swarm optimization and the proposed technique for finding optimal parameter settings of the presented method. Thereafter, exploration and exploitation abilities of HSPO and SPO are compared by solving five benchmark design problems. Numerical results indicate that the convergence speed is enhanced, especially in the exploitation phase of the HSPO. The optimum designs found by the improved version are highly competitive with the best solutions reported in the literature.

A modified stiffness spreading method for layout optimization of truss structures

The stiffness spreading method (SSM) was initially proposed for layout optimization of truss structures, in which an artificial elastic material of low modulus is uniformly distributed in the design domain to create connections between discrete members. In this paper, a modified stiffness spreading method is proposed by replacing the artificial elastic material with auxiliary bars to connect real members of the truss structure. Since the background continuum mesh for the elastic material is no longer required, the computational cost is significantly reduced. Like SSM, the new method is advantageous in that an initial design may consist of disconnected bars allocated in the design domain, and mathematical programming methods can be applied for the efficient solution of the formulated optimization problem. A number of solution strategies are also developed to achieve more practical designs with lower computational cost. Numerical examples of both 2-D and 3-D truss structures are presented to demonstrate the feasibility, robustness and effectiveness of the proposed method.

Sizing, layout and topology design optimization of truss structures using the Jaya algorithm

A very recently developed metaheuristic method called Jaya algorithm (JA) is implemented in this study for sizing and layout optimization of truss structures. The main feature of JA is that it does not require setting algorithm-specific parameters. The algorithm has a very simple formulation where the basic idea is to approach the best solution and escape from the worst solution. The original JA formulation is modified in this research in order to improve convergence speed and reduce the number of structural analyses required in the optimization process. The suitability of JA for truss optimization is investigated by solving six classical weight minimization problems of truss structures including sizing, layout and large-scale optimization problems with up to 204 design variables. Discrete sizing/layout variables and simplified topology optimization also are considered. The test problems solved in this study are very common benchmarks in structural optimization and practically describe all scenarios that may be faced by designers. The results demonstrate that JA can obtain better designs than those of the other state-of-the-art metaheuristic and gradient-based optimization methods in terms of optimized weight, standard deviation and number of structural analyses.

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

ABSTRACTStructural 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.

An improved fully stressed design evolution strategy for layout optimization of truss structures

During the recent decade, truss optimization by meta-heuristics has gradually replaced deterministic and optimality criteria-based methods. While they may provide some advantages regarding their robustness and ability to avoid local minima, the required evaluation budget grows fast when the number of design variables is increased. This practically limits the size of the problems to which they can be applied. Furthermore, many recent stochastic optimization methods handle the size optimization only, the potential saving from which is highly limited, when compared to the most sophisticated, and obviously the most challenging scenario, simultaneous topology, shape and size (TSS) optimization. In a recent study by the authors, a method based on combination of optimality criteria and evolution strategies, called fully stressed design based on evolution strategies (FSD-ES), was proposed for TSS optimization of truss structures. FSD-ES outperformed available truss optimizers in the literature, both in efficiency and robustness. The contribution of this study is twofold. First, an improved version of FSD-ES method, called FSD-ES-II, is proposed. In comparison with the earlier version, it takes the displacement constraints in the resizing step into account and can handle constraints governed by practically used specifications. Update of strategy parameters is also revised following contemporary and new developments in evolution strategies. Second, a test suite involving a number of complicated TSS optimization problems is chosen to overcome usual shortcomings in the available benchmark problems. For each problem, performance of FSD-ES-II is compared with the best results available in the literature, often showing a significant superiority of the proposed approach.

An improved constrained differential evolution using discrete variables (D-ICDE) for layout optimization of truss structures

Recently, an improved (μ+λ) constrainted differential evolution (ICDE) has been proposed and proven to be robust and effective for solving constrainted optimization problems. However, so far, the ICDE has been developed mainly for continuous design variables, and hence it becomes inappropriate for solving layout truss optimization problems which contain both discrete and continuous variables. This paper hence fills this gap by proposing a novel discrete variables handling technique and integrating it into original ICDE to give a so-called Discrete-ICDE (D-ICDE) for solving layout truss optimization problems. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress, displacement and buckling limitations. Numerical examples of five classical truss problems are carried out and compared to other state-of-the-art optimization methods to illustrate the reliability and effectiveness of the proposed method. The D-ICDE’s performance shows that it not only successfully handles discrete variables but also significantly improves the convergence of layout truss optimization problem. The D-ICDE is promising to extend for determining the optimal solution of other structural optimization problems which contain both discrete and continuous variables.

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.

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.

The stiffness spreading method for layout optimization of truss structures

A novel optimization method, stiffness spreading method (SSM), is proposed for layout optimization of truss structures. In this method, stiffness matrices of the bar elements in a truss structure are represented by a set of equivalent stiffness matrices which are embedded in a weak background mesh. When the proposed method is used, it is unnecessary for the bar elements in a truss structure to be connected to each other during the optimization process, and each of the bar elements can move independently in the design domain to form an optimized design. Another feature of the method is that the sensitivity analysis can be done analytically, making gradient based optimization algorithms applicable in the solution. This method realizes the size, shape and topology design optimization of truss structures simultaneously and allows for more flexibility in topology change. Numerical examples illustrate the feasibility and effectiveness of the proposed method.

Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization

The main contribution of the present paper is to propose an efficient hybrid optimization algorithm for layout optimization of truss structures. To achieve this, computational merits of the cellular automata (CA) and the particle swarm optimization (PSO) are integrated. In the proposed hybrid algorithm a CA-based mechanism is utilized as the velocity updating equation of the particles in the framework of the sequential unconstrained minimization techniques and therefore it is denoted as sequential cellular PSO (SCPSO). The numerical results demonstrate that SCPSO not only converges to better solutions but also provides faster convergence rate in comparison with other algorithms.

A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures

In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front.

Approach for layout optimization of truss structures with discrete variables under dynamic stress, displacement and stability constraints

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.