Optimum Design Of Truss Structures Research Articles

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

ABSTRACTA single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.

Improved GWO algorithm for optimal design of truss structures

In this article, an improved grey wolf optimizer (IGWO) algorithm is developed for optimal design of truss structures. Grey wolf optimizer (GWO) is a recently proposed algorithm for optimization, which is herein improved to handle structural optimization in an efficient manner. In this work, performance of the GWO in structural optimization is also investigated. A few tunable parameters are defined to provide proper adaptability for the algorithm and to optimize the structures using fewer structural analyses, while obtaining finer solutions. Hence, in addition to reduce the computational efforts, better solutions are obtained as it is shown by several benchmark examples, where both GWO and IGWO are employed for the optimization. Mathematical functions as well as various design examples from small to large truss structures with different search spaces are examined to demonstrate the ability and efficiency of the present improved version in comparison to its standard version.

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.

Optimum Design of Truss Structures Under Frequency Constraints using Hybrid CSS-MBLS Algorithm

Optimum design of truss structures under frequency constraints is a complicated highly non-linear optimization problem with nonconvex solution space. In this paper, a hybrid Charged System Search (CSS) algorithm with Migration-based Local Search (MBLS) is proposed for resolving this problem. The CSS algorithm as a developed metaheuristic optimization algorithm is inspired by the governing laws of electrostatics in physics and the governing laws of motion from the Newtonian mechanics. In the proposed hybrid CSS-MBLS algorithm, the convergence speed of the standard CSS algorithm is enhanced by the MBLS mechanism. Numerical results obtained from some design examples reveal the successfulness and effectiveness of the proposed algorithm in solving truss optimum design problem under frequency constraints.

Testing Soccer League Competition Algorithm in Comparison with Ten Popular Meta-heuristic Algorithms for Sizing Optimization of Truss Structures

Recently, many meta-heuristic algorithms are proposed for optimization of various problems. Some of them originally are presented for continuous optimization problems and some others are just applicable for discrete ones. In the literature, sizing optimization of truss structures is one of the discrete optimization problems which is solved by many meta-heuristic algorithms. In this paper, in order to discover an efficient and reliable algorithm for optimization of truss structures, a discrete optimizer, entitled Soccer League Competition (SLC) algorithm and ten popular and powerful solvers are examined and statistical analysis is carried out for them. The fundamental idea of SLC algorithm is inspired from a professional soccer league and based on the competitions among teams to achieve better ranking and players to be the best. For optimization purpose and convergence of the initial population to the global optimum, different teams compete to take the possession of the best rating positions in the league table and the internal competitions are taken place between players in each team for personal improvements. Recently, SLC as a multi-population algorithm with developed operators has been applied for optimization of various problems. In this paper, for demonstrating the performance of the different solvers for optimal design of truss structures, five numerical examples will be optimized and the results show that proposed SLC algorithm is able to find better solutions among other algorithms. In other words, SLC can discover new local optimal solutions for some examples where other algorithms fail to find that one.

Performance evaluation of local surrogate models in differential evolution-based optimum design of truss structures

PurposeThe purpose of this paper is to propose and analyze the use of local surrogate models to improve differential evolution’s (DE) overall performance in computationally expensive problems.Design/methodology/approachDE is a popular metaheuristic to solve optimization problems with several variants available in the literature. Here, the offspring are generated by means of different variants, and only the best one, according to the surrogate model, is evaluated by the simulator. The problem of weight minimization of truss structures is used to assess DE’s performance when different metamodels are used. The surrogate-assisted DE techniques proposed here are also compared to common DE variants. Six different structural optimization problems are studied involving continuous as well as discrete sizing design variables.FindingsThe use of a local, similarity-based, surrogate model improves the relative performance of DE for most test-problems, specially when using r-nearest neighbors with r = 0.001 and a DE parameter F = 0.7.Research limitations/implicationsThe proposed methods have no limitations and can be applied to solve constrained optimization problems in general, and structural ones in particular.Practical/implicationsThe proposed techniques can be used to solve real-world problems in engineering. Also, the performance of the proposals is examined using structural engineering problems.Originality/valueThe main contributions of this work are to introduce and to evaluate additional local surrogate models; to evaluate the effect of the value of DE’s parameter F (which scales the differences between components of candidate solutions) upon each surrogate model; and to perform a more complete set of experiments covering continuous as well as discrete design variables.

Optimal design of truss structures using a new optimization algorithm based on global sensitivity analysis

Global sensitivity analysis (GSA) has been widely used to investigate the sensitivity of the model output with respect to its input parameters. In this paper a new single-solution search optimization algorithm is developed based on the GSA, and applied to the size optimization of truss structures. In this method the search space of the optimization is determined using the sensitivity indicator of variables. Unlike the common meta-heuristic algorithms, where all the variables are simultaneously changed in the optimization process, in this approach the sensitive variables of solution are iteratively changed more rapidly than the less sensitive ones in the search space. Comparisons of the present results with those of some previous population-based meta-heuristic algorithms demonstrate its capability, especially for decreasing the number of fitness functions evaluations, in solving the presented benchmark problems.

Optimal Design of Truss Structures Using a Neutrosophic Number Optimization Model under an Indeterminate Environment

Abstract. This paper defines basic operations of neutrosophic numbers and neutrosophic number functions for objective functions and constraints in optimization models. Then, we propose a general neutrosophic number optimization model for the optimal design of truss structures. The application and effectiveness of the neutrosophic number optimization method are demonstrated through the design example of a two-bar truss structure under indeterminate environment to achieve the minimum weight objective under stress and stability constraints. The comparison of the neutrosophic number optimal design method with traditional optimal design methods proves the usability and suitability of the presented neutrosophic number optimization design method under an indeterminate/neutrosophic number environment.

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.

An Adaptive Multi-objective Immune Algorithm for Optimal Design of Truss Structures

In this paper, an adaptive immune clone selection algorithm for multi-objective optimization (AICSAMO) is proposed. A novel adaptive polynomial mutation operator with dynamic mutation probability is employed in AICSAMO. This adaptive mutation operator executes a rapid global search at the earlier stage of the algorithm and a fine-tuning search at the later stage of the algorithm, which adopts generation-dependent parameters to improve the convergence speed and global optimum searching ability. The effectiveness of AICSAMO is evaluated through the truss sizing and shape optimization problems of a 10-bar plane truss and a 25-bar space truss. According to the comparison of AICSAMO with various multi-objective optimization algorithms developed recently, the simulation results illustrate that AICSAMO has remarkable performance in finding a wider spread of optimal solutions and in maintaining better uniformity of the solutions with better convergence.

Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme

Abstract The paper presents an improved differential evolution (IDE) and its application for solving shape and size optimization problems of truss structures with frequency constraints. The improvements are made in mutation and selection phases but mainly focused on the mutation phase. In the mutation phase of the IDE, a new selection scheme is proposed by using multi-mutation operators that adaptively employ all four popular mutation operators, including “rand/1,” “rand/2,” “best/1,” and “best/2” for selecting target vectors in population. This new scheme helps maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. In the selection phase of the IDE, an elitist selection technique that helps save good individuals for the next generation is suggested to replace traditional selection technique of the original DE. The suggested technique can help increase the convergence rate of the IDE. The efficiency and robustness of the IDE are demonstrated through five benchmark problems. Numerical results show that in most of the cases considered, the optimum design obtained by the IDE and DE are nearly the same and they are better than those gained by some other well-known methods in the literature. However, the IDE is much better than the DE in terms of the computational cost.

Truss optimization with dynamic constraints using UECBO

In this article, hybridization of enhanced colliding bodies optimization (ECBO) with upper bound strategy (UBS) that is called UECBO is proposed for optimum design of truss structures with frequency constraints. The distinct feature of the proposed algorithm is that it requires less computational time while preserving the good accuracy of the ECBO. Four truss structures with frequency limitations selected from the literature are studied to verify the viability of the algorithm. This type of problems is highly non-linear and non-convex. The numerical results show the successful performance of the UECBO algorithm in comparison to the CBO, ECBO and some other metaheuristic optimization methods.

Proposed Algorithms for an Efficient System Reliability-Based Design Optimization of Truss Structures

AbstractThe design optimization considering the system reliability of a structural system is a computationally challenging task. This is especially the case in an indeterminate structure that has many possible modes or paths to complete failure. Accomplishing this task efficiently requires using enhanced and powerful techniques for the structural analysis, the reliability analysis, and the optimization solution. In a simulation-based reliability analysis, the actual value of the performance functions is irrelevant to the calculated probability of failure. The actual value of the performance function is merely calculated to determine whether the system failed or not. In this paper, nonlinear analysis algorithms for truss structures are proposed. These algorithms are used for determining whether the structural system failure occurs during the simulation-based system reliability analysis in a computationally efficient manner. Using these algorithms, a simulation-based system reliability design optimization o...

Multi-objective Truss Optimization Using Different Types of the BB-BC Algorithm

Optimum design of truss structures is considered as a benchmark problem in the field of the structural optimization. In order to solve this hard combinatorial problem, it is necessary to implement adequate optimization tool that would provide sufficiently wide range of possible solutions within a reasonable time as well as to obtain good exploration and exploitation of search space. The aim of presented study was to compare efficiency of different multi-objective algorithms in solving this task.

Multi-objective Truss Optimization Using Different Types of the BB-BC Algorithm

Optimum design of truss structures is considered as a benchmark problem in the field of the structural optimization. In order to solve this hard combinatorial problem, it is necessary to implement adequate optimization tool that would provide sufficiently wide range of possible solutions within a reasonable time as well as to obtain good exploration and exploitation of search space. The aim of presented study was to compare efficiency of different multi-objective algorithms in solving this task.

An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures

Recently, a Sequential Optimization and Reliability Assessment (SORA) method was proposed and proven to be effective for solving reliability-based design optimization (RBDO) problems. In the SORA, the optimization loop and the reliability assessment loop are decoupled from each other. This helps improve the efficiency of the SORA significantly. However, the SORA still exists two main drawbacks: (1) the optimal solutions are easily trapped within local extremes and (2) the optimal results depend on the initial trial points. To overcome these drawbacks, this paper integrates the SORA with the Improved Constrained Differential Evolution algorithm (ICDE) to give a so-called SORA-ICDE for solving RBDO problems. Due to the global search mechanism, the SORA-ICDE can easily obtain global solutions regardless of initial points. The numerical results obtained in the paper are compared with available results in the literature to illustrate the efficiency, applicability and precision of the SORA-ICDE in solving the RBDO problems for truss structures.

Truss layout design and optimization using a generative synthesis approach

This paper describes a generative methodology for optimum design of truss structures. The novelty of the proposed method is its combination of generative design synthesis methods with conventional gradient-based optimization and simulation models. This combination is able to achieve optimal topologies and shapes for cable trusses under various constraints: stress, displacement, stability. Furthermore, manufacturing issues properly limit the generated solutions. A graph grammar is used to define different topologies for a given load problem. The effectiveness of the method is checked by solving a variety of available test problems found in the literature as well as several new three-dimensional solutions.

A Cultural Algorithm for Optimal Design of Truss Structures

A cultural algorithm was utilized in this study to solve optimal design of truss structures problem achieving minimum weight objective under stress and deflection constraints. The algorithm is inspired by principles of human social evolution. It simulates the social interaction between the peoples and their beliefs in a belief space. Cultural Algorithm (CA) utilizes the belief space and population space which affects each other based on acceptance and influence functions. The belief space of CA consists of different knowledge components. In this paper, only situational and normative knowledge components are used within the belief space. The performance of the method is demonstrated through four benchmark design examples. Comparison of the obtained results with those of some previous studies demonstrates the efficiency of this algorithm.

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.

Two-dimensional colliding bodies algorithm for optimal design of truss structures

This paper focuses on the new version of a recently developed meta-heuristic algorithm, Colliding Bodies Optimization (CBO), and its utility for optimization of truss structures. The idea of the standard CBO is derived from one-dimensional collisions between bodies, which does not use the internal parameter and memory in its formulation. However, the exploitation phase of the CBO is weak due to not using a memory for saving the best-so-far solution in its formulation. Here, in the two dimensional version of CBO, denoted by 2D-CBO, a memory is added to the standard CBO formulation to improve the performance of the latter algorithm. This addition increases the exploitation ability and convergence rate of the CBO. Comparative studies illustrate the superiority of the 2D-CBO algorithm compared to those previously reported in the literature.