Truss layout design and optimization using a generative synthesis approach

<p>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.</p>

In recent decades, due to the limitations of resources and equipment in the construction of engineering projects, the optimal use of existing facilities for reducing the overall costs of the projects has been of great importance. Due to the significant advances in optimization techniques, the application of these methods in engineering sciences, especially civil and structural engineering, has received more attention than before. In the last years, various optimization methods and algorithms have been used for optimization purposes, including metaheuristic algorithms. In this paper, the optimum design of truss structures is considered utilizing Atomic Orbital Search (AOS) as one of the recently developed metaheuristic algorithms. The applicability of this technique in the weight optimization of complex truss structures is in perspective. Four of the benchmark problems in the truss optimization field, such as 10-bar, 25-bar, 52-bar, and 160-bar truss structures, are used as design examples. A simple penalty approach is implemented in AOS as a constraint handling scheme, while a comprehensive statistical analysis is also conducted through multiple optimization runs. The results of the AOS are compared to the results of other methods from the literature, while the AOS demonstrates a good level of weight reduction capability in dealing with these complex design problems.KeywordsTruss structureAtomic orbital searchMetaheuristic algorithmOptimization first section

This paper discusses the effect of global stability on the optimal size and shape of truss structures taking into account of a nonlinear critical load, truss weight and serviceability at the same time. The nonlinear critical load is computed by arc-length method. In order to increase the accuracy of the estimation of critical load (ignoring material nonlinearity), an eigenvalue analysis is implemented into the arc-length method. Furthermore, a pure pareto-ranking based multi-objective optimization model is employed for the design optimization of the truss structure with multiple objectives. The computational performance of the optimization model is increased by implementing an island model into its evolutionary search mechanism. The proposed design optimization approach is applied for both size and shape optimization of real world trusses including 101, 224 and 444 bars and successful in generating feasible designations in a large and complex design space. It is observed that the computational performance of pareto-ranking based island model is better than the pure pareto-ranking based model. Therefore, pareto-ranking based island model is recommended to optimize the design of truss structure possessing geometric nonlinearity.

An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures

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

The algorithmic design is a structural shape design approach based on mathematical functions that consists of several parameters. On the basis of the approach, optimual structural design problems can also be formulated with respect to a relatively limited number of design variables, generating somewhat elegant and complex resultant designs. In the current study, the approach is applied to optimal design of truss structures. We develop a formulation applicable to various types of truss structures. Some computational examples are also demonstrated.

8 - Optimum Design of Skeletal Structures via Big Bang–Big Crunch Algorithm

The genetic algorithm(GA) is efficient method for topological optimization problem of truss structures because it is possible to obtain global optimum on non-convex design space. The bottleneck of this method is that a large number of function evaluations and structural analyses are necessarily. Performance of the GA depends on first arrangement of string positions and the crossover operator strongly when the simple GA apply to the topological optimization problems. If inadequate correspondence between design variables and the string positions is used, good solution is hardly obtained in spite of numerous calculations. The objective of this study is development a new genetic algorithm specialized to the topological optimization problem of the truss structure improving the calculation efficiency and reliability to obtain optimum solution. To overcome disadvantage of the simple GA, biased crossover operation with string position rearrangement is proposed. Highly fitted gene is crated and inherited by using this procedure. Minimum weight design of the truss structure consists of nine nodes are carried out by using simple G A and proposed GA, and calculation performance is compared. From the result, it is confirmed that the proposed GA is more effective and reliable in comparison with the simple GA.

Interactive optimal design of truss structures

The purpose of this study is to develop an advanced neural network algorithm as a new optimisation for the optimal design of truss structures. The central concept of the algorithm is based on biological nerve structures and artificial neural networks. The performance of the proposed method is explored in engineering design problems. Two efficient methods for improving the standard neural network algorithm are considered here. The first is an enhanced initialisation mechanism based on opposite-based learning. The second relies on using a few tunable parameters to provide proper exploration and exploitation abilities for the algorithm, enabling better solutions to be found while the required structural analyses are reduced. The new algorithm's performance is investigated by using five well-known restricted benchmarks to assess its efficiency in relation to the latest optimisation techniques. The outcome of the examples demonstrates that the upgraded version of the algorithm has increased efficacy and robustness in comparison with the original version of the algorithm and some other methods.

An ant algorithm, consisting of the Ant System and API (after “apicalis” in Pachycondylaapicalis) algorithms, was proposed in this study to find optimal truss structures to achieve minimum weight objective under stress, deflection, and kinematic stability constraints. A two-stage approach was adopted in this study; first, the topology of the truss structure was optimized from a given ground structure employing the Ant System algorithm due to its discrete characteristic, and then the size and/or shape of member was optimized utilizing the API algorithm. The effectiveness of the proposed ant algorithm was evaluated through numerous different 2-D and 3-D truss-structure problems. The proposed algorithm was observed to find truss structures better than those reported in the literature. Moreover, multiple different truss topologies with almost equal overall weights can be found simultaneously.

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

Size optimization of space trusses using Big Bang–Big Crunch algorithm

The structural optimization of trusses is a complex problem that can be affected by many different factors. In this research, the authors investigated the optimization of trusses performing a geometric nonlinear analysis under dynamic loading, using two different metaheuristic algorithms: the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The objective function was to minimize the weight of the structure. A number of benchmark test problems for spatial trusses considering a geometric nonlinear analysis, and dynamic loading are analyzed to verify the performance of the optimization algorithms. The results showed that both algorithms were able to find efficient solutions to the optimization problem and suggest that the choice of the optimization algorithm can have a significant impact on the performance of the optimization process.

There are two general methods of robust design optimization (RDO) and reliability-based robust design optimization (RBRDO) for the optimal design of structures with non-deterministic variables. In the problem-solving process of both RDO and RBRDO, assessing the probabilistic constraints of the problem and the standard deviation of the structural responses is time-consuming and costly. In this study, by presenting a multi-step approach, for a probable optimal solution, the deterministic constraints are first investigated. Then the limit state functions related to probabilistic constraints are computed based on the mean value of random variables (in the RBRDO problem) and in the step of uncertainties effects simulation on the response of the structure, probabilistic constraints are evaluated (in the RBRDO problem). Designs that not meeting the deterministic constraints or in the unsafe area for the mean values of the random variables are not included in calculating the first and second terms of the objective function and reliability assessment. This leads to reduce the volume of calculations. The Monte Carlo simulation method is used to assess the probabilistic constraints, and the EVPS metaheuristic algorithm is used for the optimization process. Three benchmark trusses of 10, 25, and 72 bars were studied to assess the efficiency of the proposed approach. The first objective function in these problems was the mean weight of trusses and the second objective function was the standard deviation of the displacement of a specific node in a certain direction.