Size Optimization Of Truss Structures Research Articles

Accelerated multi-gravitational search algorithm for size optimization of truss structures

Abstract Weak local exploitation capability of the gravitational search algorithm (GSA) and its slow convergence rate in final iterations have been demonstrated in the literature. This paper presents a modified GSA denoted here as the accelerated multi-gravitational search algorithm (AMGSA) that exhibits an improved convergence rate. In AMGSA, the simplex crossover (SPX) and the operator mutation of the breeder genetic algorithm (BGA) are incorporated with the multi-gravitational search algorithm (MGSA) to achieve an algorithm with a good exploration-exploitation balance. MGSA is adopted to prevent stagnation of the search into a local optimum (i.e. to improve the exploration capability), while the SPX and the BGA mutation operator are used to bias the search toward promising areas of the search space (i.e. to promote local exploitation). The performance of AMGSA is evaluated using several benchmark truss optimization examples. Results indicate that AMGSA not only exhibits an improved balance between the exploration and exploitation schemes but also shows competitive promise in effectively and efficiently solving large-scale optimization problems as it requires a significantly lower number of structural analyses compared to other algorithms that it is checked against.

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.

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.

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.

Water cycle, mine blast and improved mine blast algorithms for discrete sizing optimization of truss structures

This paper presents the applications of the mine blast algorithm (MBA) and the water cycle algorithm (WCA), in addition to an improved version of MBA for weight minimization of truss structures including discrete sizing variables. The MBA mimics the explosion of landmines, while the WCA is inspired by the observation of water cycle process. An improved version of MBA (IMBA), is also presented. The efficiency of the three optimization algorithms is tested using classical benchmark discrete truss design problems. Optimization results show that MBA, IMBA, and WCA offer a good degree of competitiveness against other state-of-the-art metaheuristic techniques.

Simultaneous topology, shape and size optimization of truss structures by fully stressed design based on evolution strategy

The most effective scheme of truss optimization considers the combined effect of topology, shape and size (TSS); however, most available studies on truss optimization by metaheuristics concentrated on one or two of the above aspects. The presence of diverse design variables and constraints in TSS optimization may account for such limited applicability of metaheuristics to this field. In this article, a recently proposed algorithm for simultaneous shape and size optimization, fully stressed design based on evolution strategy (FSD-ES), is enhanced to handle TSS optimization problems. FSD-ES combines advantages of the well-known deterministic approach of fully stressed design with potential global search of the state-of-the-art evolution strategy. A comparison of results demonstrates that the proposed optimizer reaches the same or similar solutions faster and/or is able to find lighter designs than those previously reported in the literature. Moreover, the proposed variant of FSD-ES requires no user-based tuning effort, which is desired in a practical application. The proposed methodology has been tested on a number of problems and is now ready to be applied to more complex TSS problems.

Weight optimization of truss structures by a new feasible boundary search technique hybridized with firefly algorithm

In most metaheuristic optimization techniques, constraint handling is accomplished by traditional penalty function method which may generate infeasible solutions. The main objective of this paper is to introduce a new technique for constraint handling in size optimization of truss structures. The method restricts the searching space on the feasible boundary and hence it is referred to as Feasible Boundary Search (FBS) technique. By limiting the searching space on the feasible boundary, the problem constraints are automatically satisfied. The method generates absolutely feasible high-quality solutions. Its generality enables the scheme to be hybridized with most metaheuristics. By presenting some modifications on the standard Firefly Algorithm (FA), a powerful hybridized technique which is denoted by FBSFA is then developed for fast weight optimization of truss structures. Several design examples show the effectiveness, robustness and accuracy of FBSFA.

The Great Salmon Run Metaheuristic for Robust Shape and Size Design of Truss Structures with Dynamic Constraints

In this investigation, the authors intend to demonstrate the applicability of a recent spotlighted metaheuristic called the great salmon run (TGSR) algorithm for shape and size design of truss structures. The algorithmic functioning of TGSR emulates the annual migration of salmons together with dangers laid through their pathways. In a previous study by the authors, it has been proved that the method is as effective as most of the state-of-the-art metaheuristics for a wide range of numerical benchmark problems. Here, the authors utilize TGSR together with some rival metaheuristics, i.e. bee algorithm (BA), scale factor local search differential evolutionary algorithm (SFLSDEA), chaotic particle swarm optimization (CPSO) algorithm, self adaptive penalty function genetic algorithm (SAPFGA) and mutable smart bee algorithm (MSBA), for optimal design of truss structures with dynamic frequency constraints. To effectively handle the constraints, the authors take the advantage of self-adaptive penalty function (SAPF) constraint handling technique to free the user from any priori penalty coefficient tuning. Therefore, an algorithm for automation of constraint shape and size design of truss structures is proposed here. Furthermore, for more elaboration, the authors consider the results of some previous reports for same problems to find out whether TGSR is capable of yielding comparative results as compared to other metaheuristics. Through the experiments, the exploration/exploitation capabilities of TGSR for truss design are investigated. It is proved that TGSR is not only able to handle the nonlinearities and decision making difficulties associated with shape and size optimization of truss structures but also can show comparative results as compared to powerful state-of-the-art metaheuristics.

Chaotic swarming of particles: A new method for size optimization of truss structures

A new combination of swarm intelligence and chaos theory is presented for optimal design of truss structures. Here the tendency to form swarms appearing in many different organisms and chaos theory has been the source of inspiration, and the algorithm is called chaotic swarming of particles (CSP). This method is a kind of multi-phase optimization technique which employs chaos theory in two phases, in the first phase it controls the parameter values of the particle swarm optimization (CPVPSO) and the second phase is utilized for local search (CLSPSO). Some truss structures are optimized using the CSP algorithm, and the results are compared to those of the other meta-heuristic algorithms showing the effectiveness of the new method.

Fully Stressed Design Evolution Strategy for Shape and Size Optimization of Truss Structures

Following the principles of the state-of-the-art Evolution Strategies in continuous optimization, a novel algorithm is introduced which simultaneously optimizes shape and size of truss structures. The algorithm, called Fully Stressed Design Evolution Strategy (FSD-ES), combines advantages of the well-known deterministic approach of Fully Stressed Design and potent global search of Evolutionary Algorithms. Based on available engineering knowledge on truss analysis, a novel adaptive penalty term is also introduced and utilized to reinforce the near-bound search abilities of the algorithm. Following recent advances in empirical evaluation, the performance of FSD-ES is assessed on a reasonable test suite and compared to the best results available in the literature. Performance for the case without grouping members or exploiting symmetry are also reported which significantly increase the problem dimension, leading to more challenging test problems, more discriminating results and more reliable conclusions. Result comparison demonstrates that for more complicated problems FSD-ES reaches the same fitness noticeably faster and finds a relatively lighter structure than those previously reported in the literature.

Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms

Mass optimization on shape and sizing with multiple natural frequency constraints are highly nonlinear dynamic optimization problems. Multiple natural frequency constraints normally cause difficult dynamic sensitivity analysis and, in addition, two different types of design variables, nodal coordinates and cross-sectional areas, often lead to divergence. Thus, the choice of the appropriated method to solve this kind of problem is of paramount importance. Within this context, in this paper two of the most recent metaheuristic algorithms developed in the last decade, Harmony Search (HS) and Firefly Algorithm (FA), are used, for the first time here, to solve truss shape and sizing optimization with multiple natural frequency constraints. Since these metaheuristic algorithms are not a gradient-based search, they avoid most of the pitfalls of any gradient-based search algorithms. The effectiveness of Harmony Search and Firefly Algorithm is demonstrated through four benchmark structural optimization problems for solving shape and sizing optimization of trusses with multiple frequency constraints. The results showed that both metaheuristic algorithms reached, in a relatively low computational time, better results than the literature in three of the four examples considered, and in the other example the structure is approximately equal to the best one found, emphasizing the excellent capacity of both methods.

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.

A multi-set charged system search for truss optimization with variables of different natures; element grouping

Optimization problems may include variables of different natures. In structural optimization for example different variables representing cross-sectional, geometrical, topological and grouping properties of the structure may be present. Having different interpretations, the effects of these variables on the objective function are not alike and their search spaces may represent different characteristics. Thus, it is helpful to take these variables apart and to control each set separately. Based on the above considerations, in this paper a multi set charged system search (MSCSS) is introduced for the element grouping of truss structures in a weight optimization process. The results are compared to those obtained through predefined grouping by different algorithms. The comparisons show the efficiency and the effectiveness of the proposed algorithm. Although this paper only considers size optimization of truss structures where sizing and grouping variables are present and regarded as variables of different natures, the algorithm can be extended to cover the simultaneous shape and size optimization and topology optimization of different types of structures.

A hybrid meta-heuristic method for continuous engineering optimization

In this study we present an efficient new hybrid metaheuristic for solving size optimization of truss structures. The proposed ANGEL method combines ant colony optimization (ACO), genetic algorithm (GA) and local search (LS) strategy. In the presented algorithm ACO and GA search alternately and cooperatively in the solution space. The powerful LS algorithm, which is based on the local linearization of the constraint set, is applied to yield a better feasible or less unfeasible solution when ACO or GA obtains a solution. Test examples show that ANGEL can be more efficient and robust than the conventional gradient based deterministic or the traditional population based heuristic methods in solving explicit (implicit) optimization problems. ANGEL produces highly competitive results in significantly shorter run-times than the previously described approaches.

Angel method for discrete optimization problems

In this study we present an efficient new hybrid meta-heuristic - named in other context ANGEL - for solving discrete size optimization of truss structures. ANGEL combines ant colony optimization (ACO), genetic algorithm (GA) and local search (LS) strategy. The procedures of ANGEL attempt to solve an optimization problem by repeating the following steps. First time, ACO searches the solution space and generates structure designs to provide the initial population for GA. After that, GA is executed and the pheromone set in ACO is updated when GA obtains a better solution. When GA terminates, ACO searches again by using the new pheromone set. ACO and GA search alternately and cooperatively in the solution space. In this study we propose an efficient local search procedure. The procedure, in an iterative process, tries to make a better (a lighter feasible or a less unfeasible) truss from the current truss obtained by ACO or GA. The geometrically and materially nonlinear space trusses are formulated as a large d isplacement structural model. The treatment of elastic-plastic collapse analysis is based on a path-following method \cite 6. The applied method is a combination of the perturbation technique of the stability theory and the non-linear modification of the classical linear homotopy method. With the help of the higher-order predictor-corrector terms, the method is able to follow the load- deflection path even in case of elastic-plastic material law.

Optimal truss design including plastic collapse constraints

A new algorithm is presented for size optimization of truss structures with any kind of smooth objectives and constraints, together with constraints on the collapse loading obtained by limit analysis, for several loading conditions. The main difficulty of this problem is the fact that the collapse loading is a nonsmooth function of the design variables. In this paper we avoid nonsmooth optimization techniques based on the fact that limit analysis constraints are linear by parts. Our approach is based on a feasible directions interior point algorithm for nonlinear constrained optimization. Three illustrative examples are discussed. The numerical results show that the calculation effort when limit analysis constraints are included is only slightly increased with respect to classic constraints.

Minimum weight shape and size optimization of truss structures made of uncertain materials

Truss structures are optimized with respect to minimum weight with constraints on the value of some displacement and on the member stresses. The truss is considered made of an uncertain material, i.e. the value of the material constants are not known in a deterministic way, and each member may then exhibit a different value of stiffness, within a limited range of variation. The optimization must be done so that optimal solutions remain feasible for each value that the material constants may take for the considered uncertainty. In the present work a nonprobabilistic approach to uncertainty is used, and a variation of the material moduli with a, probabilistically speaking, uniform distribution over a convex and linearly bounded domain is considered. The two-step method is used to include the uncertainty within the optimization, where a diagonal quadratic approximation is used for the Objective function and the constraints. Solutions for some of the most classical truss examples are found and compared with those obtained using nominal values of material constants.

Minimum weight shape and size optimization of truss structures made of uncertain materials

Minimum weight shape and size optimization of truss structures made of uncertain materials

Numerical Experiments on Size Optimization of Truss Structures by Use of Genetic Algorithm (An Approach for Optimization Using Fully Stressed Designand Genetic Algorithm).

Genetic Algorithm (GA) is known to be excellent in searching globally optimal solutions, though it requires a large population size of the chromosomes and a large number of generation. Some studies are carried out in order to reduce the population size and the number of generations to obtain the solutions. For the purpose, the Authors try to discuss size optimization of truss structures whose members are discretized in the cross-sectional areas by using GA. The structure is coded by a binary string consisting of substrings, which represent the cross-sectional areas of the members and whose numbers are equal to the numbers of the members. Two types of GA models are adopted. In one type the operations are applied to all the substrings simulataneously during a generation. On the other hand, in the other the operations are applied to each substring, one at time. Various kinds of GA strategies, such as simple GA, elite strategy, hybrid strategy combained GA with fully stressed design, etc, are tested in numerical experiments. From their results the authors confirm that the hybrid strategy are most efficient and stable for searching globally optimal solutions.

STUDY ON TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS

Abstract The paper studies the relation between topology optimization and size optimization of truss structures. The goal of the optimization is to minimize the structural weight under stress constraints and side constraints on member cross sectional areas. The limiting stress concept is defined and the computational formula of limiting stress for truss structures calculated by a finite element method is given. Based on the limiting stress concept the continuity of the stress function at zero cross sectional area is carefully examined which enables us to understand the dilemma of defining the stress function in the closed interval up to zero cross sectional area. By considering the relation between the limiting stress and allowable stress the feasibility of stress constraints is discussed and the difficulty of adding a new bar to the truss or deleting an existing one is better understood. We have also shown that for topology optimization of truss structures the feasible design domain in the design space i...