Optimal design of skeletal structures via the charged system search algorithm

A new meta-heuristic optimization algorithm is presented for design of skeletal structures. The algorithm is inspired by the Coulomb and Gauss’s laws of electrostatics in physics, and it is called charged system search (CSS). CSS utilizes a number of charged particle (CP) which affects each other based on their fitness values and separation distances considering the governing laws of Coulomb and Gauss from electrical physics and the governing laws of motion from the Newtonian mechanics. Some truss and frame structures are optimized with the CSS algorithm. Comparison of the results of the CSS with those of other meta-heuristic algorithms shows the robustness of the new algorithm.     

Optimum design of steel frames using harmony search algorithm

In this article, harmony search algorithm was developed for optimum design of steel frames. Harmony search is a meta-heuristic search method that has been developed recently. It bases on the analogy between the performance process of natural music and searching for solutions to optimization problems. The objective of the design algorithm is to obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Strength constraints of AISC load and resistance factor design specification and displacement constraints were imposed on frames. The effectiveness and robustness of harmony search algorithm, in comparison with genetic algorithm and ant colony optimization-based methods, were verified using three steel frames. The comparisons showed that the harmony search algorithm yielded lighter designs.     

Optimal design of large-scale space steel frames using cascade enhanced colliding body optimization

In structural size optimization usually a relatively small number of design variables is used. However, for large-scale space steel frames a large number of design variables should be utilized. This problem produces difficulty for the optimizer. In addition, the problems are highly non-linear and the structural analysis takes a lot of computational time. The idea of cascade optimization method which allows a single optimization problem to be tackled in a number of successive autonomous optimization stages, can be employed to overcome the difficulty. In each stage of cascade procedure, a design variable configuration is defined for the problem in a manner that at early stages, the optimizer deals with small number of design variables and at subsequent stages gradually faces with the main problem consisting of a large number of design variables. In order to investigate the efficiency of this method, in all stages of cascade procedure the utilized optimization algorithm is the enhanced colliding bodies optimization which is a powerful metaheuritic. Three large-scale space steel frames with 1860, 3590 and 3328 members are investigated for testing the algorithm. Numerical results show that the utilized method is an efficient tool for optimal design of large-scale space steel frames.     

Optimal design of frames with substructuring

This paper presents a formulation for optimal design of large scale, two and three dimensional framed structures. Von Mises equivalent stress constraints and displacement constraints are imposed at all points in the structure. Member size constraints and constraints based on Schilling's approach for member buckling are also imposed. Three example problems of varying degrees of difficulty are solved, using a gradient projection algorithm with state space design sensitivity analysis and substructuring. Results of these examples are analyzed and conclusions are presented.     

An integrated genetic algorithm complemented with direct search for optimum design of RC frames

This paper presents an improved optimum design method for reinforced concrete (RC) frames using an integrated genetic algorithm (GA) with a direct search method. A conventional genetic algorithm occasionally has limitations due to a low convergence rate in spite of high computing times. The proposed method in this research uses a predetermined section database (DB) when determining trial sections for the next iteration.From an initial section determined by substituting calculated member forces into a regression formula, a direct search that determines a final discrete solution is followed within a limited range in the section database. Due to the fast convergence and the sequential determination of feasible trial sections close to the final optimum solution, an introduction of the search procedure at each iteration allows difficulties to be solved during the application of a conventional GA to large RC structures.Finally, the effectiveness of the introduced design procedure is verified through correlative tests of the introduced design procedure.     

Optimal design of steel structures using standard sections

The problem of optimal structural design having linked discrete variables is addressed. For such applications, when a discrete value for a variable is selected, values for other variables linked to it must also be selected from a table. The design of steel structures using available sections is a major application area of such problems. Three strategies that combine a continuous variable optimization method with a genetic algorithm, simulated annealing, and branch and bound method are presented and implemented into a computer program for their numerical evaluation. Three structural design problems are solved to study the performance of the proposed methods. CPU times for solution of the problems with discrete variables are large. Strategies are suggested to reduce these times.     

A revised discrete Lagrangian-based search algorithm for the optimal design of skeletal structures using available sections

Issues relating to the application of the discrete Lagrangian method (DLM) to the discrete sizing optimal design of skeletal structures are addressed. The resultant structure, whether truss or rigid frame, is subjected to stress and displacement constraints under multiple load cases. The members’ sections are selected from an available set of profiles. A table that contains sectional properties for all the available profiles is used directly in structural optimization. Each profile in the table is assigned by a unique profile number, which is used as the integer design variable for each of the structural members. It is proposed that we use a revised DLM search algorithm with static weighting to design trusses and rigid frames for minimum weight. Five examples are used to demonstrate the feasibility of the method. It is shown that, for monotonic as well as nonmonotonic constraint functions, the DLM is effective and robust for the discrete sizing design of skeletal structures.     

Amended harmony search algorithm with perturbation strategy for large-scale system reliability problems

Large-scale system reliability problem is a nonconvex integer nonlinear programming problem, traditional mathematical programming methods have computation limits and can not optimize an effective solution in a reasonable time. This paper employed an amended harmony search algorithm(AHS) to solve large-scale system reliability problems. In AHS, perturbation strategy, key parameter adjustment and global dimension selection strategy are designed to balance the capability of exploitation and exploration. A comprehensive comparison is carried out to assess the search efficiency and convergence performance of AHS. Function test and large-scale system reliability case results show that AHS is superior to many previously reported well-known and excellent algorithms.     

Optimal non-periodic inspection scheme for a multi-component repairable system using A search algorithm

This paper proposes an approach for finding an optimal non-periodic inspection scheme on a finite time horizon for a multi-component repairable system. The system consists of several components, each of which is subjected to soft failure. Soft failures of each component do not cause the system to stop functioning, but increase the system operating costs and are detected only if inspection is performed. Thus, the system is inspected at the scheduled inspection instances and if any of its components is found to have failed, the failed component is minimally repaired. The system’s expected total cost associated with a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between the actual occurrence of a soft failure of the components and its detection at an inspection. The objective is to determine the optimal inspection scheme which minimizes system’s expected total cost.     

改进克隆选择算法的层叠滤波器的优化设计

层叠滤波器优化设计的核心是正布尔函数最优化的问题.为了提高优化速度并对层叠滤波器进行全局优化设计,提出了一种改进的克隆选择算法.该算法引入多克隆算子和记忆单元及保留群体同时进化的思想.多克隆算子中的个体克隆规模根据个体的亲和度浓度自适应变化;重组操作在父代记忆个体与子代变异后的记忆个体之间展开,避免了近亲繁殖;保留群体的变异保证了群体的多样性.实验结果证明,该算法优化的层叠滤波器能在较短的时间内得到较好的滤波结果.     

Harmony search algorithm for minimum cost design of steel frames with semi-rigid connections and column bases

Harmony search-based algorithm is developed to determine the minimum cost design of steel frames with semi-rigid connections and column bases under displacement, strength and size constraints. Harmony search (HS) is recently developed metaheuristic search algorithm which is based on the analogy between the performance process of natural music and searching for solutions of optimum design problems. The geometric non-linearity of the frame members, the semi-rigid behaviour of the beam-to-column connections and column bases are taken into account in the design algorithm. The results obtained by semi-rigid connection and column base modelling are also compared to one developed by rigid connection modelling. The efficiency of HS algorithm, in comparison with genetic algorithms (GAs), is verified with three benchmark examples. The results indicate that HS could obtain lighter frames and less cost values than those developed using GAs.     

Optimum design of frames with multiple constraints using an evolutionary method

This paper presents a simple evolutionary method for the optimum design of structures with stress, stiffness and stability constraints. The evolutionary structural optimization method is based on the concept of slowly removing the inefficient material and/or gradually shifting the material from the strongest part of the structure to the weakest part until the structure evolves towards the desired optimum. The iterative method presented here involves two steps. In the first step, the design variables are scaled uniformly to satisfy the most critical constraint. In the second step, a sensitivity number is calculated for each element depending on its influence on the strength, stiffness and buckling load of the structure. Based on the element sensitivity number, material is shifted from the strongest to the weakest part of the structure. These two steps are repeated in cycles until the desired optimum design is obtained. Illustrative examples are given to show the applicability of the method to the optimum design of frames and trusses with a large number of design variables.     

Optimal non-periodic inspection scheme for a multi-component repairable system using A1 search algorithm

This paper proposes an approach for finding an optimal non-periodic inspection scheme on a finite time horizon for a multi-component repairable system. The system consists of several components, each of which is subjected to soft failure. Soft failures of each component do not cause the system to stop functioning, but increase the system operating costs and are detected only if inspection is performed. Thus, the system is inspected at the scheduled inspection instances and if any of its components is found to have failed, the failed component is minimally repaired. The system’s expected total cost associated with a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between the actual occurrence of a soft failure of the components and its detection at an inspection. The objective is to determine the optimal inspection scheme which minimizes system’s expected total cost.In the proposed approach, the system’s expected total cost is first formulated in terms of inspection scheme. Then, A¹ search algorithm, with a proposed heuristic cost function for calculating lower bounds, is employed to search through alternative inspection schemes to determine the optimal one. The proposed approach is illustrated through a numerical example.     

Engineering design optimization using an improved local search based epsilon differential evolution algorithm

Many engineering problems can be categorized into constrained optimization problems (COPs). The engineering design optimization problem is very important in engineering industries. Because of the complexities of mathematical models, it is difficult to find a perfect method to solve all the COPs very well. \(\varepsilon \) constrained differential evolution (\(\varepsilon \)DE) algorithm is an effective method in dealing with the COPs. However, \(\varepsilon \)DE still cannot obtain more precise solutions. The interaction between feasible and infeasible individuals can be enhanced, and the feasible individuals can lead the population finding optimum around it. Hence, in this paper we propose a new algorithm based on \(\varepsilon \) feasible individuals driven local search called as \(\varepsilon \) constrained differential evolution algorithm with a novel local search operator (\(\varepsilon \)DE-LS). The effectiveness of the proposed \(\varepsilon \)DE-LS algorithm is tested. Furthermore, four real-world engineering design problems and a case study have been studied. Experimental results show that the proposed algorithm is a very effective method for the presented engineering design optimization problems.     

Optimal design of truss structures using ant algorithm

An ant algorithm, consisting of the Ant System and API (after “apicalis” in Pachycondyla apicalis) 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.     

Optimum weight design of steel space frames with semi-rigid connections using harmony search and genetic algorithms

In this paper, an optimization process using MATLAB-SAP2000 Open Application Programming Interface (OAPI) is presented for optimum design of space frames with semi-rigid connections. A specified list including W-profiles taken from American Institute of Steel Construction (AISC) is used in the selection of suitable sections. The stress constraints as indicated in load and resistance factor design of AISC, lateral displacement constraints being the top- and inter-storey drift and geometric constraints are considered in the optimization process. Genetic algorithm method based on biological principles and harmony search algorithm method based on the processes of musical harmony are used for optimum designs. Two different space frames are solved for the cases of rigid and semi-rigid connections, separately. A computer program is coded in MATLAB for the purpose interacting with SAP2000 OAPI. Results obtained from the analyses show that type of semi-rigid connections plays a crucial role in the optimization of steel space frames and increases the optimum weight.

     

Geometry and topology optimization of geodesic domes using charged system search

Dome structures provide cost-effective solutions for covering large areas without intermediate supports. In this article, simple procedures are developed to reach the configuration of the geodesic domes. A new definition of dome optimization problems is given which consists of finding optimal sections for elements (size optimization), optimal height for the crown (geometry optimization) and the optimum number of elements (topology optimization) under determined loading conditions. In order to find the optimum design, the recently developed meta-heuristic algorithm, known as the Charged System Search (CSS), is applied to the optimum design of geodesic domes. The CSS takes into account the nonlinear response of the domes. Using CSS, the optimum design of the geodesic domes is efficiently performed.     

桥式吊车系统的伪谱最优控制设计

对于桥式吊车系统的最优控制问题,根据实际的工况要求,性能指标有时不一定是标准的二次形式.同时,在实际的控制问题中,状态和控制输入往往会受到一些边界条件和路径过程中的约束.针对这一问题,本文应用Chebyshev伪谱优化算法来处理,它可以处理状态和控制约束的非线性最优化问题以及一个非标准的目标函数.首先对桥式吊车系统模型进行一系列的坐标变换,将其转变为上三角系统形式的误差模型.然后将桥式吊车最优控制问题转化成具有一系列代数约束的参数优化问题,即非线性规划问题.通过求解离散化后的参数优化问题,得到桥式吊车的最优控制律.本文还给出了Chebyshev伪谱最优解的可行性和一致性分析.最后,在仿真研究中验证该控制器的有效性.     

Optimal placement of braces for steel frames with semi-rigid joints by scatter search

A heuristic method called Scatter Search (SS) is applied to optimize the placement of braces for steel frames with semi-rigid joints. The standard SS is modified such that the hierarchical clustering is used for the update of the solutions needed to diversify the solution set. The nonlinear analysis called refined plastic hinge method is used for structural analysis. The nonlinear relations between rotations and bending moments of semi-rigid joints are modeled by the three-parameter models. Three design problems are formulated as combinatorial problems and solved by SS. Finally, the characteristics of the optimal solutions are discussed.     

Optimal shakedown design of frames by linear programming

A mathematical model of flexural framed structures subjected to cyclic loadings is presented, and the problem of minimum-weight shakedown design of these structures is formulated as a pair of dual linear programming problems. Such a formulation reflects the duality between static and kinematic theorems of shakedown theory. An optimal solution for plastic moment distribution realizes a minimum volume of a structure and ensures a given safety factor against plastic collapse by inadaptation to a prescribed cyclic loading program. The reduced-size form of the problem is presented where the bending moments are expressed in terms of independent redundants. This form is more attractive from the computational point of view for the use of linear programming codes. Several examples illustrate the presented method.