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Showing 20 results for Sizing

K.s. Lee, S.w. Han, Z.w. Geem,
Volume 1, Issue 1 (3-2011)
Abstract

Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discrete sizing variables and integrated discrete sizing and continuous geometric variables. The HS algorithm uses a stochastic random search instead of a gradient search so the former has a new-paradigmed derivative. Several truss examples from the literature are also presented to demonstrate the effectiveness and robustness of the new method, as compared to current optimization methods.
S. Kazemzadeh Azad, S. Kazemzadeh Azad ,
Volume 1, Issue 2 (6-2011)
Abstract

Nature-inspired search algorithms have proved to be successful in solving real-world optimization problems. Firefly algorithm is a novel meta-heuristic algorithm which simulates the natural behavior of fireflies. In the present study, optimum design of truss structures with both sizing and geometry design variables is carried out using the firefly algorithm. Additionally, to improve the efficiency of the algorithm, modifications in the movement stage of artificial fireflies are proposed. In order to evaluate the performance of the proposed algorithm, optimum designs found are compared to the previously reported designs in the literature. Numerical results indicate the efficiency and robustness of the proposed approach.
S. Kazemzadeh Azad , S. Kazemzadeh Azad, A. Jayant Kulkarni,
Volume 2, Issue 1 (3-2012)
Abstract

The present study is an attempt to propose a mutation-based real-coded genetic algorithm (MBRCGA) for sizing and layout optimization of planar and spatial truss structures. The Gaussian mutation operator is used to create the reproduction operators. An adaptive tournament selection mechanism in combination with adaptive Gaussian mutation operators are proposed to achieve an effective search in the design space. The standard deviation of design variables is used as a key factor in the adaptation of mutation operators. The reliability of the proposed algorithm is investigated in typical sizing and layout optimization problems with both discrete and continuous design variables. The numerical results clearly indicated the competitiveness of MBRCGA in comparison with previously presented methods in the literature.
S.h. Mirmohammadi, Sh. Shadrokh, K. Eshghi,
Volume 2, Issue 2 (6-2012)
Abstract

The purpose of this paper is to present a polynomial time algorithm which determines the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand with zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system and resale of the excess units is possible at the ordering time. The properties of an optimal order policy are argued and on the basis of them, a branch and bound algorithm is presented to construct an optimal sequence of order policies. In the proposed B&B algorithm, some useful fathoming rules have been proven to make the algorithm very efficient. By defining a rooted tree graph, it has been shown that the worst-case time complexity function of the presented algorithm is polynomial. Finally, some test problems which are randomly generated in various environments are solved to show the efficiency of the algorithm.
S. Shojaee, M. Arjomand, M. Khatibinia,
Volume 3, Issue 1 (3-2013)
Abstract

An efficient method for size and layout optimization of the truss structures is presented in this paper. In order to this, an efficient method by combining an improved discrete particle swarm optimization (IDPSO) and method of moving asymptotes (MMA) is proposed. In the hybrid of IDPSO and MMA, the nodal coordinates defining the layout of the structure are optimized with MMA, and afterwards the results of MMA are used in IDPSO to optimize the cross-section areas. The results show that the hybrid of IDPSO and MMA can effectively accelerate the convergence rate and can quickly reach the optimum design.
H. Eskandar, A. Sadollah , A. Bahreininejad,
Volume 3, Issue 1 (3-2013)
Abstract

Water cycle algorithm (WCA) is a new metaheuristic algorithm which the fundamental concepts of WCA are derived from nature and are based on the observation of water cycle process and how rivers and streams flow to sea in the real world. In this paper, the task of sizing optimization of truss structures including discrete and continues variables carried out using WCA, and the optimization results were compared with other well-known optimizers. The obtained statistical results show that the WCA is able to provide faster convergence rate and also manages to achieve better optimal solutions compared to other efficient optimizers.
M. Shahrouzi , A. Yousefi,
Volume 3, Issue 1 (3-2013)
Abstract

Meta-heuristics have already received considerable attention in various engineering optimization fields. As one of the most rewarding tasks, eigenvalue optimization of truss structures is concerned in this study. In the proposed problem formulation the fundamental eigenvalue is to be maximized for a constant structural weight. The optimum is searched using Particle Swarm Optimization, PSO and its variant PSOPC with Passive Congregation as a recent meta-heuristic. In order to make further improvement an additional hybrid PSO with genetic algorithm is also proposed as PSOGA with the idea of taking benefit of various movement types in the search space. A number of benchmark examples are then treated by the algorithms. Consequently, PSOGA stood superior to the others in effectiveness giving the best results while PSOPC had more efficiency and the least fit ones belonged to the Standard PSO.
O. Hasançebi, S. Kazemzadeh Azad, S. Kazemzadeh Azad,
Volume 3, Issue 2 (6-2013)
Abstract

The present study attempts to apply an efficient yet simple optimization (SOPT) algorithm to optimum design of truss structures under stress and displacement constraints. The computational efficiency of the technique is improved through avoiding unnecessary analyses during the course of optimization using the so-called upper bound strategy (UBS). The efficiency of the UBS integrated SOPT algorithm is evaluated through benchmark sizing optimization problems of truss structures and the numerical results are reported. A comparison of the numerical results attained using the SOPT algorithm with those of modern metaheuristic techniques demonstrates that the employed algorithm is capable of locating promising designs with considerably less computational effort.
M. H. Makiabadi, A. Baghlani, H. Rahnema , M. A. Hadianfard,
Volume 3, Issue 3 (9-2013)
Abstract

In this study, teaching-learning-based optimization (TLBO) algorithm is employed for the first time for optimization of real world truss bridges. The objective function considered is the weight of the structure subjected to design constraints including internal stress within bar elements and serviceability (deflection). Two examples demonstrate the effectiveness of TLBO algorithm in optimization of such structures. Various design groups have been considered for each problem and the results are compared. Both tensile and compressive stresses are taken into account. The results show that TLBO has a great intrinsic capability in problems involving nonlinear design criteria.
S. Kazemzadeh Azad, O. Hasançebi,
Volume 3, Issue 4 (10-2013)
Abstract

This paper attempts to improve the computational efficiency of the well known particle swarm optimization (PSO) algorithm for tackling discrete sizing optimization problems of steel frame structures. It is generally known that, in structural design optimization applications, PSO entails enormously time-consuming structural analyses to locate an optimum solution. Hence, in the present study it is attempted to lessen the computational effort of the algorithm, using the so called upper bound strategy (UBS), which is a recently proposed strategy for reducing the total number of structural analyses involved in the course of design optimization. In the UBS, the key issue is to identify those candidate solutions which have no chance to improve the search during the optimum design process. After identifying those non-improving solutions, they are directly excluded from the structural analysis stage, diminishing the total computational cost. The performance of the UBS integrated PSO algorithm (UPSO) is evaluated in discrete sizing optimization of a real scale steel frame to AISC-LRFD specifications. The numerical results demonstrate that the UPSO outperforms the original PSO algorithm in terms of the computational efficiency.
M. Shahrouzi , A. Mohammadi,
Volume 4, Issue 3 (9-2014)
Abstract

Dynamic structural responses via time history analysis are highly dependent to characteristics of selected records as the seismic excitation. Ground motion scaling is a well-known solution to reduce such a dependency and increase reliability to the dynamic results. The present work, formulate a twofold problem for optimal spectral matching and performing consequent sizing optimization based on such scaled ground motion via numerical step-by-step analyses. Particle swarm optimization as a widely used meta-heuristic is specialized and improved to solve this problem treating a number of examples. The scaling error is evaluated using both traditional procedure and the developed method. In this regard, some issues are studied including the effect of structural period and shape of the design spectrum on the results. Contribution of the proposed enhancement on the standard particle swarm intelligence has improved its explorative capability resulting in higher efficiency of the algorithm.
M. Shahrouziand , S. Sardarinasab,
Volume 5, Issue 1 (1-2015)
Abstract

For most practical purposes, true topology optimization of a braced frame should be synchronized with its sizing. An integrated layout optimization is formulated here to simultaneously account for both member sizing and bracings’ topology in such a problem. Code-specific seismic design spectrum is applied to unify the earthquake excitation. The problem is solved for minimal structural weight under codified stress, deformation and also user-defined weak-storey and architectural constraints. Particle swarm optimization is hybridized with an extra memory consideration strategy to solve this problem. As another issue, Baldwin effect of memetic algorithm is utilized in the proposed method to enhance its search capability regarding the geometrical and topological constraints. Treating a number of planar braced frames revealed superior performance of the proposed hybrid method partiqularly in avoiding premature convergence over the common particle swarm optimiztion for such a discrete problem.
M. Shahrouzi, A. Meshkat-Dini , A. Azizi,
Volume 5, Issue 2 (3-2015)
Abstract

Practical design of tall frame-tube and diagrids are formulated as two discrete optimization problems searching for minimal weight undercodified constraints under gravitational and wind loading due to Iranian codes of practice for steel structures (Part 6 & Part 10). Particular encoding of design vector is proposed to efficiently handle both problems leading to minimal search space. Two types of modeling are employed for the sizing problem one by rigid floors without rotational degrees of freedom and the other with both translational and rotational degrees of freedom. The optimal layout of diagrids using rigid model is searched as the second problem. Then performance of Mine Blast Optimization as a recent meta-heuristic is evaluated in these problems treating a number of three-dimensional structural models via comparative study with the common Harmony Search and Particle Swarm Optimization. Considerable benefit in material cost minimization is obtained by these algorithms using tuned parameters. Consequently, effectiveness of HS is observed less than the other two while MBO has shown considerable convergence rate and particle swarm optimiztion is found more trustable in global search of the second problem.
Y. Malekian , S.h. Mirmohammadi,
Volume 5, Issue 3 (8-2015)
Abstract

In this study, a two-echelon supplier-manufacturer system with finite production rate and lead time is proposed. It is assumed that shortage is not permitted and the lot size of manufacturer (second echelon) is m-factors of the lot size of supplier (first echelon) and supplier can supply the manufacturer’s lot size in several shipments in each cycle. So, the production rate of supplier is greater than manufacturer’s. The proposed model aims to determine the optimal lot-size of each echelon such that the total cost of system is minimized. First, the problem is studied regardless of lead time and the optimal value of the lot sizes and the number of shipments is determined through analytical relations. Then, an exact solution algorithm for the problem is presented for the case with non-zero lead time. Finally, the performance of the proposed algorithm is reviewed by solving some numerical instances of the problem.
S. Khosravi, S. H. Mirmohammadi,
Volume 6, Issue 2 (6-2016)
Abstract

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In 
this paper, stochastic dynamic lot sizing problem with considering the quantity discount is defined  and  formulated.  Since  the  considered  model  is  mixed  integer  non-linear programming,  a  piecewise  linear  approximation  is  also  presented.  In  order  to  solve  the mixed integer non-linear programming, a branch and bound algorithm are presented. Each node in the branch and bound algorithm is also MINLP which is solved based on dynamic programming framework. In each stage in this dynamic programming algorithm, there  is a sub-problem which can be solved with lagrangian relaxation method. The numeric results found in this  study indicate that the proposed algorithm solve the problem faster than the mathematical  solution  using  the  commercial  software  GAMS.  Moreover,  the  proposed algorithm for  the  two  discount  levels  are  also  compared  with  the  approximate  solution  in mentioned software. The results indicate that our algorithm up to 12 periods not only can reach to the exact solution, it consumes less time in contrast to the approximate model.


A. Khajeh, M. R. Ghasemi, H. Ghohani Arab,
Volume 7, Issue 2 (3-2017)
Abstract

This paper combines particle swarm optimization, grid search method and univariate method as a general optimization approach for any type of problems emphasizing on optimum design of steel frame structures. The new algorithm is denoted as the GSU-PSO. This method attempts to decrease the search space and only searches the space near the optimum point. To achieve this aim, the whole search space is divided into a series of grids by applying the grid search method. By using a method derived from the univariate method, the variables of the best particle change values. Finally, by considering an interval adjustment to the variables and generating particles randomly in new intervals, the particle swarm optimization allows us to swiftly find the optimum solution. This method causes converge to the optimum solution more rapidly and with less number of analyses involved. The proposed GSU-PSO algorithm is tested on several steel frames from the literature. The algorithm is implemented by interfacing MATLAB mathematical software and SAP2000 structural analysis code. The results indicated that this method has a higher convergence speed towards the optimal solution compared to the conventional and some well-known meta-heuristic algorithms. In comparison to the PSO algorithm, the proposed method required around 45% of the total number of analyses recorded and improved marginally the accuracy of solutions.


S. A. Hosseini, A. Zolghadr,
Volume 7, Issue 4 (10-2017)
Abstract

Offshore jacket-type towers are steel structures designed and constructed in marine environments for various purposes such as oil exploration and exploitation units, oceanographic research, and undersea testing. In this paper a newly developed meta-heuristic algorithm, namely Cyclical Parthenogenesis Algorithm (CPA), is utilized for sizing optimization of a jacket-type offshore structure. The algorithm is based on some key aspects of the lives of aphids as one of the highly successful organisms, especially their ability to reproduce with and without mating. The optimal design procedure aims to obtain a minimum weight jacket-type structure subjected to API-RP 2A-WSD specifications. SAP2000 and its Open Application Programming Interface (OAPI) feature are utilized to model the jacket-type structure and the corresponding loading. The results of the optimization process are then compared with those of Particle Swarm Optimization (PSO) and its democratic version (DPSO).


M. Shahrouzi, H. Farah-Abadi,
Volume 8, Issue 1 (1-2018)
Abstract

The most recent approaches of multi-objective optimization constitute application of meta-heuristic algorithms for which, parameter tuning is still a challenge. The present work hybridizes swarm intelligence with fuzzy operators to extend crisp values of the main control parameters into especial fuzzy sets that are constructed based on a number of prescribed facts. Such parameter-less particle swarm optimization is employed as the core of a multi-objective optimization framework with a repository to save Pareto solutions. The proposed method is tested on a variety of benchmark functions and structural sizing examples. Results show that it can provide Pareto front by lower computational time in competition with some other popular multi-objective algorithms.


S. Gholizadeh, R. Sojoudizadeh,
Volume 9, Issue 2 (4-2019)
Abstract

This paper proposes a modified sine cosine algorithm (MSCA) for discrete sizing optimization of truss structures. The original sine cosine algorithm (SCA) is a population-based metaheuristic that fluctuates the search agents about the best solution based on sine and cosine functions. The efficiency of the original SCA in solving standard optimization problems of well-known mathematical functions has been demonstrated in literature. However, its performance in tackling the discrete optimization problems of truss structures is not competitive compared with the existing metaheuristic algorithms. In the framework of the proposed MSCA, a number of worst solutions of the current population is replaced by some variants of the global best solution found so far. Moreover, an efficient mutation operator is added to the algorithm that reduces the probability of getting stuck in local optima. The efficiency of the proposed MSCA is illustrated through multiple benchmark optimization problems of truss structures.
M. Shahrouzi, A. Barzigar, D. Rezazadeh,
Volume 9, Issue 3 (6-2019)
Abstract

Opposition-based learning was first introduced as a solution for machine learning; however, it is being extended to other artificial intelligence and soft computing fields including meta-heuristic optimization. It not only utilizes an estimate of a solution but also enters its counter-part information into the search process. The present work applies such an approach to Colliding Bodies Optimization as a powerful meta-heuristic with several engineering applications. Special combination of static and dynamic opposition-based operators are hybridized with CBO so that its performance is enhanced. The proposed OCBO is validated in a variety of benchmark test functions in addition to structural optimization and optimal clustering. According to the results, the proposed method of opposition-based learning has been quite effective in performance enhancement of parameter-less colliding bodies optimization.

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