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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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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Partricular features of overpassing local optima and providing near-optimal soultion in practical time has led researchers to apply metaheuristics in several engineering problems. Optimal design of diagrids as one of the most efficient structural systems in tall buildings has been concerned here. Jaya algorithm as a recent paramter-less optimization method is employed to solve the problem using a set of available sections. Furthermore, passive congregation is embedded in Jaya without adding any extra control parameters. Applyig the method in a number of real-size structural examples including diagrids, exhibits performance improvement by the new hybrid algorithm with respect to Jaya.

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This study is devoted to discrete sizing optimization of truss structures employing an efficient discrete evolutionary meta-heuristic algorithm which uses the Newton gradient-based method as its updating scheme and it is named here as Newton Meta-heuristic Algorithm (NMA). In order to enable the NMA population-based meta-heuristic to effectively explore the discrete design space, a term containing the best solution found is added to the basic updating rule of the algorithm. The efficiency of the proposed NMA metaheuristic is illustrated by presenting five benchmark discrete truss optimization problems and comparing the results with literature. The numerical results demonstrate that the NMA is a robust and powerful meta-heuristic algorithm for dealing with the discrete sizing optimization problems of steel trusses.

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Despite comprehensive literature works on developing fitness-based optimization algorithms, their performance is yet challenged by constraint handling in various engineering tasks. The present study, concerns the widely-used external penalty technique for sizing design of pin-jointed structures. Observer-teacher-learner-based optimization is employed here since previously addressed by a number of investigators as a powerful meta-heuristic algorithm. Several cases of penalty handling techniques are offered and studied using either maximum or summation of constraint violations as well as their combinations. Consequently, the most successive sequence, is identified for the treated continuous and discrete structural examples. Such a dynamic constraint handling is an affordable generalized solution for structural sizing design by iterative population-based algorithms.
 

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In most practical cases, structural design variables are linked to a discrete list of sections for optimal design. Cardinality of such a discrete search space is governed by the number of alternatives for each member group. The present work offers an adaptive strategy to detect more efficient alternatives and set aside redundant ones during optimization. In this regard, the difference between the lower and the upper bounds on such variables is gradually reduced by a procedure that adapts history of the selected alternatives in previous iterations. The propsed strategy is implemented on a hybrid paritcle swarm optimizer and imperialist competitive algorithm. The former is a basic swarm intelligent method while the later utilizes subpopulations in its search. Spatial and large-scale structures in various shapes are treated showing successive performance improvement. Variation of a diversity index and resulting band size are traced and discussed to declare behavior merits of the proposed adaptive band strategy.