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Structural optimization, when approached by conventional (gradient based) minimization algorithms presents several difficulties, mainly related to computational aspects for the huge number of nonlinear analyses required, that regard both Objective Functions (OFs) and Constraints. Moreover, from the early '80s to today's, Evolutionary Algorithms have been successfully developed and applied as a computational alternative to many optimization problems, such as structural ones. In this study the effectiveness of a relatively new Evolutionary Algorithm, namely Differential Evolutionary, is investigated for constrained optimization. This presents many interesting advantages and so that it is a candidate to be widely used in many real structural optimization problems. The algorithm version here used has been developed by hybridizing some recent versions of Differential Evolutionary algorithms proposed in literature, and uses a specific way for dealing with constraints which, always, concern real structural optimization problems. The effectiveness of proposed approach has been demonstrated by developing two cases of study, which regard simple but very significant structural problems for steel structures, one of which is a standard benchmark in structural optimization. The analyses show the simplicity and effectiveness of the proposed approach, so that it can be suitably ready for practical uses out of academic contest.

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This paper presents an improved multi-objective evolutionary algorithm (IMOEA) for the design of planar steel frames. By considering constraints as a new objective function, single objective optimization problems turned to multi objective optimization problems. To increase efficiency of IMOEA different Crossover and Mutation are employed. Also to avoid local optima dynamic interference of mutation and crossover are considered. Feasible particles called elites which are very helpful for better mutation and crossover considered as a tool to increase efficiency of proposed algorithm. The proposed evolutionary algorithm (IMOEA) is utilized to solve three well-known classical weight minimization problems of steel moment frames. In order to verify the suitability of the present method, the results of optimum design for planar steel frames are obtained by present study compared to other researches. Results indicate that, as far as the convergence, speed of the optimization process and quality of optimum design are concerned behavior, IMOEA is significantly superior to other meta-heuristic optimization algorithms with an acceptable global answer.

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This paper proposes a GA-based reduced search space technique (GA-RSS) for the optimal design of steel moment frames. It tries to reduce the computation time by focusing the search around the boundaries of the constraints, using a ranking-based constraint handling to enhance the efficiency of the algorithm. This attempt to reduce the search space is due to the fact that in most optimization problems the optimal solution lies on or near the boundaries of the feasible region. All the analyses/optimization steps have been implemented in MATLAB and the method has been validated by optimizing three moment-frame benchmark problems. According to the results, the algorithm performs fit and needs relatively fewer analyses than other metaheuristic algorithms to reach a global optimum solution.

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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 this paper an enhanced ant colony optimization algorithm with a direct constraints handling strategy is proposed for the optimization of reinforced concrete frames. The construction cost of reinforced concrete frames is considered as the objective function, which should be minimized subject to geometrical and behavioral strength constraints. For this purpose, a new probabilistic function is added to the ant colony optimization algorithm to directly satisfy the geometrical constraints. Furthermore, the position of an ant in each iteration is updated if a better solution is found in terms of objective value and behavioral strength constraints satisfaction. Five benchmark design examples of planar reinforced concrete frames are presented to illustrate the efficiency of the proposed algorithm.