Structural Engineering Optimization Research Articles

Design cost minimization of a reinforced concrete column section using overnew swarm-based optimization algorithms

It is very tiresome for a practiser to detect the best feasible sizing design of structural members including reinforced concrete columns that is a highly nonlinear and complicated structural engineering optimization problem. This is due to such a design is practically conducted via conventional trial-and-error computing methods in which resistance to external loads, cost efficiency, and aesthetic factors, etc. have to be considered. This study focuses on minimizing the design cost of primarily proposed reinforced concrete column design problem via three overnew swarm-based optimizers such as Coati Optimization Algorithm, Fox Optimizer and Pelican Optimization Algorithm (POA) that are firstly utilized for this purpose. In this regard, the type of steel rebar distribution, the characteristic strength of the concrete, the height and width of the column section, and the number and diameter of the rebars are treated as discrete design variables of the newly proposed complex reinforced concrete column design cost optimization problem. In solution, the design requirements specified in practice code provisions should also be met. Here, Turkish Building Earthquake Code 2018 specifications are considered as practice structural design constraints. Consequently, the algorithmic performances of three overnew swarm-based metaheuristic optimization algorithms are compared and evaluated in detail. Amongst them, the POA shows most fruitful algorithmic design solution performance.

Can the global optimum of a combinatorial optimization problem be reliably estimated through extreme value theory?

The accurate estimation of the global optimum of a non-polynomial optimization problem would provide certainty and reliability to the solutions obtained by metaheuristics. Different statistical approaches have been proposed to perform this type of estimation, being the Extreme Value Theory currently one of the most widespread. The contribution of this paper is to provide empirical evidence on how unreliable the estimates of global optima of combinatorial optimization problems can be when using Extreme Value Theory. This study uses a structural engineering optimization problem as a case study. Four metaheuristics with different performances are used to solve the problem: two genetic algorithms and two evolution strategies with different search parameters. The study shows that the use of Extreme Value Theory can lead to wrong conclusions because its global optimum estimates depend on the search algorithm's performance. The results also show that samples generated by poorly performing search algorithms produce estimates of the global optimum with high variability. Additionally, it was observed that high-performing algorithms generated samples with low variability, which paradoxically made the statistical estimation of the global optimum inviable. The conclusions derived from the study are of great relevance for anyone interested in using the Extreme Value Theory to estimate the global optimum of a combinatorial optimization problem.

Population-based optimization in structural engineering: a review

Population-based optimization in structural engineering: a review

An adaptive augmented radial basis function–high-dimensional model representation method for structural engineering optimization

A new engineering optimization approach using an adaptive metamodeling method is developed and studied. The adaptive metamodels are based on a high-dimensional model representation framework, and the high-dimensional model representation component functions are created using radial basis functions or augmented radial basis functions. The proposed optimization approach starts with an explicit first-order augmented radial basis function–high-dimensional model representation metamodel, before a numerical optimization algorithm is applied. In each subsequent iteration, an additional sample point is found, and a high-order high-dimensional model representation component function is created and added to the first-order augmented radial basis function–high-dimensional model representation metamodel. The accuracy of the augmented radial basis function–high-dimensional model representation metamodel is improved in an adaptive manner, especially in the neighborhood of the optimal design point. Several numerical examples are solved to demonstrate the method, including a practical three-dimensional reinforced concrete high-rise building structure. The proposed approach works well, and the convergence of the optimal solutions for each of the examples is obtained within a few adaptive iterations.

A hybrid whale optimization algorithm based on modified differential evolution for global optimization problems

Whale optimization algorithm(WOA) is a biological-inspired optimization algorithm with the advantage of global optimization ability, less control parameters and easy implementation. It has been proven to be effective for solving global optimization problems. However, WOA can easily get stuck in the local optimum and may lose the population diversity, suffering from premature convergence. In this work, a hybrid whale optimization algorithm called MDE-WOA was proposed. Firstly, in order to enhance local optimum avoidance ability, a modified differential evolution operator with strong exploration capability is embedded in WOA with the aid of a lifespan mechanism. Additionally, an asynchronous model is employed to accelerate WOA's convergence and improve its accuracy. The proposed MDE-WOA is tested with 13 numerical benchmark functions and 3 structural engineering optimization problems. The results show that MDE-WOA has better performance than others in terms of accuracy and robustness on a majority of cases.

An adaptive penalty scheme to solve constrained structural optimization problems by a Craziness based Particle Swarm Optimization

The use of Evolutionary Algorithms (EAs) to solve optimization problems has been increasing. One of the most used techniques is Particle Swarm Optimization (PSO), which is considered robust, efficient and competitive in comparison with other bio-inspired algorithms. EAs were originally designed to solve unconstrained optimization problems. However, the most significant problems, particularly those from real world optimization, present constraints. It is not trivial to define a strategy to handle constraints and, in general, penalty functions containing parameters to be set by the user and it may affect the search considerably. This paper consists of a combination of the Craziness based Particle Swarm Optimization (CRPSO) with an adaptive penalty technique, called Adaptive Penalty Method (APM), to solve constrained optimization problems. A CRPSO is adopted here in order to avoid premature convergence using a new velocity expression and an operator called “craziness velocity”. APM and its variants were applied in other EAs, originally in a Genetic Algorithm, which demonstrated its robustness. APM deals with inequality and equality constraints, and it is free of parameters to be defined by the user. In order to assess the applicability and performance of the algorithm, several structural engineering optimization problems traditionally found in the literature are used in the computational experiments.

Game Theory Based Evolutionary Algorithms: A Review with Nash Applications in Structural Engineering Optimization Problems

A general review of game-theory based evolutionary algorithms (EAs) is presented in this study. Nash equilibrium, Stackelberg game and Pareto optimality are considered, as game-theoretical basis of the evolutionary algorithm design, and also, as problems solved by evolutionary computation. Applications of game-theory based EAs in computational engineering are listed, with special emphasis in structural optimization and, particularly, in skeletal structures. Additionally, a set of three problems are solved: reconstruction inverse problem, fully stressed design problem and minimum constrained weight, for discrete sizing of frame skeletal structures. We compare panmictic EAs, Nash EAs using 4 different static domain decompositions, including also a new dynamic domain decomposition. Two frame structural test cases of 55 member size and 105 member size are evaluated with the linear stiffness matrix method. Numerical experiments show the efficiency of the Nash EAs approach, confirmed with statistical significance analysis of results, and enhanced with the dynamic domain decomposition.

A Hybrid Flower Pollination Algorithm for Engineering Optimization Problems

pollination algorithm (FP) is a new nature-inspired algorithm, based on the characteristics of flowering plants. Combining with the features of flower pollination algorithm, an improved simulated annealing algorithm is proposed in this paper (FPSA). It can improve the speed of annealing. The initial state of simulated annealing and new solutions are generated by flower pollination. Therefore, it has the advantage of high quality and efficiency. The method combines the standard flower pollination algorithm (FP) with simulated annealing to enhance the search performance and speeds up the global convergence rate. Structural engineering optimization problems are presented to demonstrate the effectiveness and robustness of the proposed algorithm. The experimental results showed that the accuracy of finding the best solution and convergence speed performance of the proposed algorithm is competitive to those achieved by the

Applications of Topology Optimization in Structural Engineering : High - Rise Buildings and Steel Components

Applications of Topology Optimization in Structural Engineering : High - Rise Buildings and Steel Components

A novel class of niche hybrid Cultural Algorithms for continuous engineering optimization

This paper proposes a novel class of niche hybrid Cultural Algorithms for solving engineering problems with continuous design variables. The first algorithm, Niche Cultural Algorithm (NCA), embeds niching within the cultural framework to maintain multiple groups within the population of agents in order to locate multiple optima. The second algorithm, hybridizes niche Cultural Algorithms with Tabu search (H-NCA). This technique offers a novel architecture of hybrid approaches, which combines Niche Cultural Algorithms (NCA) with Tabu search (TS). The proposed hybridization scheme enables the algorithm to overleap local optima and improve performance. The third algorithm, Improved Hybrid Niche Cultural Algorithms (IH-NCA), is employed to enhance convergence rate and accuracy of H-NCA with fewer computations. In IH-NCA, the algorithm switches between two selection strategies based on roulette wheel and stochastic tournament selection. This enhances the algorithm’s ability to further escape stagnation and premature convergence with varying stochastic noise and selection pressure. Simulations were performed over miscellaneous engineering optimization problems that include minimization of constrained functions and structural engineering optimization. A comparative study is carried out with other state-of-the-art optimization techniques. The findings affirm the efficiency and robustness of the new methodologies over the other existing relevant approaches.

A survey of non-gradient optimization methods in structural engineering

In this paper, we present a review on non-gradient optimization methods with applications to structural engineering. Due to their versatility, there is a large use of heuristic methods of optimization in structural engineering. However, heuristic methods do not guarantee convergence to (locally) optimal solutions. As such, recently, there has been an increasing use of derivative-free optimization techniques that guarantee optimality. For each method, we provide a pseudo code and list of references with structural engineering applications. Strengths and limitations of each technique are discussed. We conclude with some remarks on the value of using methods customized for a desired application.

A comparison of swarm intelligence algorithms for structural engineering optimization

SUMMARYThis paper compares the performance of three swarm intelligence algorithms for the optimization of hard engineering problems. The algorithms tested were bacterial foraging optimization (BFO), particle swarm optimization (PSO), and artificial bee colony (ABC). Besides the regular BFO, two other variants reported in the literature were also included in the study: adaptive BFO and swarming BFO. Both PSO and ABC were tested using the regular algorithm and variants that include explosion (mass extinction). Three optimization problems of structural engineering were used: minimization of the cost of a welded beam, minimization of the construction cost of a pressure vessel, and minimization of the total weight of a 10‐bar plane truss. All problems are strongly constrained. The algorithms were evaluated using two criteria: quality of solutions and the number of function evaluations. The results show that PSO presented the best balance between these two criteria. For the optimization problems approached in this paper, we can also conclude that the explosion procedure resulted in no significant improvements. Copyright © 2012 John Wiley & Sons, Ltd.

Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems

In this study, a new metaheuristic optimization algorithm, called cuckoo search (CS), is introduced for solving structural optimization tasks. The new CS algorithm in combination with Levy flights is first verified using a benchmark nonlinear constrained optimization problem. For the validation against structural engineering optimization problems, CS is subsequently applied to 13 design problems reported in the specialized literature. The performance of the CS algorithm is further compared with various algorithms representative of the state of the art in the area. The optimal solutions obtained by CS are mostly far better than the best solutions obtained by the existing methods. The unique search features used in CS and the implications for future research are finally discussed in detail.

Two improved harmony search algorithms for solving engineering optimization problems

This paper describes two new harmony search (HS) meta-heuristic algorithms for engineering optimization problems with continuous design variables. The key difference between these algorithms and traditional (HS) method is in the way of adjusting bandwidth (bw). bw is very important factor for the high efficiency of the harmony search algorithms and can be potentially useful in adjusting convergence rate of algorithms to optimal solution. First algorithm, proposed harmony search (PHS), introduces a new definition of bandwidth (bw). Second algorithm, improving proposed harmony search (IPHS) employs to enhance accuracy and convergence rate of PHS algorithm. In IPHS, non-uniform mutation operation is introduced which is combination of Yang bandwidth and PHS bandwidth. Various engineering optimization problems, including mathematical function minimization problems and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of these algorithms. In all cases, the solutions obtained using IPHS are in agreement or better than those obtained from other methods.

Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the performance of the proposed hybrid HS–Solver algorithm, several unconstrained, constrained, and structural-engineering optimization problems have been solved and their results are compared with other deterministic and stochastic solution methods. Also, an empirical study has been carried out to test the performance of the proposed hybrid HS–Solver algorithm for different sets of HS solution parameters. Identified results showed that the hybrid HS–Solver algorithm requires fewer iterations and gives more effective results than other deterministic and stochastic solution algorithms.

A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice

Most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point. These algorithms, however, reveal a limited approach to complicated real-world optimization problems. If there is more than one local optimum in the problem, the result may depend on the selection of an initial point, and the obtained optimal solution may not necessarily be the global optimum. This paper describes a new harmony search (HS) meta-heuristic algorithm-based approach for engineering optimization problems with continuous design variables. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. Various engineering optimization problems, including mathematical function minimization and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of the HS algorithm. The results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms.

A comparison of search mechanisms for structural optimization

In the majority of structural engineering optimization problems, the objective is to minimize the cost of the structure. These problems use a variety of objective functions formulating cost as a function of the variables involved in the design of the structure. They also use a number of search mechanisms ranging from an exhaustive search to several heuristic searches. Typical search mechanisms include tabu search, simulated annealing, genetic algorithms, and branch-and-bound. The goal of this paper is to compare some of the search mechanisms in the light of their applicability to structural engineering optimization. Since practical structural engineering problems have discrete variables, only those search mechanisms capable of solving discrete structural optimization problems are considered.

Hopfield neuron based nonlinear constrained programming to fuzzy structural engineering optimization

Using the continuous Hopfield network model as the basis to solve the general crisp and fuzzy constrained optimization problem is presented and examined. The model lies in its transformation to a parallel algorithm which distributes the work of numerical optimization to several simultaneously computing processors. The method is applied to different structural engineering design problems that demonstrate this usefulness, satisfaction or potential. The computing algorithm has been given and discussed for a designer who can program it without difficulty.

Improved genetic operators for structural engineering optimization

The initial motivation for the development of algorithms inspired by biological principles of evolution was the design and implementation of robust adaptive systems. Among the most utilized of these techniques are the Genetic Algorithms (GAs) which combine principles of population genetics and natural selection. Their growing popularity may be attributed to the ability of GAs as powerful function optimizers of general application to combinatorial problems that have been traditionally difficult to optimize. [1, 2] (De Jong, K. A. and Spears, W. M., Using genetic algorithms to solve NP-complete problems. In Proceedings of the Third International Conference on Genetic Algorithms, June 1989, pp. 124–132; Hurley, S., Using Genetic Algorithms Based Search in Optimization. The Institute of Mathematics and its Applications, Vol. 29, March/April 1993, pp. 43–46.) Considerable progress has been made in identifying the limitations of the GAs resulting in a range of approaches and modifications which attempt to improve the efficiency of the GAs as function optimizers. These adaptive approaches in such GA-based optimizers are in general tailored to classes of functions. The engineering optimization problems may be governed by different classes of functions which result in very complex design spaces. In this paper a general purpose optimization technique is investigated, the best of the traditional methods may perform well but only in a narrow class of problems. Revised genetic operators and a new recombination scheme are presented in this paper. These features respectively increase the exploratory power of the GA while simultaneously introducing additional selection pressure to increase the speed of convergence. These features are designed to ensure the balance between effective exploration and selective pressure to exploit the better solutions which are the main power behind the GAs. The gain of exploratory power not only extends the applicability of the method and improves the quality of the results but also helps prevent premature convergence. On the other hand, selective pressure applied locally may speed up the convergence while still refining the results. Finally, in order to map GAs onto engineering optimization problems, this paper draws some guidelines for handling the constraints using transformation methods.

Methods of pairwise comparisons and fuzzy global criterion for multiobjective optimization in structural engineering

The method of pairwise comparison inherently contains information of ambiguity, fuzziness and conflict in design goals for a multiobjective structural design, This paper applies the principle of paired comparison so that the vaguely formulated problem can be modified and a set of numerically acceptable weight would reflect the relatively important degree of multiple objectives. This paper also presents a fuzzy global criterion method (FGCM(lambda)) included fuzzy constraints that coupled with the objective weighting rank obtained from the modified pairwise comparisons for fuzzy multiobjective optimization problems. Descriptions in sequence of this combined method and problem solving experiences are given in the current article. Multiobjective design examples of truss and mechanical spring structures illustrate this optimization process containing the revising judgement techniques.