Means and Effects оf Constraining the Number of Used Cross-Sections in Truss Sizing Optimization

This paper looks at sizing optimization results, and attempts to show the practical implications of using a novel constraint. Most truss structural optimization problems, which consider sizing in order to minimize weight, do not consider the number of different cross-sections that the optimal solution can have. It was observed that all, or almost all, cross-sections were different when conducting the sizing optimization. In practice, truss structures have a small, manageable number of different cross-sections. The constraint of the number of different cross-sections, proposed here, drastically increases the complexity of solving the problem. In this paper, the number of different cross-sections is limited, and optimization is done for four different sizing optimization problems. This is done for every number of different cross-section profiles which is smaller than the number of cross-sections in the optimal solution, and for a few numbers greater than that number. All examples are optimized using dynamic constraints for Euler buckling and discrete sets of cross-section variables. Results are compared to the optimal solution without a constrained number of different cross-sections and to an optimal model with just a single cross-section for all elements. The results show a small difference between optimal solutions and the optimal solutions with a limited number of different profiles which are more readily applicable in practice

Metaheuristic optimization of reinforced concrete footings

The primary goal of an engineer is to find the best possible economical design and this goal can be achieved by considering multiple trials. A methodology with fast computing ability must be proposed for the optimum design. Optimum design of Reinforced Concrete (RC) structural members is the one of the complex engineering problems since two different materials which have extremely different prices and behaviors in tension are involved. Structural state limits are considered in the optimum design and differently from the superstructure members, RC footings contain geotechnical limit states. This study proposes a metaheuristic based methodology for the cost optimization of RC footings by employing several classical and newly developed algorithms which are powerful to deal with non-linear optimization problems. The methodology covers the optimization of dimensions of the footing, the orientation of the supported columns and applicable reinforcement design. The employed relatively new metaheuristic algorithms are Harmony Search (HS), Teaching-Learning Based Optimization algorithm (TLBO) and Flower Pollination Algorithm (FPA) are competitive for the optimum design of RC footings

Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

A Novel Algorithm for Solving Structural Optimization Problems

In the past few decades, metaheuristic optimization methods have emerged as an effective approach for addressing structural design problems. Structural optimization methods are based on mathematical algorithms that are population-based techniques. Optimization methods use technology development to employ algorithms to search through complex solution space to find the minimum. In this paper, a simple algorithm inspired by hurricane chaos is proposed for solving structural optimization problems. In general, optimization algorithms use equations that employ the global best solution that might cause the algorithm to get trapped in a local minimum. Hence, this methodology is avoided in this work. The algorithm was tested on several common truss examples from the literature and proved efficient in finding lower weights for the test problems

A Brief Survey on Intelligent Swarm-Based Algorithms for Solving Optimization Problems

This chapter presents an overview of optimization techniques followed by a brief survey on several swarm-based natural inspired algorithms which were introduced in the last decade. These techniques were inspired by the natural processes of plants, foraging behaviors of insects and social behaviors of animals. These swam intelligent methods have been tested on various standard benchmark problems and are capable in solving a wide range of optimization issues including stochastic, robust and dynamic problems

Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently

INFLUENCE OF USING DISCRETE CROSS-SECTION VARIABLES FOR ALL TYPES OF TRUSS STRUCTURAL OPTIMIZATION WITH DYNAMIC CONSTRAINTS FOR BUCKLING

The use of continuous variables for cross-sectional dimensions in truss structural optimization gives solutions with a large number of different cross sections with specific dimensions which in practice would be expensive, or impossible to create. Even slight variations from optimal sizes can result in unstable structures which do not meet constraint criteria. This paper shows the influence of the use of discrete cross section sizes in optimization and compares results to continuous variable counterparts. In order to achieve the most practically applicable design solutions, Euler buckling dynamic constraints are added to all models. A typical space truss model from literature, which use continuous variables, is compared to the discrete variable models under the same conditions. The example model is optimized for minimal weight using sizing and all possible combinations of shape and topology optimizations with sizing

Optimum design of reinforced concrete retaining walls with the flower pollination algorithm

The flower pollination algorithm (FPA) is anefficient metaheuristicoptimizationalgorithm mimickingthe pollinationprocessof flowering species. In this study, FPA is applied, for first time, to the optimum design of reinforced concrete (RC) cantilever retaining walls. It is foundthat FPA offers important savings with respect to conventional design approachesand that it outperformsgenetic algorithm (GA)andthe particle swarm optimization (PSO) algorithm in this designproblem.Furthermore, parameter tuning reveals that the best FPA performance is achieved for switch probability values ranging between 0.4 and 0.7, a population size of 20 individualsand aLévy flightstep sizescale factor of 0.5. Finally, parametric optimum designs show that theoptimumcost of RC retaining walls increases rapidly with the wallheight and smoothly with the magnitude of surcharge loadin

An evolutionary-based optimization algorithm for truss sizing design

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required