Elsevier

Engineering Structures

Volume 34, January 2012, Pages 225-232
Engineering Structures

Design of planar steel frames using Teaching–Learning Based Optimization

https://doi.org/10.1016/j.engstruct.2011.08.035Get rights and content

Abstract

This paper presents a design procedure employing a Teaching–Learning Based Optimization (TLBO) technique for discrete optimization of planar steel frames. TLBO is a nature-inspired search method that has been developed recently. It simulates the social interaction between the teacher and the learners in a class, which is summarized as teaching–learning process. The design algorithm aims to obtain minimum weight frames subjected to strength and displacement requirements imposed by the American Institute for Steel Construction (AISC) Load and Resistance Factor Design (LRFD). Designs are obtained selecting appropriate W-shaped sections from a standard set of steel sections specified by the AISC. Several frame examples from the literature are examined to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of the TLBO creating of an optimal design for frame structures. The results of the TLBO are compared to those of the genetic algorithm (GA), the ant colony optimization (ACO), the harmony search (HS) and the improved ant colony optimization (IACO) and they shows that TLBO is a powerful search and applicable optimization method for the problem of engineering design applications.

Highlights

► TLBO has simple numerical structure. ► TLBO is independent on a number of parameters to define the algorithm’s performance. ► TLBO algorithm is accurate, effective and robust. ► TLBO has great potential for solving constrained discrete problems.

Introduction

Optimization can be defined as finding solution of problems where it is necessary to maximize or minimize a real function within a domain which contains the acceptable values of variables while some restrictions are to be satisfied. There might be the large amount of set of variables in the domain that maximizes or minimizes the real function while satisfying the described restrictions. They are called as the acceptable solutions and the solution which is the best among them that satisfy constrains are obtained as the optimum solution of the problem.

Analogously the definition given above, the aim of the optimum structural design methods is to minimize the size of the structural elements considering their load carrying capacity in order to reduce the total cost by reducing the material necessary for construction. The methods taking discrete design variables and seeking for the global optimum under the constraints that change depending on type of the problems have drawn a lot of attention among the researchers and the engineers in practice.

Among the optimization methods developed and used in the structural optimization, the recent novel and innovative stochastic search techniques emerged use nature as a source of inspiration to establish a numerical search algorithm for solving complex engineering problems and they do not suffer the discrepancies of mathematical programming based optimum design methods [1]. The basic idea behind these techniques is to simulate the natural phenomena such as survival of the fittest, the cooling process of molten metals through annealing, the social interaction of ant colonies, swarm intelligence, the musical performance process, the process of food foraging of honey bees, etc. into a numerical algorithm [2], [3], [4], [5], [6], [7]. These methods are very suitable and effective in finding the solution of discrete structural optimization problems [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]. On the other hand, the emergence of new computational techniques that are based on the simulation of paradigms found in nature has still continued due to its ability of solving different optimization problems.

Rao et al. [21] developed a new optimization method, the so-called Teaching–Learning Based Optimization (TLBO), as an innovative optimization algorithm inspiring the natural phenomena, which mimics teaching–learning process in a class between the teacher and the students (learners) and they applied the TLBO for solving the mechanical design optimization problems taken from the literature. In their model, the “Teaching Phase” produces a random ordered state of points called learners within the search space. Then a point is considered as the teacher, who is highly learned person and shares his or her knowledge with the learners, and others learn significant group information from the teacher. However, during the “Learning Phase” the learners learn by interaction between each other. After a number of sequential Teaching–Learning cycles, where the teacher convey knowledge among the learners and those level increases toward his or her own level, the distribution of the randomness within the search space becomes smaller and smaller about to point considering as teacher. It means knowledge level of the whole class shows smoothness and the algorithm converges to a solution.

This paper presents a design procedure employing a Teaching–Learning Based Optimization (TLBO) technique for discrete optimization of planar steel frames. The total weight of the frame structures subjected to constraints in the form of strength and displacement requirements imposed by the American Institute for Steel Construction (AISC) Load and Resistance Factor Design (LRFD) [22] is considered as the objective function. Several frame examples from the literature are examined to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of the TLBO creating of an optimal design for frame structures.

Section snippets

Formulation of the optimum design problem

The design of steel frames requires the selection of steel sections for its columns and beams from a standard steel section tables such that the frame obeys the serviceability and strength requirements specified by the code of practice while the economy is observed in the overall or material cost of the frame [1]. This turns out to be discrete optimum design problem which has the following mathematical form:findX=[A1,A2,,Ang]minimizeW(X)=i=1ngAij=1mnρiLisubjected tockσ0k=1,,nccrδ0r=1,,ns1

Teaching–Learning Based Optimization

The TLBO mimics the teaching–learning process in a class between the teacher and the learners (students). Teacher desires to reach best harmony on the out put of learners in a class, which can be obtained through their grades considered as the output. Output is evaluated by means of exam taken by the teacher. Since the teacher is generally considered as a highly learned person who shares his or her knowledge with the learners, the quality of a teacher affects the outcome of the learners. It is

Optimum design using TLBO

Based on the above teaching–learning process, a mathematical model of a novel optimization technique called Teaching–Learning-Based Optimization (TLBO) was developed by Rao et al. [21]. It consists of two phases: a Teaching Phase, where candidate solutions are randomly distributed over the search space and the best solution is determined among those then it shares the information with others; and a Learning Phase, where the solutions put effort into passing the own information through the

Design examples

The optimal designs of planar steel two-bay three-story, one-bay ten-story and three-bay twenty four-story frames, respectively, are evaluated by using the TLBO to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of its. Since they are already optimized by the researcher using different algorithms, i.e. the genetic algorithm (GA) [24], the ant colony optimization (ACO) [23], the harmony search (HS) [25] and the improved ant colony optimization

Observations and conclusions

A novel optimization method, TLBO, based on concepts proposed by Rao et al. [21], is applied to discrete forms of structural optimization to design low-weight planar steel frames. Through a series of benchmark-type frame optimization problems, the TLBO algorithm demonstrates that it can routinely minimize the overall weight of frame structures while satisfying material and performance constraints.

The main characteristics of the TLBO algorithm over other evolutionary methods are its simplified

Acknowledgments

The author is grateful to Assoc. Prof. Dr. S.O. Değertekin Dicle University, Diyarbakir, Turkey for discussion on the examples, and Dr. Prof. Rao-S.V. National Institute of Technology, Surat, India for help and comments concerning TLBO.

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