Design optimization of truss structures with continuous and discrete variables by hybrid of biogeography‐based optimization and differential evolution methods

Abstract

This paper presents a hybrid BBO-DE algorithm by hybridizing biogeography-based optimization (BBO) and differential evolution (DE) methods for optimum design of truss structures with continuous and discrete variables. In BBO-DE, the migration operator of BBO method serves as a local exploiter mechanism during the search process. Besides, DE has a role of the global exploration by performing multiple search directions in the search space to preserve more diversity in the population. By embedding of DE algorithm in BBO method as a mutation mechanism, the balance between the exploration and exploitation abilities is further improved. The comparative results with some of the most recently developed methods demonstrate the fast convergence properties of the proposed algorithm and confirm its effectiveness to solve optimum design problems of truss structures with continuous and discrete variables. KEYWORDSbiogeography-based optimization, continuous, differential evolution, discrete, optimum design, truss structures | INTRODUCTIONIn recent years, increasing the consumption of materials in the building sector and the limitation of natural resources have intensified competitions among the structural engineers to such an extent that attaining optimum designs for structures is more vital now than ever before. Structural optimization has achieved a great advance as a result of modern computers entering the stage. By using today's computational machines, a large-scale structure with complex geometry and thousands of members can be iteratively processed to get a more economical design. For such structures, the number of design variables is high and the optimum design procedure may require huge computational effort. As a result, developing efficient optimization techniques to achieve a fast convergence rates with more accurate results is one of the active research topics in the field of structural optimization. In the sizing of truss structures, the cross-sectional areas of structural members are considered as design variables, and the design constraints are some limitations imposed on the stresses and displacements as well as free vibrational frequencies. The objective function is generally considered as to minimize the weight or volume of the structure. However, there are many critical factors that can affect the objective function or costs of a structure.From the optimization point of view, the sizing of truss structures can be classified into two main types based on design variables: continuous and discrete. Mathematical optimization techniques have some features that are later found to be not very much suitable for practical structural design optimization problems, [1] such as assuming of continuous design variables, requiring gradient computations of the objective function and constraints, and depending on the initial estimate of solution vector. These methods have some serious difficulties when it is required to assign cross sections from a discrete set of practically available sections. Moreover, when both of the nodal ...

An optics inspired optimization method for optimal design of truss structures

“…The ratio of existing stresses to the allowable values in the members of the 120-bar dome truss structure Kaveh and Mahdavi [36] Jalili and Hosseinzadeh [50,52] Jalili et al [35] Current study Design variables (cm 2 ) Kaveh and Mahdavi [36] Jalili and Hosseinzadeh [50,52] Jalili et al [35] Figure 19 shows the convergence curves of OIO among the 30 trial runs of this case study. It can be observed from the figure that OIO requires less than 12,000 structural analyses to find near-optimal solutions.…”

“…For each parameter setting, the statistical results are obtained from 30 independent runs; the best parameter setting is shown in bold; the maximum structural analysis for each case is equal to 20,000. [13] Camp [14] Degertekin [51] Degertekin and Hayalioglu [17] Kaveh et al [37,49] Jalili and Hosseinzadeh [19,50,52] than OIO (i.e., WEO has a smaller standard deviation value), OIO can find higher quality solution with fewer structural analyses than the WEO method. Moreover, although the weight obtained by CA method is lighter than those obtained by other methods, the design yielded by CA method slightly violates the design constraints (i.e., the design is unfeasible).…”

“…The results of OIO were compared in Table to those reported using CBO, EM‐MS, BBO‐DE, and LCA‐Tie‐II methods. As indicated in Table , not only OIO is capable to obtain a better design than CBO method for this design example but it also requires fewer structural analyses than CBO method.…”

“…As indicated in Table , not only OIO is capable to obtain a better design than CBO method for this design example but it also requires fewer structural analyses than CBO method. However, when the performance of OIO is investigated against hybrid/improved EM‐MS, BBO‐DE, and LCA‐Tie‐II methods, the situation is reverse. From the results listed in Table , it can be seen that the hybrid/improved methods perform significantly better than the standard approaches (i.e., OIO and CBO).…”

Advanced energy‐based analyses of trusses employing hybrid metaheuristics

“…[34,35] The mostly investigated structural optimization problem is the weight optimization of truss structures by finding optimum sizing and topology of the system. [36][37][38][39][40] According to Sörensen, [17] the future will be a scientific period and the solving of problems will be more important than the metaphor (phenomena). For that reason, the usage of hybrid algorithms is important comparing with generation of new algorithms using similar trends of existing ones.…”