Automatic innovative truss design using grammatical evolution
Introduction
A major part of engineering design is the process of satisfying hard constraints. In structural engineering, topology optimization is known as the science of “optimal layout theory” [1]. It allows engineers to design highly optimized structures—maximizing material efficiency while minimizing waste and reducing material cost. This allows for structures that are stiff yet lightweight, which can lead to savings in terms of resources and cost [2], [3], [4]. Engineering optimization is an important problem as minor savings in weight or cost on a small scale can have larger implications when extrapolated over a larger design or project.
The theory of topology optimization in structural engineering states that it is possible to create a structurally “perfect” design with both optimal shape topology and member sizes by both rearranging the topological layout of the members and by varying the sizes of those individual members [4]. All members in the design should have similar high states of stress at, or close to (but not exceeding) the limits of the material as specified by design codes of practice and manufacturer specifications. This eliminates redundancy, minimizes material usage and creates a more economical design. This is most usually achieved by minimizing the cross-sectional area of each structural member, which consequently minimizes the overall weight of the entire structure.
Genetic Programming (GP) has been shown to be routinely capable of achieving human-competitive performance in a number of real-world scenarios [5], [6], [7]. Evidence of an increase in use of GP in industry can be found in the increasing number of patent applications using GP [8]. GP is particularly well suited for engineering tasks for a number of reasons, including its ability to handle multiple conflicting objectives [14], [15] and its capacity to optimize both the structure and the contents of that structure in parallel [14]. Since the solution is unknown (due to incomplete information or theory), GP is one method in particular which can uncover its optimal structure/topological form [1], [11], [16], [17]. Sizing optimization is similar in theory to solving a simple linear equation: the form (topology) is known, and the variables (member sizes) are increased/decreased to fit. It is therefore possible to use both GP and linear optimization as a hybrid approach towards topology optimization.
Grammatical Evolution (GE) is a version of GP that uses a formal grammar [9], [11], [12], allowing the user to easily embed domain knowledge (such as structure boundary conditions, loading conditions, and basic form including span and depth), and to generate output in any language [11]. Both GE and topology optimization represent the cutting edge of both GP and structural engineering fields respectively.
This paper introduces a new method of topology optimization: Dual Optimization in Grammatical Evolution (DO-GE). While existing structural optimization methods in GE [14], [16], [18] primarily focus on a structural topology scale (optimization of the structural layout), optimization of individual element sizes is also possible [1], [19], [20]. The combination of both topology and sizing optimization is established [1], [16], [17], [19], [29], but the use of both standard construction elements and compliance to design codes of practice in the process is novel. Standard practice is to optimize element sizings by specifying the required cross-sectional area. While this gives theoretically optimized results, the output is of little use to structural engineers as in practice trusses are constructed using structural elements with preset cross section and geometry. This highlights a fundamental weakness in traditional sizing optimization methods: by omitting knowledge of section geometry and orientation, it is not possible to include accurate buckling calculations as a constraint for structural design and thus structures cannot be designed according to standard codes of practice. The approach presented in this paper addresses this deficiency by allowing for any number of standard construction elements to be specified for any elements within a design, leading to code-compliant construction-ready designs which truly represent their evolved form.
The DO-GE approach has a number of advantages over a two-stage approach of optimizing topology and element sizes separately. With a single stage approach, a large number of designs can be assessed in a relatively short space of time, whereas a two-stage approach would be slower and would fail to allow for interactions between structural topology and element sizes parameters. A single-stage approach also allows for real-time analysis of both design variables and structural properties of the individuals as evolution progresses.
Section 2 will begin with a summary of related research in this area, along with a description of the DO-GE method, including our approach to design generation and analysis. Section 3 compares and contrasts recent research methods with the DO-GE method using examples from the literature, and a discussion on the implications of those results is presented in Section 4. Finally, our conclusions and suggestions for future work are presented in Section 5.
Section snippets
Evolutionary approaches to structural engineering
The use of computers in structural design has been growing rapidly in recent years. The advent of techniques such as Topology Optimization [1] and Evolutionary Computation (EC) [17] has heralded engineering applications ranging from analog circuit design [5] to the design of structures such as shelters [30] and bridges [14].
Numerical examples
The aim of this paper is not to find fully optimized solutions for absolute minimum required cross-sectional areas in standard structures; the literature contains numerous examples of efficient processes for achieving this. Instead, the focus of this paper is to show that real-world solutions very close to the theoretical optimum can be achieved using standard construction elements. Benchmarking tests are completed for common truss optimization problems against popular or recently published
Discussion
While the best solution for each load case found using DO-GE was consistently heavier than the best solutions from previous works, this is due to both the use of different materials (aluminium was used in the case of the 10-bar truss) and a more restricted range of available materials. Traditional optimization methods [1], [16], [17], [19], [34], [35], [38] calculate the minimum required cross-sectional area, while the DO-GE method presented here matches the closest commercially available
Conclusions and future work
Although truss optimization methods exist, this study finds that the most popular methods are not fully appropriate for everyday use in the construction industry as they focus purely on optimizing minimum element cross-sectional area, neglecting crucial section properties and material specifications. Furthermore, the widespread use of identical tensile and compressive stress limits on the material and the lack of use of design codes and standards of practice in such optimization methods give a
Acknowledgments
This research is based upon works supported by the Graduate Research Education Programme in Sustainable Development, jointly funded by IRCSET and IRCHSS, and based upon works supported by the Science Foundation Ireland under Grant no. 08/IN.1/I1868 and 08/RFP/CMS1115.
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