Automated optimum design of structures using genetic programming
Introduction
In the architecture, engineering and construction industry, design is an important activity which requires much intelligence. The design process involves the creation of structures to satisfy user-defined requirements, and typically entails trade-offs between competing considerations. For example, the design of a truss structure begins with a high-level description of the truss' desired behaviour and characteristics, and entails the creation of the truss' topology and shape, and the selection of the cross-sectional areas of each of the truss' members. Designers also need to comprise between competing factors, for example, the amount of the materials versus the requirements of the design code.
Structural optimum design problem traditionally starts with the conceptual design which is often based on ground structures. The topology of a ground structure should include the topology of any possible optimum designs. Thus, the topology of the final optimum design should be a subset of the set of connections between the nodal points of the ground structure.
In the last decade, various genetic algorithms (GAs) [3], [6] have been employed to solve sizing and/or configuration and/or topology optimization problems, partially or totally based on ground structures [2], [4], [5], [7], [16], [17]. Recently, Shrestha and Ghaboussi [18] presented a GA-based methodology, without using ground structure, to search for the optimum structural design in an open-domain. However, their method requires relatively long chromosomes and has to iterate for a great number of generations. This is also a major problem with other GA applications. Nevertheless, GA has shown to be a very powerful search and optimisation technique which has been successfully implemented to solve many sophisticated engineering problems and a great deal of research resources around the world have been devoted to the application of GAs to solve engineering problems [13], [14], [20], [22], [23], [24], [25], [26], [27], [28].
For a specified open-domain design problem, the ground structure chosen by the different designers may be different. Whatever it is, a large number of nodal points should be used in the ground structure since the topology of the optimum design is a subset of that of the ground structure. Therefore, the final optimum design is greatly affected by the initially chosen ground structure. In order to present a suitable ground structure of the problem under consideration, one needs relatively deep understanding of the problem. Moreover, the ground structure of a design is problem-dependent, i.e., for different loading cases, constraints, and requirements, there are different topological patterns of the ground structure. Hence, if a design problem can be approached without the use of ground structure, this kind of approach would be a general and less problem-dependent design method. Moreover, it is possible to generate more efficient and innovative designs that are not a subset of the chosen ground structure, especially when more complex design problems are attempted.
We believe that such a design approach is possible if we use the genetic programming (GP) based methodology as proposed in this paper. The proposed automated design methodology is capable of creating optimum designs of structures within an open-domain, while simultaneously satisfying the various constraints and design requirements. As there is no need for any ground structure, it has few requirements about the domain knowledge of the problem and is thus less problem-dependent. Besides, the illustrative example also shows that the proposed method is more flexible and has higher search efficiency than the GA-based approach.
Section snippets
The genetic programming and the genetic algorithms
The GP can be viewed as an extension of the GA. It is a technique for the automatic generation of computer programs by means of natural selection [9]. The GP process starts by creating a large initial population of programs that are random combinations of elements from the problem-specific function sets and terminal sets. The programs are usually denoted as the GP parse trees. Each program in the initial population is then assessed for its fitness. This is usually accomplished by running each
Mapping scheme
The key issue for application of the GP to structural design is to establish a mapping scheme between the kind of point-labelled parse trees found in the world of GP and the node-element-labelled diagrams employed in the analysis of structures. In Holland's work [6] on the GA, encoding is carried out using binary strings. For many the GA applications, especially for the problems in industrial engineering, the conventional GA was difficult to apply directly because the binary string is not a
Problem description
This section introduces the concept of design domain, which is a specified physical space within which the generated truss must be fully enclosed (Fig. 2). The design domain may have any arbitrary shape enclosing a multi-connection area (including “void”). The support and the load of the truss may be at the boundary of the design domain or inside the design domain. The truss can evolve within the design domain; it can acquire any topology and shape as long as it is confined within the design
GP-based methodology for structural optimum design
The proposed methodology uses the GP to evolve optimum design of trusses. After choosing the terminal set and function set, a population of randomly generated designs are represented in the GP parse trees. The genetic operators, consisting of reproduction, crossover and mutation, act on them over a number of generations, evolving increasingly fitter designs. The evolution of fitter designs proceeds under selection pressure, which depends on the relative fitness of the individual designs,
Illustrative example
To validate the effectiveness and the efficiency of the proposed methodology, one illustrative example is presented in this section. The example shows that the GP-based methodology is actually more flexible and has higher search efficiency than the GA approach.
The design domain is shown in Fig. 4. Six loads are specified to be along the bottom chord of the truss. All the truss members are selected from a set of 30 standard AISC sections [15], i.e., W14×22 through W14×426. The material
Conclusion
In this paper, a GP-based methodology for automated optimum design of structures has been presented. The proposed approach is free from conceptual designs or ground structures, thus it has few requirements about the domain knowledge of the problem and is therefore less problem-dependent.
The illustrative example presented shows that the proposed GP-based approach is able to search for an optimum structure confined within a design domain and constrained by specified loading and supporting
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