We only consider planar trusses with (initially) rectangular profiles. As will be shown later the converged solution's profile may no longer be rectangular. A truss' geometry and topology may be defined by a set of joints, or to borrow from the terminology of finite element analysis, a set of nodes. A set of members connect these nodes. The set of nodes and their locations defines the geometry of a truss, while the set of members and the nodes they connect defines the topology.
There are three approaches to using domain knowledge in genetic search. We can place this knowledge 1) in the initial population 2) in the encoding of the genotype, and 3) in the genetic operators of crossover and mutation.
Initializing the genetic algorithm with individuals that our domain knowledge tells us are highly fit usually results in quicker convergence and/or better adaptability in changing environment [Grefensttete and Ramsey, 1993]. However, the reduced diversity that may result can lead to premature convergence. To alleviate this problem we use high crossover and mutation probabilities.
Domain knowledge in the form of constraints on the range of variables is usually placed in the encoding of the genotype. In addition, ensuring that only viable offspring are produced is a task that depends on both the encoding and the recombination operators. In our task we use bit strings to encode member cross sections and top chord node heights. The topology and the rest of the geometry are encoded as more complex data structures with correspondingly different and ``smarter'' crossover and mutations operators. Instead of randomized crossover and mutation, these ``smarter'' operators use domain knowledge to guide crossover and mutation and usually lead to quicker convergence.
Note that as more domain knowledge is used to guide search, the less robust the algorithm becomes. Ideally we would like to start with a robust algorithm and using domain knowledge tune it to the domain.
The next section provides more detail on our representation and engineering heuristics used to seed the initial population.