Keywords: genetic algorithm, optimisation, truss, design, integrated optimisation.

It is stiffness, weight, manufacturing cost or a particular property of a truss that normally becomes the objective of sizing and, or geometry and, or topology optimisation problems. In cases in which a truss supports a distributed load, there is an interaction between the truss domain and the physical domain producing the distributed load. The present work attempts to take an integrated approach in design of trusses supporting distributed loads by bringing considerations from the distributed load domain into truss design. In an integrated approach, the distribution of the loaded-nodes becomes a design variable which affects the distributed load domain. Minimisation of the negative effect of the load conversion on the distributed load domain, or in other words maximisation of the load conversion expediency, can be referred to as a new objective along with the traditional objectives in truss design. The present paper describes a new genetic algorithm (GA) for geometry optimisation of plane trusses designed for supporting distributed loads. The objective of the optimisation is to minimise the weight of the truss subject to a constraint on the number and locations of the load bearing nodes. The origin of this constraint is in the distributed load domain rather than the truss domain.

The proposed GA does not require a ground structure. It uses a variable-length vector of design variables representing the number of nodes and nodal coordinates. The mutation operator used is dynamic arithmetic. It is a combination of a growing mutation rate and a shrinking mutation interval. This is aimed at avoiding local optimum traps in the early stages of the optimisation, where the mutation rates are low, and fine tuning at later stages, where the mutation rates are higher. A single-cut geometric cross-over generates trusses of the next generation. This can be compared with the conventional multi-point cross-over. However, defining one cut point on trusses themselves makes the cross-over operation easier to implement compared to defining multiple cut-points on the locations of genes in variable-length chromosomes. The number of nodes may change through each cross-over operation leading to the creation of new topologies. Besides the traditional fitness defined for each individual two other partial fitnesses, namely left and right fitnesses, are assigned to each individual in the population. Individuals with higher left fitnesses are mated with individuals with higher right fitnesses.

In all cases the topology convergence was achieved before the geometry convergence. This is mainly because of not implementing a direct mutation operation for the topology of the trusses. Using the concept of partial fitness in performing cross-over increases the convergence rate mainly through accelerating the topology convergence. The effect of implementing the concept of partial fitness for generating fitter individuals and improving the convergence rate can be observed from the results of design case studies.

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