Keywords: genetic algorithms, shape discovery, optimisation, heuristics, unguided search, domain knowledge.

Constrained shape discovery and optimisation is a difficult engineering problem. Shape discovery deals with evolving randomly generated solutions into useful intermediate solutions. These intermediate solutions are then optimised to suite their environment. In this paper a Genetic Algorithm (GA) is applied to the problem of finding the optimum cross section of a beam. Previous work using GAs for this problem has only managed to evolve satisfactory solutions through applying heuristics that operate directly on the genotype. Such heavy guidance of the GA potentially stifles innovation, can only be applied to situations where the correct answer is known, and limits the applicability of the search.

This research demonstrates the ability of the GA, in its purest form (unbiased and unguided search) to evolve good, near optimal results. Performing an unbiased search, using only the evolutionary process to locate for good solutions, allows the GA to be applied to problems where the solution is not know in advance and so suitable heuristics are not available. The ability of a GA to provide novel solutions is also encouraged through an unbiased search without restrictions.

The initial test case for the proposed GA system is the evolution of an optimal beam cross-section, subject to several load cases. For each applied load case, the optimal solution is already known, allowing a direct comparison with the result obtained from the GA. Increasingly complex loading cases are applied to the solution space, requiring the GA to evolve solutions with multiple conflicting constraints and criteria.

It is shown that advanced 2-dimensional genetic operators are needed, in conjunction with a suitably designed fitness function, to allow a productive evolutionary search. Modular evaluation software is applied to the core GA, each module analysing a particular stress condition or general criteria resulting from applied loads. The primary evaluation modules deal with normal stress, shear stress, weight, and surface area. It is shown that the modules can be used simultaneously, allowing the evolution of solutions for real-world complex load cases. Only the fitness function guides the form of the solutions, with constraints and criteria prioritised through a finite reduction of an individuals fitness value proportional to the degree of violation.

Within 2000 generations, the GA is able to evolve near optimal solutions for all load cases. The system successfully demonstrates how the use of heuristics is not necessary.

Solutions are encoded with a Voxel representation, which also defines the maximum dimensions available for a solution. Increasing the solution space to a size larger than that required for optimal solutions, requires the GA to evolve solutions within the imposed boundaries, thus reducing the size constraint. It is show that the method can cope with this additional difficulty and still evolves optimal solutions. Overall it is shown that the techniques developed consistently produce good solutions despite the complexity of the processes involved. .

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