Solving metameric variable-length optimization problems using genetic algorithms

In many optimization problems, one of the goals is to determine the optimal number of analogous components to include in the system. Examples include the number of sensors in a sensor coverage problem, the number of turbines in a wind farm problem, and the number of plies in a laminate stacking problem. Using standard approaches to solve these problems requires assuming a fixed number of sensors, turbines, or plies. However, if the optimal number is not known a priori this will likely lead to a sub-optimal solution. A better method is to allow the number of components to vary. As the number of components varies, so does the dimensionality of the search space, making the use of gradient-based methods difficult. A metameric genetic algorithm (MGA), which uses a segmented variable-length genome, is proposed. Traditional genetic algorithm (GA) operators, designed to work with fixed-length genomes, are no longer valid. This paper discusses the modifications required for an effective MGA, which is then demonstrated on the aforementioned problems. This includes the representation of the solution in the genome and the recombination, mutation, and selection operators. With these modifications the MGA is able to outperform the fixed-length GA on the selected problems, even if the optimal number of components is assumed to be known a priori.