Multi-objective optimization of wideband spiral arrays

A challenging task in array design is to synthesize an array working at multiple frequencies within a large frequency band, with constraints imposed to the radiation pattern in terms of side lobe level (SLL). This kind of array synthesis requires a multi-objective approach since there is no single solution which can be considered the best at the multiple investigated frequencies for all the compulsory requirements. Therefore this class of problems, instead of a single one, is characterized by an ideal set of solutions, the Pareto front (PF), which comprises solutions over which no other solution of the population dominates [1]. This set provides a range of solutions for which no one can simultaneously satisfy the required performance but represents a tradeoff of the design requirements. Multi-objective genetic algorithms (MOAs) can be a useful tool for determining the Pareto front. They perform similarly to conventional genetic algorithms but they search for the set of solution which belongs to the PF, rather than providing only a single optimal solution. In particular, we have adopted a multi-objective genetic algorithm, called Non-dominated Sorting Genetic Algorithm (NSGA-II) [2] to optimize the array factor of a Spiral Array.