The dimensions of trapezoidal roof sheeting supporting solar panels are optimized so that a minimum amount of steel is required for a specific range of wind loads. Sheets of different grades and different thicknesses along with different ranges of wind speeds are considered. In order to simulate the behavior of the corrugated sheets analysis is carried out for two limit states: strength and serviceability. For both limit states, the objective is to minimize the weight per unit area of the panels. First, optimum cross-section is obtained to meet the strength conditions. Then the deflection is controlled for serviceability. The optimum dimensions for each steel grade and loading condition are determined. The optimization problem is formulated as a multi-objective problem that aims to minimize the section's weight and maximize the section elastic modulus under the wind loading condition. A graph theory based approach is presented for the sizing optimization, employing an applied graph theory approach for the multi-objective all pairs shortest path problem. The proposed methodology addresses the sizing optimization problem to determine the geometry of the thin-walled cold-formed steel cross-sections that satisfy the design topological constraints.