How did Airbus A380 overcome corrosion issue in which aluminium wiring used?
The mechanisms by which aluminum corrodes are well-know and the measures needed to prevent it are similarly known to design engineers. 

Aluminum corrosion via direct attack is an issue where the aluminum is exposed to air and the air contains moisture, and is made worse when salts are present in the environment and at certain pH ranges. It is prevented by encapsulating the aluminum in either an impervious coat of paint or plastic or a coating of intentionally-grown aluminum oxide. In an airplane, the insulation on the wire will prevent corrosion by direct attack. 

Aluminum corrosion by galvanic action occurs when the aluminum is bonded directly to or in contact with a piece of metal that has a different position in the galvanic series, and the joint is wet or at least moist with water. You prevent it by excluding water from the joint by sealing the joint with glue or enclosing it in a housing that is airtight, and by coating the joint with a grease or oil that excludes water. In an airplane's wiring system, this would be done with a plastic plug-and-receptacle for the joint that keeps water out. 

Electrical fires in wiring system connectors that contain aluminum wire joined with copper wire occur when the physical joint between them is vibrated or worked back and forth, which scrapes the native oxide off the aluminum in the joint, promoting more oxide growth which is scraped off, etc. which eventually leads to loading the joint with aluminum oxide and creating high contact resistance between the aluminum and the copper wire at the joint. I-squared-R heating at the degraded joint then sets the insulation on fire. This can also happen by temperature-cycling the joint which will cause the joint surfaces to be worked back and forth and once the joint begins to show resistance, then the heating occurs right inside the joint and the process accelerates itself. 

In airplanes, houses, and cars where aluminum and copper wire must be joined, a special connector is used where the metals meet in which the crimp joint is exceptionally tight and the joint is loaded with a grease or chemical paste containing inhibitors that halt the oxidation of the aluminum.