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Flight trajectory optimization algorithms reduce flight cost and fuel consumption, thereby reducing the polluting emissions released to the atmosphere. Ground teams and avionics equipment such as the Flight Management System evaluate different routes to minimize flight costs. The optimal trajectory represents the flight plan given to the crew. The resulting flight plan contains waypoints and weather information such as the wind speed and direction and the temperature for each waypoint. The flight plan is normally introduced manually into the Flight Management System. In this paper, genetic algorithms were applied to the waypoints available in a flight plan to find the altitudes that minimize total fuel consumption, taking into account the cruise-climb and cruise-descent steps' costs. The genetic algorithms emulate the evolution process through a predefined number of generations.

This paper describes an optimization algorithm that provides an economical Vertical Navigation profile plan by finding the combinations of climb, cruise and descent speeds, as well as the altitudes for an aircraft to minimize flight costs. The computational algorithm profits from a space search reduction algorithm to reduce the initial number of speed and altitude combinations. Additional search space reductions were performed with the implementation of the branch and cut algorithm. A bounding function that correctly estimates the flight cost considering step climbs was developed to reduce the number of calculations. The full flight fuel burn cost was obtained using a performance database- based method. The fuel flight cost was computed using the cost index. This algorithm used a performance database instead of equations of motion to compute fuel burn. This database was developed and validated by our industrial partner using real flight experimental data.