# Optimization of a simplified Fleet Assignment Problem with metaheuristics: Simulated Annealing and GRASP

• Danuta Sosnowska
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 42)

## Abstract

The Fleet Assignment Problem consists of assigning aircrafts to flights, taking into consideration operational constraints of the airline company. This paper presents heuristics based on simulated annealing and GRASP for solving a simplified version of the Fleet Assignment Problem. The application of heuristics is essential as the space of feasible solutions grows exponentially with the size of the fleet and the number of flights. It allows to quickly find near-optimal results, by exploring only small part of the space of solutions.

A sequence of flight legs assigned to an aircraft is called a rotation cycle. Both methods presented are based on the operation of swapping parts of rotation cycles between two randomly selected aircrafts.

In simulated annealing the exchange is directed by a so called cooling schedule converging to 0 in either an exponential, logarithmic or asymptotic rate, while the number of iterations grows. A solution which gives a better cost is always accepted, other solutions are accepted only with some probability depending on the cooling schedule.

In GRASP, only exchanges leading to a better result are permitted and every fixed number of swaps the solution is rearranged, i.e. the potentially best part of the assignment is conserved and the rest is reattributed randomly.

The problem is tested on real data of a medium size airline company (about 20 aircrafts and 3000 flights), for a period of one month. The experimental results show that simulated annealing gives solutions with slightly lower cost than the GRASP algorithm.

## Keywords

GRASP simulated annealing fleet assignment.

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