Solution methods for the balancing of jet turbines

Turbine balancing is an important and regular maintenance operation at airline companies. Because of manufacturing inaccuracies, variations occur in the weights of the blades that can, in turn, lead to significant out-of-balance forces on the engine. The overall time required for balancing can be significantly decreased if the best placement of turbine blades is first determined mathematically. This problem is formulated as a variation of the quadratic assignment problem and a number of solution schemes are investigated. A neighbourhood search algorithm is found to significantly outperform the other solution approaches when applied to data from a major South Pacific airline. The neighbourhood search algorithm can be combined with various strategies to initialize starting points. The use of starting points obtained from a Lagrangean dual scheme is shown to improve results for large problems. Scope and Purpose The balancing of turbines is a regular maintenance operation at airlines. Typically an engine will be dismantled and tested for defects, and any faulty blades replaced by new ones. The turbine then needs to be reassembled and balanced, an operation complicated by differences in blade weights. The overall balancing can be a time consuming task, particularly for those engines where the turbine must be dismantled and reassembled whenever blades are interchanged. The problem can be formulated as a variation of the quadratic assignment problem, a problem known to be NP-hard. Furthermore, experiments have shown that finding solutions to this balancing problem is complicated by the presence of many local optima. We propose a number of local search methods which all outperform the current method used by a major South Pacific airline when tested on a number of problems provided by the airline.