IHS ESDU Application of multivariate optimisation techniques to determination of optimum flight trajectories. 94012

ESDU 94012 explains in broad terms the method of optimisation used by such techniques and emphasises that numerical optimisation will not locate an absolute minimum but requires the user to set a tolerance on the result, the choice of which is critical. The value of seeking an optimum from two diverse starting points is suggested, and will usually allow any sub-optimum located to be eliminated and will enable an assessment to be made of the choice of tolerance. Using results obtained in the work of ESDU 93021 optimising a complete sortie, the information to be gleaned from exploration around the calculated optimum is illustrated. Also, it is noted that non-optimum results can be obtained and it is important to assess the trends in the results as an aid to eliminating them, again illustrated with data obtained for ESDU 93021. To use the optimiser, sub-routines have to be written, in the case of ESDU 93021 to calculate the segments of the flight profile. Because the optimiser needs gradients of the variables and constraints, the sub-routines may have to work in unrealistic areas and any optimal results obtained in such regions must be trapped and discounted. The treatment of finite steps in a variable is considered (in this case cruise height as constrained by air traffic rules). The particular features of the optimiser RQPMIN, developed at the then Royal Aerospace Establishment, are discussed, and the format of its input and output files illustrated.