A Global Optimization Approach to Solve Multi-Aircraft Routing Problems

A Global Optimization Approach to Solve Multi-Aircraft Routing Problems

S.P. Wilson (Numerical Optimisation Centre, University of Hertfordshire, UK), M.C. Bartholomew-Biggs (Numerical Optimisation Centre, University of Hertfordshire, UK) and S.C. Parkhurst (Numerical Optimisation Centre, University of Hertfordshire, UK)
DOI: 10.4018/978-1-60566-800-0.ch012
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Abstract

This chapter describes the formulation and solution of a multi-aircraft routing problem which is posed as a global optimization calculation. The chapter extends previous work (involving a single aircraft using two dimensions) which established that the algorithm DIRECT is a suitable solution technique. The present work considers a number of ways of dealing with multiple routes using different problem decompositions. A further enhancement is the introduction of altitude to the problems so that full threedimensional routes can be produced. Illustrative numerical results are presented involving up to three aircraft and including examples which feature routes over real-life terrain data.
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The Simplified Route Model (Srm) Route Cost Function

We first summarise the main features of the Simplified Route Model; more details can be found in (Wilson, 2003). In the two-dimensional case we can attempt to find the ground plan of a route, avoiding a number of obstacles that we shall henceforth call “threats”. A route will be defined by its (given) start and end points and by a number of intermediate waypoints. The co-ordinates of these waypoints will be optimization variables; and we assume that the flight path follows straight lines between them. We shall now describe a Simplified Route Model (SRM) route cost calculation.

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