Formulation of multicriteria problem of routing and scheduling of manned and unmanned aircraft in a dynamic environment and approach to its solution using genetic algorithms

Abstract

The article deals with the multi-criteria task of routing and scheduling of unmanned and manned aircraft using the method of penalty functions. The authors describe the urgency of the problem being solved for the airline management under the conditions of the existing changes in the dynamic situation with a great variety of flight situations. A mathematical statement of the problem is formulated and a universal optimality criterion is proposed in the form of a sum of additive and multiplicative forms, including partial quality indicators. The search for optimal and rational solutions to the problem of optimal flight routing, taking into account the airline fleet resources, airspace users' offers, constant and variable restrictions, associated, for example, with unfavorable weather conditions, can be implemented using a one-criteria and multi-criteria approach, but as a result, it is proposed to use a genetic algorithm that has low computational complexity and offers as solutions ("ancestors"), close to the optimal and rational result. With this approach, an "elite" is formed at the beginning of the algorithm, which allows the crossing operation to be performed at each step of the iteration (evolution). As a result, we get new "descendants", and by rearranging at least one item from one block to the next one, we can get a sufficiently large number of representatives, from which a new "elite" can be selected with the help of the criterion. The practice of using genetic algorithms has shown that along with the achievement of a global extremum with it, the process of substantial improvement of planning results is achieved in several evolution steps, and their number is clearly less than the number of steps when using numerical methods of parametric optimization. The proposed approach will significantly improve the efficiency and quality of flight planning for the airline, taking into account the diversity of aircraft fleet, payload and environmental impact. This task is especially important under the conditions of joint management (CDM), where aeronautical data can be considered as additional criteria.

Keywords

• penalty functions
• optimal control
• aircraft
• genetic algorithm
• collaborative decision-making (cdm)