Low-Thrust Orbit Transfer Optimization using a Combined Method

Abstract

A genetic algorithm is used together with calculus of variations to optimize an interplanetary trajectory for the Bryson-Ho Earth-to-Mars orbit transfer problem. The global search properties of genetic algorithm combine with the local search capabilities of calculus of variations to produce solutions that are superior to those generated with the calculus of variations alone, and these solutions require less user interaction than previously possible. The genetic algorithm is not hampered by ill-behaved gradients and is relatively insensitive to problems with a small radius of convergence, allowing it to optimize trajectories for which solutions had not yet been obtained. The use of the calculus of variations within the genetic algorithm optimization routine increased the precision of the final solution to levels uncommon for a genetic algorithm.

Interval‐valued variational programming problem with Caputo–Fabrizio fractional derivative

“…Recently, the calculus of variation and optimization theory have allowed us to investigate many different types of mathematical problems, including engineering, social sciences, economics, and control theory, in a unified model. For example, rigid body dynamics, orbit optimization [17], and flight design [18,19] all use the variation calculus. Mond and Hanson [20] developed duality results for variational programming problems based on convexity assumptions.…”

Exponential type duality for η-approximated variational problems

“…Calculus of variation is a technique used to solve the problems appearing in diverse fields, eg., dynamics of rigid body, optimization of orbit [10], flight design [9,13], etc. Optimality conditions and duality results for various classes of nonconvex variational problems have been of much interest in recent years, and several contributions have been made to its development (see, for example, [1,6,12,14,15,20]).…”