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For expeditions to faraway destinations such as Mars or Jupiter, the differential evolution, or DE, algorithm uses "parameter vectors" to point the way. Parameter vectors are like mathematical genes composed of bits and bytes that a computer interprets. Just as human genetic information determines brown hair or blue eyes, DE's digital DNA codes for launch date, rocket boost intervals and other mission-critical elements.

Along every parameter vector, the differential evolution program assigns a value to each bit of digital DNA, locating it between the upper and lower limits of a range. Using this method, a parameter vector might code for a morning or evening launch, a Monday or Friday rocket boost or a planetary approach farthest from or nearest to the Sun. The algorithm makes this happen by taking advantage of the mathematical equivalents of mutation, selection and reproduction, allowing progeny vectors to give "birth," as it were, to new generations of vectors, each intent on mapping ever-more-efficient routes.

ROCKET SCIENTIST: Craig Kluever is the James C. Dowell Professor of Mechanical and Aerospace Engineering at MU.

This propagation of progeny vectors goes on until an "optimal" route emerges from the original vector family, Kluever says. His colleague, Olds, likens this digital evolution process to the creation of "children that will survive into the next generation if they are an improvement over their parents."

A long-distance space voyage is like a road trip over "a substantial number of hills and valleys," explains Olds, now a project engineer at Analytical Mechanics Associates, Inc., in Hampton, Va. The differential evolution algorithm takes advantage of those ups and downs by helping the spacecraft make use of gravity's peaks and valleys.

In the parlance of space science, this is known as a "gravity assist," the fuel-saving process whereby a spacecraft uses a planet's gravitational field to change course or slingshot itself farther into space. Olds likens the process to a pedal-free bike ride down a steep street.

As planets orbit around the sun, they create dozens of gravity boost opportunities. Unfortunately, such boost scenarios are riddled with potential trajectory pitfalls. Here differential evolution algorithms really shine, Olds says. By charting "propulsion maneuvers" -- fuel burns that keep the ship on track -- the algorithms correct for such variables as unequal incoming or outgoing velocities. Once the ship is in place, the programs allow the ship to use smaller burns at scheduled intervals to remove errors in the trajectory.

By the end of the 1980s, evolutionary and genetic computer algorithms had became so widely accepted that budding digital geneticists could purchase a software package called Evolver for their desktop computers. Today the Ithaca, N.Y. -based Palisade Corporation makes Evolver as a supplement for the Microsoft Excel spreadsheet. Interplanetary travel software is also available commercially, Olds says, most notably through the Satellite Tool Kit from Analytical Graphics in Exton, Penn.

The MU research team has shown, in a study published in a recent edition of the Journal of Spacecraft and Rockets, that these and their own differential evolution algorithms offer several advantages over proprietary programs. Such programs include, most notably, the MIDAS program currently used by NASA and the Jet Propulsion Laboratory.

Whereas NASA's space mission design software acts locally, Kluever says, differential evolution acts globally.

"MIDAS and other programs break one large space flight into several smaller flights. They use a gradient method that strings together local minima, areas along the route that consume minimal amounts of fuel, into one long trip."

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