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Local optimization programs minimize propellant use "by starting with a trajectory guess," Aaron Olds adds. "The term 'local' is used because the minimum fuel consumption point will be found only for the valley in which the initial guess is placed. The algorithm will not climb out of one valley in hopes of finding a lower one." At least, not without help from programmers and engineers.

Differential evolution, on the other hand, visualizes the entire trip, from point A to point Z, rather than just individual stages. "Our software looks for a global minimum -- the most fuel-efficient route mapped out ahead of time that provides perspective all at once," Kluever says. This approach "allows more missions to be analyzed more rapidly."

The ability to analyze several potential missions ahead of time makes the differential evolution algorithm "a very good feasibility tool," says Dave Brody, media director and science writer for Imaginova, the parent company of Space.com and publisher of Space News. "It seems like a good top-level way to analyze a mission or missions from an initial or proposal stage," Brody says. "In that respect, it represents a new paradigm for space travel: up front, rather than stage-by-stage mission optimization."

BOLDY GOING: The MU research team found planning for journeys to destinations such as Mars or Jupiter would likely benefit from differential evolution algorithms employing 'parameter vectors.'

Image courtesy of Courtesy NASA/JPL-Caltech/T. Pyle

Designed as "open source" -- for use and modification by just about everyone -- differential evolution space flight software will, of necessity, be easy to use. Such an advantage is a plus for the private and commercial space flights Brody says will soon be commonplace.

"NASA's current software is user generated. As a result, it's arcane and complex," he explains. "To expect it to transfer to another information technology culture may not be realistic. The differential evolution algorithm may be a much better way for planners to talk to one another across organizations and across the globe."

Potential investors will likely also appreciate the evolution solution. "As a private investor, if I can get an overview of an entire trip rather than a series of snapshots, that's much better," Brody says.

To test their algorithm, Kluever and Olds programmed it to map what they call "challenging interplanetary optimization" problems: the 1997 Cassini Mission to Saturn, the 1989 Galileo mission to Jupiter, a mission to the comet Tempel 1, and a round trip to Mars.

One of the most complicated space explorations in history, Cassini's seven-year journey began from Earth, included two gravity assists from Venus, an Earth gravity assist and, finally, a boost from Jupiter's gravity before its arrival at Saturn. The differential evolution algorithm globally optimized the Cassini mission in 1.2 minutes, Kluever reported. It optimized the Galileo mission in 51 seconds, with even faster times for the Mars and comet missions.

"For the Cassini and Galileo cases, Kluever says, "the optimal route determined by the DE algorithm essentially matched the actual space missions."

A Mars mission is a relatively simple trip, Kluever says. He envisions differential evolution tackling more ambitious missions to asteroids, a Jovian moon, or beyond. Long-distance missions to smaller targets require lots of "travel tricks," Kluever says. Feats of interplanetary prestidigitation might include coasting for more than a year with lots of trajectory-correction maneuvers, then using Venus, Earth and Jupiter for multiple gravity assists.

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