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A New Challenge: Saving Mark Whitney

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In the last blog entry Adding Crossover to CMA-ES we provided further details to the new optimimization algorithm GCMA-ES designed to partly replace search by optimization for space mission design, but also can be applied to hard optimization problems in other areas. As test method we used ESAs GTOP messenger full problem . We observed that ESAs current implementation is flawed, but can easily be fixed by updating the Lambert solver implementation. Even the updated version has a problem: It is quite "easy" to solve for new algorithms. On a powerful single processor machine like the TR2990WX the same optimum is found every few hours. We cannot be sure it is a global optimum, but would prefer a problem where better solutions as the ones currently found are expected, enabling us to measure further improvements of real parameter optimization algorithms. If you know of such a problem, specially if it is not related to space mission planning, please comment. Extending ESAs
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Adding Crossover to CMA-ES

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In GCMA-ES we introduced a new optimization algorithm and applied it to different real world problems Around the World in Eighty Days and GTOC1 today . Not only are these problems related to a real world tasks - space flight planning - we validated the optimization results by using them as basis for further optimization using a more detailed model of reality: continous low thrust. Using a genetic crossover operation in the context of a CMA-ES retry mechanism feels quite natural so we are probably not the first ones exploring this idea. But the devil is in the details: How to define the crossover operation  How to select ancestors for crossover  How to parameterize the CMA-ES runs  Here we will present more details together with some thoughts about metaparameter optimization. We are aware that the notion G-CMA-ES exists in some early CMA-ES papers in a different context, but we think nevertheless Genetic CMA-ES (GCMA-ES) is a good name for this retry approach. Please comme
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How to solve GTOC1 today

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In this blog entry we review methods described in (1) "1st ACT global trajectory  optimization  competition: Results found at  the Jet Propulsion Laboratory" (Acta Astronautica 61 (2007) 806–815)"  to solve the GTOC 1 problem back in 2006. Different aspects of the methods used back then are compared to what we regard more suitable to the set of tools available today.  Analysis of the JPL method How did JPL determine the planet sequence ? JPL used forward search using a sims flanagan approximation of the required  continuous  thrust transfers between the GA  maneuvers . Forward search is motivated by the fact that there are only very few valid transfers with v_inf <= 2.5 km/s because of the very low max_thrust constraint of  0.04N.  Problem is to find a search heuristics to be used for pruning targeting at a high impact velocity at the asteroid. Searching backwards from the impact can be motivated in a similar way: Very few valid transfers to the asteroid with im
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