Genetic algorithms provide attractive options for performing nonlinear multi-objective combinatorial design optimization, and they have proven very useful for optimizing individual systems. However, conventional genetic algorithms fall short when performing holistic portfolio optimizations in which the decision variables also include the integer counts of multiple system types over multiple time periods. When objective functions are formulated as analytic functions, we can formally differentiate with respect to system counts and use the resulting gradient information to generate favorable mutations in the count variables. We apply several variations on this basic idea to an idealized hanging chain example to obtain >> 1000x speedups over conventional genetic algorithms in both single - and multi-objective cases. We develop a more complex example of a notional military portfolio that includes combinatorial design variables and dependency constraints between the design choices. In this case, our initial results are mixed, but many variations are still open to further research.
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