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My problem is as follows:

I want to generate a series of 24 dimensional random numbers to act as the starting population for a genetic algorithm. These numbers need to fully span the space which is limited by a series of nonlinear boundary conditions.

The 24 dimensional vector is a scaling vector which scales currents flowing in 64 different coils. There is a linear transformation matrix (call it A) [64x24] which maps the scaling vector (call it x) to the current space (call this vector B). So the problem is Ax = B.

The problem is the boundary conditions for the space are in the 64 dimensional current space. The conditions are:

1) The current in a given coil cannot exceed abs(500mA) (each abs(B(< 500mA)

2) The total sum of positive currents cannot exceed 6000mA

3) The total sum of negative currents cannot exceed -6000mA

4) The difference between positive and absolute value of negative currents cannot exceed 2500mA.

How can I bound the problem space so that the random number generator doesn't continuously generate illegal values?

Any insight would be greatly appreciated.

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# Mapping Conditions in Transformational Space

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