TODO-hv

Trivial 2D: https://github.com/anyoptimization/pymoo/blob/main/pymoo/cython/vendor/hypervolume.cpp#L1597

Hypervolume contributions:

https://hpi.de/en/friedrich/research/the-hypervolume-indicator.html

0) The default reference point has changed. Update all tests with
   either explicit reference points or updated results.

1) Robust read of floating-point numbers:

a) Issue error if number is infinite or NaN
   x = strtod(str, &endp);
   if(!isnormal(x)) error("x is infinite or NaN");

b) check overflow/underflow: strtod() returns plus or minus HUGE_VAL
   (HUGE_VALF, HUGE_VALL) is returned (according to the sign of the
   value), and ERANGE is stored in errno.  If the correct value would
   cause underflow, zero is returned and ERANGE is stored in errno.

   errno = 0;
   x = strtod(str, &endp);
   if(errno != 0) { error("Overflow/underflow");


2) [DONE in 1.3] Specifying a reference point smaller than the max of
   all points could also be permitted, as long as points outside the
   desired region are eliminated when building the linked lists. This
   would be useful when optimizing with goals, but saving all
   non-dominated points to files.

3) [DONE in 1.2] Instead of computing the volume of the union of all
   sets, I would let hv compute the volumes of each set individually,
   but using the same reference (eventually computed from the union of
   those sets). The reason is that it is easy to compute the union as

   grep '[0-9]' file1.dat ... filen.dat | hv

   if you have multiple files or multiple sets per file.

4) Minimization/maximization could be handled by switching signs when
   reading the data/building the linked list. It would be no big deal.

5) Permutations of the objectives could be included at this stage as
   well, because it is difficult to permutate columns with the
   standard unix tools. (I don't agree. It is true that there is no
   standard tool for permuting columns. One can do it with some
   combination of cut and paste. However, this is easier to implement
   in perl or python. Moreover, I would prefer to implement it in C as
   a general purpose and independent tool.)

6) Sort array in memory by 3rd (or 2nd) dimension, depending on
   special case used. This may (or may not) improve performance
   significantly for large sets, by speeding up the special case.

7) verify the handling of repeated coordinate values and of dominated
   points, to avoid performing more math operations than actually
   required in these cases.

8) I think setup_cddllist() could be further simplified and
   clarified. What we currently do with 'head' and 'scratch' is
   difficult to understand. Also, I don't get why the nodes of the
   tree must be in the list or, if they must, why the nodes are not
   initialised instead of calling repeatedly avl_init_node() in
   hv_recursive(). Why the nodes of the tree must be included in the
   list? I see no reason since we destroy the whole tree at every
   iteration... Solution: dynamic malloc() and free() required tnodes
   and replace pp->tnode by newtnode. If we require a tnode for each
   point, then this can be slower, so we keep old behaviour but move
   avl_init_node() to setup_cdllist().

9) Provide example data set in the webpage.