In this question, @Carl Love posted an example of finding one shortest possible tour through several 3D points. His code only took he around four minutes, and just took @dharr about six minutes. Unexpectedly, executing it takes me nigh on 9 min! Well, these may be determined by one's computer. But how about Steam Deck's performance?
 

Download testTSP.mws (Sorry for a typo in it.) 

The selection works for sets as well.

@mmcdara For a small problem, minimizing the unsquared sum of actual distances (something like perpendicular offsets) remains possible in practice.

But it seems that Maple haven't collected this method yet, so one has to implement these by hand!

@lcz Replace "\n" and/or "\t" between term and datum with " ". For example, 

fontName	"Dialog"

is replaced by 

fontName "Dialog"

and 

LabelGraphics
		[

is replaced by 

LabelGraphics [

@acer Thanks again. It's what I want.

@sand15 Cheers. I believe the "smooth" means "antialiased", but I'm unfamiliar with these technical terms, and don't know how to define them.

@lcz Thanks. Maybe Maple is more geared towards graph computations rather than graph representations. I'm not familiar with Gephi, but it looks superb. At present, if I really wanna plot a graph emphasizing layered structure in Maple, I have to specify the co-ordinates of the vertices manually only after obtaining vertex placement in Mathematica (using GraphEmbedding). This vexed matter is very irritating.

@sand15 I think that the third line is with(ComputationalGeometry):. Also, the boundary is less smooth, but this is a constructive approach indeed. Thanks!

@acer This time the boundary is very rough (in contrast to Mathematica's default output). However, these approaches are not so easy-to-use. (What about other possible ways?) It is often alleged that there exists an inverse relationship between the power of the tool and how easy it is to use. Still, I wish there to be a more intelligent Maple functionality in this respect.

@mmcdara Thanks as well. It seems that if we hope to transform a complicated plot, this approach may fail. Am I correct in saying this?

@acer Thanks very much. I never knew these before. But I wonder why plottools[transform] works in the first example instead. Any distinctions?

Are your codes correct? An error is issued at last:  By the way, running these on my computer takes about 32 minutes!

@C_R Thanks. It's very strange indeed—It appears that using the standard plot is always recommended.

@mmcdara Incidentally, an alternative method of the given problem is using certain CAD-based algorithms: 

try
    unwith(Logic):
catch:
    ;
finally
    RegularChains:-SemiAlgebraicSetTools:-QuantifierElimination(&E [x, y, a], ((x^3 + y^2 - x = a) &and (a^2 = 4/27) &and (a < 0)) &and ((x^2 + y^2 = R^2) &and (R >= 0)), 'output' = 'rootof');
end try;
               /    1  (1/2)\     /2  (1/2)     \
               |R = - 3     | &or |- 3      <= R|
               \    3       /     \3            /

Nonetheless, this is really beyond layman's ken (despite its correct result).

Unfortunately, extrema just returns (constrained) relative extrema of n algebraic expression; the "extreme values" must be checked later. In addition, in this problem, x, y, and z are all positive real numbers, so you need at least

extrema(x^2*y^2*z^2, x^2 + y^2 + z^2 = 6, {x, y, z}, 'S');

or 

Student[MultivariateCalculus][LagrangeMultipliers](x*y*z, [x + y + z - 6, -sx^2 + x, -sy^2 + y, -sz^2 + z], [x, y, z, sx, sy, sz], output = detailed);

for exact solutions.