Hi V Dogg,
the engine is not "fire and forget". First, the auto-reduce option is used in cases when we do not have somehow an approximation of b to start with. In that case, we could set an arbitrary high b value and enable the auto-reduce check-box. The engine will detect the surplus of blocks and remove them accordingly. After the bulk of blocks have been removed by the auto-removal operation, there is not much use for this checkbox, it has done its purpose.
A particular use of this checkbox is when you want open-cover constructions (less than 100% coverage). This is where this option shines most as it will automatically remove blocks as long as the coverage requested is achieved. So, if you want e.g. the best 95% cover, set your desired L% (or click on the text to enter a more precise % number) enable this auto-remove and let the engine run overnight. Also this check-box is useful in more complex coverings which involve filters where finding a proper b setting to begin with is impossible.
Typically however, if you have a source for a good b value, you use it instead. Such sources are wheel repositories where b is indicated. Check out LaJolla covering repository as a starting point but there are others around too.
https://www.dmgordon.org/cover/
and an older reference is Rade Belic's listings although most have been surpassed but still a good source for b values
https://rbelic.home.xs4all.nl/mainpage.htm
Now, about the actual optimization process. The user has to manipulate the optimization parameters. It is virtually impossible to reach a good quality wheel without altering the bias as needed. To keep it simple, use standard algorithm, tension bias always to 0 and we'll adjust only the expansion slider and bias multiplier. Initially have multiplier to x1 and bias to 0. Start the optimization. What we want here is this:
1) have the main coverage indicated fluctuate a bit up and down. The jumps should be small or big depending on the 1-block cover indicated at the bottom. So, if 1-block line suggests e.g. a value of 10 and you see jumps of like 20, this is too big. If jumps are like 1-3 or so, it looks more natural. Don't dive too much into that detail, it is just a guide and not applicable in all coverings but this is just to get an idea of how big jumps we should have more or less. Like, if 1-block suggests a value of 5000, a fluctuation of 1-5 is probably a small one.
2) give the impression is reaches the best coverage found (in the parenthesis) once in a while.
If you observe the above two conditions, we are good and no action is needed. We just wait for the engine to find better improvements.
Now, if we don't get any improvement after a while, or the conditions 1 & 2 above are not met, we need to take some action as this means the current optimization settings are not effective. The single most important setting is the bias expansion slider. If the main coverage fluctuation is quite above the best found and case 2 never occurs, we typically have to lower the bias slider. I usually do this in steps of 200 or 250. So, from the initially 0 value, I change it to -250 or so and continue optimization observing case 1 & 2 as usual to see when my next change to this control will be.
If the fluctuation is too small, we increase the bias slider in a similar manner, like +300.
The bias multiplier just multiply or lower the impact of the bias expansion slider. In small coverings like the above you attempt it will probably slay only to x1. Bigger values (x10-x10000) are used in very big coverings like having hundred or thousands of blocks or having a very large value indicated at the 1-block line at the bottom of the program. Smaller values (x0.1 and below) are available to give more precise adjustment to the bias expansion when we have moved the expansion slider and we are willing to keep searching. This is a situation that we should generally avoid doing and optimization is considered complete when we have moved the bias expansion slider quite to the left (like a value of -900) and minimal coverage fluctuation occurs (after we have gone through all the mentioned gradual bias adjustments). That means we have no more adjustments to make.
Typically x0.1 and below has lower operational value in normal coverings like the one you attempt but it is available to anyone who wants to keep searching and the x1 setting is not sufficient anymore. Where this setting (x0.1 and below) has actual value is when we build around filters. In this situation even the typical x1 setting might be too much and cause a large undesirable coverage fluctuation.
To understand the bias multiplier, assume a setting of x1. Going from bias expansion of 0 to 1000 (maximum value) is equivalent as doubling the bias effect. x10 and bias 0 is 10 times the impact of x1 and 0. x1 and -900 is equivalent to x0.1 and 0.
Once we covered how optimization works, to your real questions:
Now my problem comes at 7 and 8. If I do it as stated and I check the best covering menu, the combinations don't change even after an hour or two of running it.
The particular covering in fact needs quite many combinations. If you check at the bottom of the program, the 1-cover line at the end suggests a theoretical minimum like 204 blocks. This is actually a minimum theoretical value and most of the time, the real possible achievable can be double or triple or more of what this value suggests. So clearly, with just b=10 blocks total, there isn't much more that can be found. Along that line, also check the main coverage line, it actually states 3 values, the current coverage and in the parenthesis it suggests two other values: the first is the best coverage found so far and the other is the best possible coverage that can be achieved with the current b setting. With just 10 blocks in your covering, you'll see that your current best covering has matched that best possible coverage. Obviously there is nothing more that can be found in that case and therefore no further changes will occur at the covering.
Now if I set b to, say, 2000 like the help file suggests and check auto reduce, after about an hour or two it leaves me with about 100 combinations, which is unaffordable for me.
It is impossible to be left with just 100 blocks with the settings you have set. Recall, even the theoretical minimum for this covering is 204 blocks. From the Rade Belic's site, this covering 20,5,4,5 requires around 359 blocks - the record stated at this site - might have been improved a bit over the years but you get the point of how many blocks are needed.