ABS() in Excel (Simplex) Solver (Dartboard problem)

Hi

I am trying to solve a linear programming problem. Essentially, it is trying to model the optimum layout for a dartboard by maximising the difference between the numbers (so 20 being next to 1 and 5, would give a difference of 19+15 = 34, and so on for all 20 numbers).

My decision variables, are numbers 1..20 (let's say that are in B1..B20) and to calculate the difference I say '=ABS(B1-b2)' - and so on for all the other numbers. I do ABS as you do not know what order the decision variables will be presented.

Of course, the ABS function in non-linear, so the problem cannot be solved using Simplex, but I'd really like to do that to ensure that I get the optimal solution.

I have looked around and there are some posts that say how ABS can be represented in Excel Solver but, to be honest, I just don't get it.

Can anybody help? I have attached my spreadsheet, in case anybody finds this useul.

Note: This is not homework. I have a genuine interest as I want to develop some research from a few papers that I have been reading recently.

Thx

G

Thanks for this. squaring the difference is fine BUT it is still non-linear so suffers the same problem as ABS. That is the simplex algorithm will not work. But thanks for the suggestion.