problem based optimization-multiple solutions - constraints

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Christian Schumacher 2019-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/484469-problem-based-optimization-multiple-solutions-constraints

Hello,

I attempted to solve an optimizationn problem using intlinprog with the solver based approach. After adding all constraints I wanted to solve the problem again with a littel adjustment. My problem in short: i have n players and want to choose k = 9 players from this player pool. After this I want to do the same thing again, with one new constraint: the overlap between the chosen players between run 1 und run 2 should be a maximum of 7. I wrote this to solve my problem:

i8 = 1:num_skaters;
 i9 = 1:num_goalies;
overlap = sum(s_lineups(i8).*skaters_lineup(i8)) + sum(g_lineups(i9).*goalies_lineup(i9));
lineup_creator.Constraints.overlaprule = overlap  <= 7;

before the loop s_lineup and g_lineup are consisting only zeros. skaters_lineup and goalies_lineup are are my binary optimization variables. I get a vector with 8 skaters (8 ones)and 1 goalie (1 one) from every step in the loop. in the end of every iteration I added this:

s_lineups = s_lineups + sol.skaters_lineup;
g_lineups = g_lineups + sol.goalies_lineup;

To test my constraint I set:

lineup_creator.Constraints.overlaprule = overlap <= 9;

this should lead to yield the same solution for every iteration, because I only have 9 players per solution, if the overlap is 9 the solution shouldnt change.

Unfortunaly, this is not the case. After a few iteration I get less optimal solution.

If i try to use it as intended with 7, I am not able to get more than 10 solutions, although it is definitly possible.

Does anyone have a idea for this?