solver:here

$title Modified version of model library example DICE $Ontext Modified version of model library example "Non-transitive Dice Design (DICE,SEQ=176)". This model uses the GAMS BCH facility with GAMS/CPLEX in order to save incumbent solutions in GDX files during the solution process. Probabilistic dice - an example of a non-transitive relation. We want to design a set of dice with an integer number on each face such that on average dice1 beats dice2, and dice2 on average beats dice3 etc, but diceN has to beat dice1. MIP codes behave very erratic on such a problem and slight reformulations can result in dramatic changes in performance. Also note the face value will be integers automatically. Gardner, M, Scientific American. Robert A Bosh, Mindsharpener, Optima, MP Society Newsletter, Vol 70, June 2003, page 8-9 Robert A Bosh, Monochromatic Squares, Optima, MP Society Newsletter, Vol 71, March 2004, page 6-7 $Offtext sets f faces on a dice / face1*face6 / dice number of dice / dice1*dice3 / ; scalars flo lowest face value / 1 / fup highest face value wn wins needed - possible bound ; fup = card(dice) * card(f); wn = floor(0.5 * sqr(card(f))) + 1; alias(f,fp); alias(dice,dicep); variables wnx number of wins fval(dice,f) value of dice - will be integer comp(dice,f,fp) one if f beats fp ; binary variable comp; fval.lo(dice,f) = flo; fval.up(dice,f) = fup; fval.fx("dice1","face1") = flo; equation eq1(dice) count the wins eq3(dice,f,fp) definition of non-transitive relation eq4(dice,f) different face values for a single dice; eq1(dice).. sum((f,fp), comp(dice,f,fp)) =e= wnx; eq3(dice,f,fp) .. fval(dice,f) + (fup-flo)*(1-comp(dice,f,fp)) =g= fval(dice++1,fp) + 1; eq4(dice,f-1) .. fval(dice,f-1) + 1 =l= fval(dice,f); model xdice /all /; $if set nosolve $exit xdice.reslim = 20; xdice.optfile=1; option mip=cplex; solve xdice using mip max wnx; option fval:0; display wn,fval.l; parameter rep1 Chance of winning against next; rep1(dice,f) = 100*sum(fp, comp.l(dice,f,fp)) / card(f); rep1(dice,'chance') = sum(f, rep1(dice,f))/card(f); option rep1:0; display rep1; * Write incumbent solutions with objective value>15 to a GDX file during the * solution process by utilizing GAMS BCH facility (www.gams.com/docs/bch.htm). $onecho > cplex.opt userincbicall reportsol.gms lo=2 $offecho $onecho >reportsol.gms variable wnx; $gdxin bchout_i.gdx $load wnx $gdxin if (wnx.l>15, execute 'copy bchout_i.gdx dicesol%ncalls%.gdx'); $offecho

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solver/here.txt · Last modified: 2013/05/24 17:48 by support