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Type 'q()' to quit R. > library(kappalab) Loading required package: lpSolve Loading required package: quadprog Loading required package: kernlab > > ## number of criteria > n <- 5 > > ## the number of alternatives > n.a <- 10000 > > ## a randomly generated 5-criteria matrix > C <- matrix(rnorm(n*n.a,10,2),n.a,n) > > ## the corresponding global scores > g <- numeric(n.a) > > ## generate a random capacity > x <- runif(2^n-1) > for (i in 2:(2^n-1)) + x[i] <- x[i] + x[i-1] > mu <- normalize(capacity(c(0,x))) > for (i in 1:n.a) + g[i] <- Choquet.integral(mu,C[i,]) > > mu.in <- as.capacity(uniform.capacity(n)) > > ## the full solution > lsc <- heuristic.ls.capa.ident(n,mu.in,C,g) hlms: L2 ending value of criterion: 1.21321e-06 at iteration: 12 > mu.sol <- lsc$solution > > ## the difference between mu and mu.sol > mu@data - mu.sol@data [1] 0.000000e+00 -3.522443e-08 -4.906649e-08 -5.316262e-07 -5.992587e-08 [6] -5.023292e-07 -4.846805e-07 5.351777e-07 -1.577456e-08 -5.396926e-07 [11] -6.878902e-07 6.565388e-07 -5.457276e-07 6.189191e-07 6.742132e-07 [16] -1.246369e-08 -5.368207e-08 -5.230773e-07 -5.475642e-07 5.413461e-07 [21] -4.798226e-07 4.936815e-07 5.334443e-07 2.348382e-08 -5.671783e-07 [26] 5.038961e-07 6.485151e-07 2.498161e-08 6.052968e-07 -6.298760e-09 [31] -2.267549e-09 0.000000e+00 > > lsc $solution capacity {} 0.000000 {1} 0.026050 {2} 0.058285 {3} 0.099691 {4} 0.144950 {5} 0.178874 {1,2} 0.180894 {1,3} 0.226954 {1,4} 0.250660 {1,5} 0.279490 {2,3} 0.286239 {2,4} 0.322617 {2,5} 0.356156 {3,4} 0.382280 {3,5} 0.429992 {4,5} 0.466275 {1,2,3} 0.475881 {1,2,4} 0.525531 {1,2,5} 0.564987 {1,3,4} 0.600594 {1,3,5} 0.635365 {1,4,5} 0.682040 {2,3,4} 0.724505 {2,3,5} 0.730893 {2,4,5} 0.777221 {3,4,5} 0.814643 {1,2,3,4} 0.844375 {1,2,3,5} 0.883594 {1,2,4,5} 0.902337 {1,3,4,5} 0.941525 {2,3,4,5} 0.976921 {1,2,3,4,5} 1.000000 $n.iter [1] 12 $residuals [1] -7.103332e-07 1.079007e-07 -6.233566e-07 3.935247e-07 -8.947932e-07 [6] -4.789840e-07 -3.652484e-07 1.832779e-07 -4.474373e-07 -6.944863e-08 [11] -3.403500e-08 7.603507e-07 6.354869e-07 1.247293e-06 2.307613e-07 [16] 4.074909e-07 -5.829784e-07 -1.520181e-07 -6.131563e-07 3.720640e-07 [21] 1.395540e-06 1.065956e-07 -5.512375e-07 -8.556089e-07 8.714789e-07 [26] -3.624766e-07 -9.878235e-07 -2.708986e-07 7.821725e-07 -8.662299e-07 [31] 5.234519e-07 1.191003e-07 -1.913403e-09 1.605659e-06 -1.860521e-06 [36] -1.014957e-06 4.956513e-07 1.597095e-07 -3.280278e-07 -8.873239e-07 [41] -2.745193e-07 1.345490e-06 -9.728984e-07 3.758580e-07 1.179021e-07 [46] -4.396028e-07 -1.303402e-06 9.629176e-07 -1.825614e-07 -2.312037e-07 [51] -1.154092e-07 -3.715055e-07 1.508694e-06 -6.679592e-07 4.885355e-07 [56] 5.770008e-07 -6.388194e-07 5.594079e-07 -1.921721e-07 1.518107e-07 [61] 5.364491e-07 -4.546227e-07 -2.549846e-07 8.203380e-08 -1.254120e-06 [66] 1.283748e-07 4.810528e-08 -6.079509e-07 -4.482041e-07 1.313398e-07 [71] 7.166836e-07 2.879537e-07 -6.740019e-07 -2.762886e-08 8.967858e-09 [76] 6.057102e-07 6.817931e-08 -1.757133e-07 -1.916739e-07 2.972470e-07 [81] 7.667960e-07 -7.337973e-07 -1.530523e-07 1.217429e-06 -8.639035e-07 [86] -9.406471e-07 8.288112e-07 1.465331e-07 1.433426e-07 -3.546797e-08 [91] -2.608138e-07 1.420942e-06 -3.567097e-07 -1.214589e-08 4.646014e-07 [96] -1.450985e-07 1.091187e-07 -1.271695e-06 -2.830634e-08 -8.020376e-07 [101] -9.394346e-07 1.871998e-07 4.903627e-07 -6.903165e-08 1.130028e-06 [106] 9.411495e-07 -6.912906e-07 5.097613e-08 3.879803e-08 1.616283e-07 [111] -2.474149e-07 -7.645759e-08 9.004385e-07 2.209742e-07 8.052520e-07 [116] 7.331210e-08 -5.016730e-07 -1.064634e-07 1.852478e-07 1.358553e-06 [121] -7.300951e-07 -2.283811e-07 -3.336760e-07 -2.785741e-07 3.382512e-07 [126] -2.404112e-08 2.075178e-07 -7.195151e-07 5.976956e-08 3.145150e-07 [131] -8.669638e-08 -6.274206e-08 6.430149e-07 -3.333885e-07 -6.459070e-07 [136] -6.467635e-07 -1.521790e-07 -1.090339e-06 -4.551052e-07 -2.150966e-07 [141] 9.103478e-08 -5.613570e-07 -5.208589e-07 4.588133e-07 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1.972898e-06 5.850203e-07 [9426] -5.975701e-07 4.658877e-07 -5.337000e-07 2.329564e-08 -6.837403e-07 [9431] -2.961516e-07 1.893983e-06 4.792971e-07 1.023701e-06 -5.622467e-07 [9436] 1.930251e-07 9.520015e-08 5.542859e-08 -1.568182e-06 8.071071e-08 [9441] -2.892536e-07 1.262931e-07 1.132893e-06 3.321687e-07 1.284473e-06 [9446] 1.283609e-06 1.820321e-07 4.332397e-07 8.303900e-08 -5.506854e-07 [9451] 3.705679e-07 5.939334e-07 -6.386969e-07 -5.227018e-07 -4.946680e-07 [9456] 5.863524e-08 1.794617e-06 7.391416e-07 6.950644e-07 -1.612868e-07 [9461] 4.883122e-07 4.511820e-07 5.925502e-07 1.126161e-06 6.836188e-07 [9466] -7.755416e-07 -6.581889e-07 -4.751536e-07 2.605578e-08 1.061228e-06 [9471] -1.587968e-07 -2.773754e-07 -1.040062e-07 1.288503e-07 -5.995402e-09 [9476] -6.954161e-08 8.772116e-07 -3.235353e-07 3.882757e-06 6.053695e-07 [9481] 3.857943e-07 1.092854e-07 -2.052755e-07 -8.400324e-07 -4.414710e-07 [9486] -1.618939e-08 5.652432e-07 1.141041e-07 -2.369395e-07 5.108037e-07 [9491] 8.751414e-07 2.352899e-07 -2.090039e-07 -3.770133e-07 7.303144e-07 [9496] -4.935065e-07 -9.942587e-08 5.485912e-07 4.439711e-07 1.740139e-06 [9501] 1.819159e-07 1.940773e-07 1.236981e-07 -3.786530e-07 -6.235431e-07 [9506] -1.457937e-07 -1.569151e-06 8.340220e-08 -1.134363e-06 2.377078e-07 [9511] -7.936846e-08 3.377655e-07 -1.762539e-07 -1.673281e-07 4.303201e-07 [9516] 2.892142e-07 4.712730e-07 1.854638e-07 -4.468170e-07 1.954666e-06 [9521] 1.320270e-06 -6.946923e-07 -8.719087e-07 6.203337e-09 -2.571912e-07 [9526] -2.377320e-07 2.826368e-07 2.310776e-07 -1.165447e-07 6.766378e-07 [9531] 2.948386e-07 -1.493110e-07 6.554749e-07 1.177241e-07 -3.897567e-07 [9536] -3.369271e-08 -1.199962e-07 1.490429e-07 -1.964849e-07 3.076324e-06 [9541] 6.914621e-08 -2.201815e-07 6.786412e-07 -8.677045e-09 -1.251527e-06 [9546] -1.168870e-07 -2.672143e-07 -1.525361e-07 6.793155e-07 8.060036e-07 [9551] 1.044037e-06 2.079398e-07 7.112172e-07 1.528741e-06 8.647374e-07 [9556] -2.296715e-07 4.167102e-07 -5.167075e-07 -4.487598e-07 8.726636e-07 [9561] 4.300531e-07 1.677835e-07 -2.121867e-07 -4.305971e-07 -1.995338e-07 [9566] -2.604606e-07 -3.547142e-07 -3.114741e-07 -4.329991e-07 -7.714288e-07 [9571] 4.680307e-07 3.688135e-07 1.027954e-08 -4.508593e-07 7.526359e-07 [9576] -4.694983e-07 1.605900e-07 -8.769074e-07 3.417683e-06 -6.430372e-07 [9581] 2.624438e-07 1.742304e-07 -7.116047e-07 1.070913e-06 -2.855749e-09 [9586] -4.053695e-07 -8.094652e-07 -8.076731e-07 3.640012e-07 -3.504190e-07 [9591] -1.346804e-06 1.910497e-07 -3.981740e-07 2.421819e-07 -6.303235e-07 [9596] 1.083952e-07 -7.472845e-07 8.921449e-07 6.805946e-07 2.130392e-07 [9601] -1.335141e-07 1.482726e-06 1.621119e-07 -4.424504e-07 2.960617e-07 [9606] -4.900727e-07 5.247454e-07 -5.793313e-07 -6.146106e-07 -1.060268e-06 [9611] -5.081248e-07 -2.328820e-07 -8.769112e-07 -2.332755e-07 -2.271462e-07 [9616] -8.007564e-07 2.259008e-08 -5.534924e-07 1.765342e-07 -1.918970e-07 [9621] -7.241566e-08 1.652227e-06 -4.274972e-07 -1.355143e-06 2.931826e-07 [9626] -1.297461e-07 -6.432613e-07 3.155912e-07 1.301760e-07 -5.134730e-07 [9631] -7.975680e-08 1.120616e-07 -1.182517e-06 -4.725614e-07 -4.133484e-07 [9636] -8.399409e-07 4.957345e-08 -4.908235e-07 -3.322201e-07 4.102681e-09 [9641] -7.221222e-08 -9.434303e-07 1.012024e-06 -1.562300e-07 3.319297e-07 [9646] -3.197147e-07 -1.005803e-07 -2.910096e-07 5.840517e-07 2.593209e-07 [9651] -1.483800e-07 -5.013418e-07 -1.417434e-06 -3.643872e-07 -2.696092e-07 [9656] -1.579756e-07 6.648779e-07 5.217088e-07 7.860826e-08 -3.808589e-07 [9661] 9.035022e-07 -5.076321e-07 -9.251106e-07 9.535030e-07 -6.078071e-07 [9666] 4.221358e-07 3.252625e-07 -6.063073e-07 2.004156e-06 -1.333821e-06 [9671] -9.747575e-07 3.988246e-07 9.157578e-07 -7.432313e-07 -5.072030e-07 [9676] -1.070285e-06 -5.954270e-08 -4.656158e-07 -3.814799e-07 -5.258687e-07 [9681] 1.337746e-07 -4.755732e-08 -6.089314e-07 7.978035e-08 -1.254992e-06 [9686] -6.183793e-07 -3.309105e-07 -3.976816e-07 -1.942858e-07 -3.104303e-07 [9691] 9.657004e-09 -4.581319e-08 -9.287644e-08 -6.840007e-07 -1.666415e-07 [9696] 7.113885e-07 -1.317733e-07 9.026294e-07 1.373353e-08 -2.601874e-07 [9701] 5.006791e-07 -8.438428e-07 -1.667393e-07 -9.921762e-07 -6.095286e-07 [9706] 3.511510e-07 4.927270e-07 -2.832127e-07 -4.511839e-07 1.193921e-07 [9711] 7.715408e-08 6.040099e-08 -7.460084e-07 -5.338373e-09 -5.143085e-07 [9716] -2.627359e-07 -6.871583e-07 3.626803e-07 -4.080018e-07 2.563462e-07 [9721] -2.729749e-08 4.686501e-08 5.270382e-07 5.127923e-07 -6.769314e-07 [9726] -5.449132e-07 7.786690e-07 1.054205e-07 4.504646e-07 3.606390e-07 [9731] -7.616341e-08 6.807590e-07 7.864650e-07 -1.077018e-06 4.339258e-07 [9736] -2.366126e-07 -1.110440e-07 2.421576e-06 1.142437e-07 1.424165e-06 [9741] 4.816137e-07 -1.745883e-07 -4.161403e-07 2.018315e-07 -2.037940e-06 [9746] 1.571706e-06 7.845319e-07 -2.159380e-06 -7.938343e-07 -7.959579e-07 [9751] 4.729201e-07 7.044215e-07 -8.590754e-07 1.807126e-07 7.799794e-07 [9756] -2.787752e-07 2.717654e-07 -1.175920e-06 3.751911e-07 -1.326662e-07 [9761] -9.304754e-09 -1.018081e-06 1.066010e-07 1.242914e-06 1.438329e-06 [9766] 1.222234e-06 2.040535e-07 1.148679e-07 -7.938792e-08 7.947087e-07 [9771] 7.805259e-07 -5.215225e-07 -3.186757e-08 -1.176507e-07 -2.221917e-07 [9776] -4.574140e-07 -3.061264e-07 4.891454e-07 -6.291757e-07 -3.058685e-07 [9781] 7.191050e-08 8.580204e-07 3.911963e-07 -8.275799e-07 -2.720384e-07 [9786] 3.442825e-07 -8.970659e-08 3.687482e-07 -1.133301e-06 8.640390e-08 [9791] 4.250934e-07 4.799947e-07 -2.410121e-07 -2.994150e-07 -8.844188e-09 [9796] 4.428034e-07 -3.546538e-07 8.156493e-07 -3.924232e-07 -1.586982e-07 [9801] 7.144047e-07 -1.079165e-06 -1.014813e-06 -3.541169e-07 -4.400813e-07 [9806] -2.396889e-07 -1.146403e-06 1.984897e-07 -3.797262e-07 6.715641e-07 [9811] 4.640033e-07 6.059705e-08 -6.481656e-07 2.186594e-07 -3.434986e-07 [9816] 1.680725e-06 -8.761516e-08 3.963899e-07 1.211805e-06 -8.662910e-07 [9821] -3.676820e-07 -1.390069e-06 8.094770e-08 -2.118744e-07 -1.343326e-07 [9826] -9.064847e-07 -1.192676e-06 1.304338e-07 8.703429e-07 1.066545e-07 [9831] -9.001781e-07 2.769152e-07 1.746296e-07 -1.310114e-07 -8.590065e-08 [9836] 5.649234e-08 -5.617021e-07 8.406998e-07 2.199549e-07 -1.279063e-06 [9841] -5.198288e-07 -2.018464e-09 -4.890563e-07 3.184822e-07 -1.102661e-06 [9846] 8.331386e-07 3.656302e-07 9.746175e-07 -1.057156e-06 1.766851e-06 [9851] 1.277142e-06 -5.099335e-07 6.825043e-08 1.361870e-07 -8.672859e-07 [9856] -1.397685e-07 6.183473e-07 -5.491580e-07 -3.724568e-07 9.600878e-07 [9861] 5.299247e-07 2.553641e-07 2.799403e-07 -7.141994e-07 3.567850e-07 [9866] 1.379483e-06 -4.530728e-07 2.929710e-07 -5.518832e-07 -2.700769e-08 [9871] -1.215063e-07 4.050462e-07 -8.201675e-07 -2.188797e-07 -2.547108e-07 [9876] -8.607829e-07 -1.587275e-06 -1.205522e-08 -3.528396e-07 3.987597e-07 [9881] 1.523900e-07 -7.693491e-08 -7.296701e-07 4.694481e-07 6.283162e-07 [9886] -2.318122e-07 -3.644306e-07 5.098342e-07 -4.061715e-07 3.142159e-07 [9891] -8.476238e-07 -2.388003e-06 1.992490e-07 -3.694246e-07 5.111584e-08 [9896] 1.301000e-06 5.581955e-07 -4.777398e-07 1.396860e-06 -2.378427e-07 [9901] 3.691749e-07 -3.376282e-07 1.033168e-07 -3.957414e-07 1.751200e-07 [9906] 1.228858e-07 1.328622e-06 3.099769e-07 5.413782e-07 -1.692004e-06 [9911] 8.015888e-07 1.852022e-06 6.286407e-07 -3.614293e-07 -1.884266e-07 [9916] 3.436984e-07 5.850429e-07 -6.074509e-08 -3.807627e-07 9.807412e-07 [9921] 6.099564e-07 -3.613909e-08 4.947192e-08 2.830586e-07 -3.984161e-07 [9926] -7.304934e-07 -2.640044e-07 -2.875404e-07 1.973860e-06 -6.405774e-08 [9931] -7.652591e-08 7.771451e-07 1.391284e-06 -9.941216e-08 -1.043984e-06 [9936] 9.527882e-08 -1.631481e-06 -1.444382e-07 3.183802e-07 7.888522e-07 [9941] -7.392518e-08 -4.530549e-08 7.716347e-08 -1.440130e-07 5.002441e-07 [9946] -5.051563e-07 1.064962e-06 -5.685266e-08 3.960668e-07 3.967064e-07 [9951] -5.441719e-07 -7.657020e-08 4.323011e-07 4.567032e-07 -1.123365e-06 [9956] -5.088769e-07 3.922843e-07 6.050250e-07 -1.787416e-07 -1.157692e-06 [9961] -1.064023e-06 4.601801e-07 -3.075786e-07 3.399695e-07 2.144024e-06 [9966] 5.849654e-07 -1.909989e-07 7.801243e-07 8.911398e-09 -1.293058e-06 [9971] 4.699937e-07 -2.514566e-07 4.383514e-07 2.404275e-07 3.026510e-07 [9976] 2.469921e-08 -7.573897e-08 -2.797773e-07 6.576030e-07 1.211425e-07 [9981] 1.455101e-06 7.296319e-07 6.217982e-07 1.005924e-06 -2.129891e-07 [9986] -8.495045e-07 -4.620804e-07 -4.266221e-08 4.198281e-07 8.116516e-07 [9991] -3.221965e-07 -4.187858e-07 -4.901468e-07 -2.438716e-07 5.504698e-07 [9996] 7.994415e-07 -1.227373e-06 1.036159e-08 -2.175764e-06 6.614187e-07 $mse [1] 1.213213e-06 > > > > > > > > > > proc.time() user system elapsed 0.79 0.04 0.84