* *************************** * SET UP THE INITIAL DATA * *************************** * Problem : * ********* * * A nonlinear formulation of a 0-1 combinatorial problem * which can be described as grouping and clustering. * This version of the problem consists in grouping 20 cans * into 5 groups and the objective is to obtain groups that * are as homogeneous as possible with respect to the characteristics * of the cans. * Note that the initial point is feasible. * This problem is the contribution of a LANCELOT user in order to fulfill * the package licence agreement. * Source : * D. Tuyttens, M. Pirlot, J. Teghem, E. Trauwaert and B. Liegeois, * "Homogeneous grouping of nuclear fuel cans through simulated * annealing and tabu search", * Annals of Operations Research 50 (1994) 575-607. * SIF input: D. Tuyttens (FPMs, Mons, Belgium) Dec 1994. * classification SQR2-MN-100-125 * Problem parameters : Number of cans, groups and characteristics * The cans and their characteristics * First characteristic * Second characteristic * Average characteristics * Variables of the problem * X(j,k) = 1 can j belongs to group k * = 0 otherwise * Objective function and Constraints * Linear constraints * Non-Linear constraints * The constants of the problem. * The bounds on the variables * The starting point * A feasible solution * This solution consists into setting the first 4 cans in * group 1 and the next 4 ones in the next group and so on. * The nonlinear elements functions * The group functions * Solution parameter lots ; lots := 5 ; parameter pots ; pots :=20 ; parameter car ; car := 2 ; parameter t1_1 ; t1_1 := 4.37 ; parameter t2_1 ; t2_1 := 4.56 ; parameter t3_1 ; t3_1 := 4.26 ; parameter t4_1 ; t4_1 := 4.56 ; parameter t5_1 ; t5_1 := 4.3 ; parameter t6_1 ; t6_1 := 4.46 ; parameter t7_1 ; t7_1 := 3.84 ; parameter t8_1 ; t8_1 := 4.57 ; parameter t9_1 ; t9_1 := 4.26 ; parameter t10_1 ; t10_1 := 4.37 ; parameter t11_1 ; t11_1 := 3.49 ; parameter t12_1 ; t12_1 := 4.43 ; parameter t13_1 ; t13_1 := 4.48 ; parameter t14_1 ; t14_1 := 4.01 ; parameter t15_1 ; t15_1 := 4.29 ; parameter t16_1 ; t16_1 := 4.42 ; parameter t17_1 ; t17_1 := 4.23 ; parameter t18_1 ; t18_1 := 4.42 ; parameter t19_1 ; t19_1 := 4.23 ; parameter t20_1 ; t20_1 := 3.49 ; parameter t1_2 ; t1_2 := 5.23 ; parameter t2_2 ; t2_2 := 5.74 ; parameter t3_2 ; t3_2 := 4.93 ; parameter t4_2 ; t4_2 := 5.74 ; parameter t5_2 ; t5_2 := 5.19 ; parameter t6_2 ; t6_2 := 5.46 ; parameter t7_2 ; t7_2 := 4.65 ; parameter t8_2 ; t8_2 := 5.27 ; parameter t9_2 ; t9_2 := 5.57 ; parameter t10_2 ; t10_2 := 5.12 ; parameter t11_2 ; t11_2 := 5.73 ; parameter t12_2 ; t12_2 := 5.45 ; parameter t13_2 ; t13_2 := 5.42 ; parameter t14_2 ; t14_2 := 4.05 ; parameter t15_2 ; t15_2 := 4.26 ; parameter t16_2 ; t16_2 := 4.58 ; parameter t17_2 ; t17_2 := 3.94 ; parameter t18_2 ; t18_2 := 4.18 ; parameter t19_2 ; t19_2 := 4.18 ; parameter t20_2 ; t20_2 := 5.89 ; parameter xm1 ; xm1 :=17.1 ; parameter xm2 ; xm2 :=20.1 ; parameter potlot ; potlot := 4.0 ; Positive Variable x1_1 , x1_2 , x1_3 , x1_4 , x1_5 , x2_1 , x2_2 , x2_3 , x2_4 , x2_5 , x3_1 , x3_2 , x3_3 , x3_4 , x3_5 , x4_1 , x4_2 , x4_3 , x4_4 , x4_5 , x5_1 , x5_2 , x5_3 , x5_4 , x5_5 , x6_1 , x6_2 , x6_3 , x6_4 , x6_5 , x7_1 , x7_2 , x7_3 , x7_4 , x7_5 , x8_1 , x8_2 , x8_3 , x8_4 , x8_5 , x9_1 , x9_2 , x9_3 , x9_4 , x9_5 , x10_1 , x10_2 , x10_3 , x10_4 , x10_5 , x11_1 , x11_2 , x11_3 , x11_4 , x11_5 , x12_1 , x12_2 , x12_3 , x12_4 , x12_5 , x13_1 , x13_2 , x13_3 , x13_4 , x13_5 , x14_1 , x14_2 , x14_3 , x14_4 , x14_5 , x15_1 , x15_2 , x15_3 , x15_4 , x15_5 , x16_1 , x16_2 , x16_3 , x16_4 , x16_5 , x17_1 , x17_2 , x17_3 , x17_4 , x17_5 , x18_1 , x18_2 , x18_3 , x18_4 , x18_5 , x19_1 , x19_2 , x19_3 , x19_4 , x19_5 , x20_1 , x20_2 , x20_3 , x20_4 , x20_5 ; Variable obj ; Equation cl11 , cl12 , cl13 , cl14 , cl15 , cl21 , cl22 , cl23 , cl24 , cl25 , cl26 , cl27 , cl28 , cl29 , cl210 , cl211 , cl212 , cl213 , cl214 , cl215 , cl216 , cl217 , cl218 , cl219 , cl220 , cnl1_1 , cnl1_2 , cnl1_3 , cnl1_4 , cnl1_5 , cnl2_1 , cnl2_2 , cnl2_3 , cnl2_4 , cnl2_5 , cnl3_1 , cnl3_2 , cnl3_3 , cnl3_4 , cnl3_5 , cnl4_1 , cnl4_2 , cnl4_3 , cnl4_4 , cnl4_5 , cnl5_1 , cnl5_2 , cnl5_3 , cnl5_4 , cnl5_5 , cnl6_1 , cnl6_2 , cnl6_3 , cnl6_4 , cnl6_5 , cnl7_1 , cnl7_2 , cnl7_3 , cnl7_4 , cnl7_5 , cnl8_1 , cnl8_2 , cnl8_3 , cnl8_4 , cnl8_5 , cnl9_1 , cnl9_2 , cnl9_3 , cnl9_4 , cnl9_5 , cnl10_1 , cnl10_2 , cnl10_3 , cnl10_4 , cnl10_5 , cnl11_1 , cnl11_2 , cnl11_3 , cnl11_4 , cnl11_5 , cnl12_1 , cnl12_2 , cnl12_3 , cnl12_4 , cnl12_5 , cnl13_1 , cnl13_2 , cnl13_3 , cnl13_4 , cnl13_5 , cnl14_1 , cnl14_2 , cnl14_3 , cnl14_4 , cnl14_5 , cnl15_1 , cnl15_2 , cnl15_3 , cnl15_4 , cnl15_5 , cnl16_1 , cnl16_2 , cnl16_3 , cnl16_4 , cnl16_5 , cnl17_1 , cnl17_2 , cnl17_3 , cnl17_4 , cnl17_5 , cnl18_1 , cnl18_2 , cnl18_3 , cnl18_4 , cnl18_5 , cnl19_1 , cnl19_2 , cnl19_3 , cnl19_4 , cnl19_5 , cnl20_1 , cnl20_2 , cnl20_3 , cnl20_4 , cnl20_5 , Def_obj ; cl11.. x1_1 + x2_1 + x3_1 + x4_1 + x5_1 + x6_1 + x7_1 + x8_1 + x9_1 + x10_1 + x11_1 + x12_1 + x13_1 + x14_1 + x15_1 + x16_1 + x17_1 + x18_1 + x19_1 + x20_1 - 4.0 =e= 0; cl12.. x1_2 + x2_2 + x3_2 + x4_2 + x5_2 + x6_2 + x7_2 + x8_2 + x9_2 + x10_2 + x11_2 + x12_2 + x13_2 + x14_2 + x15_2 + x16_2 + x17_2 + x18_2 + x19_2 + x20_2 - 4.0 =e= 0; cl13.. x1_3 + x2_3 + x3_3 + x4_3 + x5_3 + x6_3 + x7_3 + x8_3 + x9_3 + x10_3 + x11_3 + x12_3 + x13_3 + x14_3 + x15_3 + x16_3 + x17_3 + x18_3 + x19_3 + x20_3 - 4.0 =e= 0; cl14.. x1_4 + x2_4 + x3_4 + x4_4 + x5_4 + x6_4 + x7_4 + x8_4 + x9_4 + x10_4 + x11_4 + x12_4 + x13_4 + x14_4 + x15_4 + x16_4 + x17_4 + x18_4 + x19_4 + x20_4 - 4.0 =e= 0; cl15.. x1_5 + x2_5 + x3_5 + x4_5 + x5_5 + x6_5 + x7_5 + x8_5 + x9_5 + x10_5 + x11_5 + x12_5 + x13_5 + x14_5 + x15_5 + x16_5 + x17_5 + x18_5 + x19_5 + x20_5 - 4.0 =e= 0; cl21.. x1_1 + x1_2 + x1_3 + x1_4 + x1_5 - 1.0 =e= 0; cl22.. x2_1 + x2_2 + x2_3 + x2_4 + x2_5 - 1.0 =e= 0; cl23.. x3_1 + x3_2 + x3_3 + x3_4 + x3_5 - 1.0 =e= 0; cl24.. x4_1 + x4_2 + x4_3 + x4_4 + x4_5 - 1.0 =e= 0; cl25.. x5_1 + x5_2 + x5_3 + x5_4 + x5_5 - 1.0 =e= 0; cl26.. x6_1 + x6_2 + x6_3 + x6_4 + x6_5 - 1.0 =e= 0; cl27.. x7_1 + x7_2 + x7_3 + x7_4 + x7_5 - 1.0 =e= 0; cl28.. x8_1 + x8_2 + x8_3 + x8_4 + x8_5 - 1.0 =e= 0; cl29.. x9_1 + x9_2 + x9_3 + x9_4 + x9_5 - 1.0 =e= 0; cl210.. x10_1 + x10_2 + x10_3 + x10_4 + x10_5 - 1.0 =e= 0; cl211.. x11_1 + x11_2 + x11_3 + x11_4 + x11_5 - 1.0 =e= 0; cl212.. x12_1 + x12_2 + x12_3 + x12_4 + x12_5 - 1.0 =e= 0; cl213.. x13_1 + x13_2 + x13_3 + x13_4 + x13_5 - 1.0 =e= 0; cl214.. x14_1 + x14_2 + x14_3 + x14_4 + x14_5 - 1.0 =e= 0; cl215.. x15_1 + x15_2 + x15_3 + x15_4 + x15_5 - 1.0 =e= 0; cl216.. x16_1 + x16_2 + x16_3 + x16_4 + x16_5 - 1.0 =e= 0; cl217.. x17_1 + x17_2 + x17_3 + x17_4 + x17_5 - 1.0 =e= 0; cl218.. x18_1 + x18_2 + x18_3 + x18_4 + x18_5 - 1.0 =e= 0; cl219.. x19_1 + x19_2 + x19_3 + x19_4 + x19_5 - 1.0 =e= 0; cl220.. x20_1 + x20_2 + x20_3 + x20_4 + x20_5 - 1.0 =e= 0; cnl1_1.. x1_1 * ( x1_1 - 1.0 ) =e= 0; cnl1_2.. x1_2 * ( x1_2 - 1.0 ) =e= 0; cnl1_3.. x1_3 * ( x1_3 - 1.0 ) =e= 0; cnl1_4.. x1_4 * ( x1_4 - 1.0 ) =e= 0; cnl1_5.. x1_5 * ( x1_5 - 1.0 ) =e= 0; cnl2_1.. x2_1 * ( x2_1 - 1.0 ) =e= 0; cnl2_2.. x2_2 * ( x2_2 - 1.0 ) =e= 0; cnl2_3.. x2_3 * ( x2_3 - 1.0 ) =e= 0; cnl2_4.. x2_4 * ( x2_4 - 1.0 ) =e= 0; cnl2_5.. x2_5 * ( x2_5 - 1.0 ) =e= 0; cnl3_1.. x3_1 * ( x3_1 - 1.0 ) =e= 0; cnl3_2.. x3_2 * ( x3_2 - 1.0 ) =e= 0; cnl3_3.. x3_3 * ( x3_3 - 1.0 ) =e= 0; cnl3_4.. x3_4 * ( x3_4 - 1.0 ) =e= 0; cnl3_5.. x3_5 * ( x3_5 - 1.0 ) =e= 0; cnl4_1.. x4_1 * ( x4_1 - 1.0 ) =e= 0; cnl4_2.. x4_2 * ( x4_2 - 1.0 ) =e= 0; cnl4_3.. x4_3 * ( x4_3 - 1.0 ) =e= 0; cnl4_4.. x4_4 * ( x4_4 - 1.0 ) =e= 0; cnl4_5.. x4_5 * ( x4_5 - 1.0 ) =e= 0; cnl5_1.. x5_1 * ( x5_1 - 1.0 ) =e= 0; cnl5_2.. x5_2 * ( x5_2 - 1.0 ) =e= 0; cnl5_3.. x5_3 * ( x5_3 - 1.0 ) =e= 0; cnl5_4.. x5_4 * ( x5_4 - 1.0 ) =e= 0; cnl5_5.. x5_5 * ( x5_5 - 1.0 ) =e= 0; cnl6_1.. x6_1 * ( x6_1 - 1.0 ) =e= 0; cnl6_2.. x6_2 * ( x6_2 - 1.0 ) =e= 0; cnl6_3.. x6_3 * ( x6_3 - 1.0 ) =e= 0; cnl6_4.. x6_4 * ( x6_4 - 1.0 ) =e= 0; cnl6_5.. x6_5 * ( x6_5 - 1.0 ) =e= 0; cnl7_1.. x7_1 * ( x7_1 - 1.0 ) =e= 0; cnl7_2.. x7_2 * ( x7_2 - 1.0 ) =e= 0; cnl7_3.. x7_3 * ( x7_3 - 1.0 ) =e= 0; cnl7_4.. x7_4 * ( x7_4 - 1.0 ) =e= 0; cnl7_5.. x7_5 * ( x7_5 - 1.0 ) =e= 0; cnl8_1.. x8_1 * ( x8_1 - 1.0 ) =e= 0; cnl8_2.. x8_2 * ( x8_2 - 1.0 ) =e= 0; cnl8_3.. x8_3 * ( x8_3 - 1.0 ) =e= 0; cnl8_4.. x8_4 * ( x8_4 - 1.0 ) =e= 0; cnl8_5.. x8_5 * ( x8_5 - 1.0 ) =e= 0; cnl9_1.. x9_1 * ( x9_1 - 1.0 ) =e= 0; cnl9_2.. x9_2 * ( x9_2 - 1.0 ) =e= 0; cnl9_3.. x9_3 * ( x9_3 - 1.0 ) =e= 0; cnl9_4.. x9_4 * ( x9_4 - 1.0 ) =e= 0; cnl9_5.. x9_5 * ( x9_5 - 1.0 ) =e= 0; cnl10_1.. x10_1 * (x10_1 - 1.0 ) =e= 0; cnl10_2.. x10_2 * (x10_2 - 1.0 ) =e= 0; cnl10_3.. x10_3 * (x10_3 - 1.0 ) =e= 0; cnl10_4.. x10_4 * (x10_4 - 1.0 ) =e= 0; cnl10_5.. x10_5 * (x10_5 - 1.0 ) =e= 0; cnl11_1.. x11_1 * (x11_1 - 1.0 ) =e= 0; cnl11_2.. x11_2 * (x11_2 - 1.0 ) =e= 0; cnl11_3.. x11_3 * (x11_3 - 1.0 ) =e= 0; cnl11_4.. x11_4 * (x11_4 - 1.0 ) =e= 0; cnl11_5.. x11_5 * (x11_5 - 1.0 ) =e= 0; cnl12_1.. x12_1 * (x12_1 - 1.0 ) =e= 0; cnl12_2.. x12_2 * (x12_2 - 1.0 ) =e= 0; cnl12_3.. x12_3 * (x12_3 - 1.0 ) =e= 0; cnl12_4.. x12_4 * (x12_4 - 1.0 ) =e= 0; cnl12_5.. x12_5 * (x12_5 - 1.0 ) =e= 0; cnl13_1.. x13_1 * (x13_1 - 1.0 ) =e= 0; cnl13_2.. x13_2 * (x13_2 - 1.0 ) =e= 0; cnl13_3.. x13_3 * (x13_3 - 1.0 ) =e= 0; cnl13_4.. x13_4 * (x13_4 - 1.0 ) =e= 0; cnl13_5.. x13_5 * (x13_5 - 1.0 ) =e= 0; cnl14_1.. x14_1 * (x14_1 - 1.0 ) =e= 0; cnl14_2.. x14_2 * (x14_2 - 1.0 ) =e= 0; cnl14_3.. x14_3 * (x14_3 - 1.0 ) =e= 0; cnl14_4.. x14_4 * (x14_4 - 1.0 ) =e= 0; cnl14_5.. x14_5 * (x14_5 - 1.0 ) =e= 0; cnl15_1.. x15_1 * (x15_1 - 1.0 ) =e= 0; cnl15_2.. x15_2 * (x15_2 - 1.0 ) =e= 0; cnl15_3.. x15_3 * (x15_3 - 1.0 ) =e= 0; cnl15_4.. x15_4 * (x15_4 - 1.0 ) =e= 0; cnl15_5.. x15_5 * (x15_5 - 1.0 ) =e= 0; cnl16_1.. x16_1 * (x16_1 - 1.0 ) =e= 0; cnl16_2.. x16_2 * (x16_2 - 1.0 ) =e= 0; cnl16_3.. x16_3 * (x16_3 - 1.0 ) =e= 0; cnl16_4.. x16_4 * (x16_4 - 1.0 ) =e= 0; cnl16_5.. x16_5 * (x16_5 - 1.0 ) =e= 0; cnl17_1.. x17_1 * (x17_1 - 1.0 ) =e= 0; cnl17_2.. x17_2 * (x17_2 - 1.0 ) =e= 0; cnl17_3.. x17_3 * (x17_3 - 1.0 ) =e= 0; cnl17_4.. x17_4 * (x17_4 - 1.0 ) =e= 0; cnl17_5.. x17_5 * (x17_5 - 1.0 ) =e= 0; cnl18_1.. x18_1 * (x18_1 - 1.0 ) =e= 0; cnl18_2.. x18_2 * (x18_2 - 1.0 ) =e= 0; cnl18_3.. x18_3 * (x18_3 - 1.0 ) =e= 0; cnl18_4.. x18_4 * (x18_4 - 1.0 ) =e= 0; cnl18_5.. x18_5 * (x18_5 - 1.0 ) =e= 0; cnl19_1.. x19_1 * (x19_1 - 1.0 ) =e= 0; cnl19_2.. x19_2 * (x19_2 - 1.0 ) =e= 0; cnl19_3.. x19_3 * (x19_3 - 1.0 ) =e= 0; cnl19_4.. x19_4 * (x19_4 - 1.0 ) =e= 0; cnl19_5.. x19_5 * (x19_5 - 1.0 ) =e= 0; cnl20_1.. x20_1 * (x20_1 - 1.0 ) =e= 0; cnl20_2.. x20_2 * (x20_2 - 1.0 ) =e= 0; cnl20_3.. x20_3 * (x20_3 - 1.0 ) =e= 0; cnl20_4.. x20_4 * (x20_4 - 1.0 ) =e= 0; cnl20_5.. x20_5 * (x20_5 - 1.0 ) =e= 0; Def_obj.. obj=e= (4.37*x1_1 + 4.56*x2_1 + 4.26*x3_1 + 4.56* x4_1 + 4.3* x5_1 + 4.46* x6_1 + 3.84*x7_1 + 4.57*x8_1 + 4.26*x9_1 + 4.37*x10_1 + 3.49*x11_1 + 4.43*x12_1 + 4.48*x13_1 + 4.01*x14_1 + 4.29*x15_1 + 4.42*x16_1 + 4.23*x17_1 + 4.42*x18_1 + 4.23*x19_1 + 3.49*x20_1 - 17.1)* (4.37*x1_1 + 4.56*x2_1 + 4.26*x3_1 + 4.56*x4_1 + 4.3*x5_1 + 4.46*x6_1 + 3.84*x7_1 + 4.57*x8_1 + 4.26*x9_1 + 4.37*x10_1 + 3.49*x11_1 + 4.43*x12_1 + 4.48*x13_1 + 4.01*x14_1 + 4.29*x15_1 + 4.42*x16_1 + 4.23*x17_1 + 4.42*x18_1 + 4.23*x19_1 + 3.49*x20_1 - 17.1) + (5.23*x1_1 + 5.74*x2_1 + 4.93*x3_1 + 5.74*x4_1 + 5.19*x5_1 + 5.46*x6_1 + 4.65*x7_1 + 5.27*x8_1 + 5.57*x9_1 + 5.12*x10_1 + 5.73*x11_1 + 5.45*x12_1 + 5.42*x13_1 + 4.05*x14_1 + 4.26*x15_1 + 4.58*x16_1 + 3.94*x17_1 + 4.18*x18_1 + 4.18*x19_1 + 5.89*x20_1 - 20.1)* (5.23*x1_1 + 5.74*x2_1 + 4.93*x3_1 + 5.74*x4_1 + 5.19*x5_1 + 5.46*x6_1 + 4.65*x7_1 + 5.27*x8_1 + 5.57*x9_1 + 5.12*x10_1 + 5.73*x11_1 + 5.45*x12_1 + 5.42*x13_1 + 4.05*x14_1 + 4.26*x15_1 + 4.58*x16_1 + 3.94*x17_1 + 4.18*x18_1 + 4.18*x19_1 + 5.89*x20_1 - 20.1) + (4.37*x1_2 + 4.56*x2_2 + 4.26*x3_2 + 4.56*x4_2 + 4.3*x5_2 + 4.46*x6_2 + 3.84*x7_2 + 4.57*x8_2 + 4.26*x9_2 + 4.37*x10_2 + 3.49*x11_2 + 4.43*x12_2 + 4.48*x13_2 + 4.01*x14_2 + 4.29*x15_2 + 4.42*x16_2 + 4.23*x17_2 + 4.42*x18_2 + 4.23*x19_2 + 3.49*x20_2 - 17.1)* (4.37*x1_2 + 4.56*x2_2 + 4.26*x3_2 + 4.56*x4_2 + 4.3*x5_2 + 4.46*x6_2 + 3.84*x7_2 + 4.57*x8_2 + 4.26*x9_2 + 4.37*x10_2 + 3.49*x11_2 + 4.43*x12_2 + 4.48*x13_2 + 4.01*x14_2 + 4.29*x15_2 + 4.42*x16_2 + 4.23*x17_2 + 4.42*x18_2 + 4.23*x19_2 + 3.49*x20_2 - 17.1) + (5.23*x1_2 + 5.74*x2_2 + 4.93*x3_2 + 5.74*x4_2 + 5.19*x5_2 + 5.46*x6_2 + 4.65*x7_2 + 5.27*x8_2 + 5.57*x9_2 + 5.12*x10_2 + 5.73*x11_2 + 5.45*x12_2 + 5.42*x13_2 + 4.05*x14_2 + 4.26*x15_2 + 4.58*x16_2 + 3.94*x17_2 + 4.18*x18_2 + 4.18*x19_2 + 5.89*x20_2 - 20.1)* (5.23*x1_2 + 5.74*x2_2 + 4.93*x3_2 + 5.74*x4_2 + 5.19*x5_2 + 5.46*x6_2 + 4.65*x7_2 + 5.27*x8_2 + 5.57*x9_2 + 5.12*x10_2 + 5.73*x11_2 + 5.45*x12_2 + 5.42*x13_2 + 4.05*x14_2 + 4.26*x15_2 + 4.58*x16_2 + 3.94*x17_2 + 4.18*x18_2 + 4.18*x19_2 + 5.89*x20_2 - 20.1) + (4.37*x1_3 + 4.56*x2_3 + 4.26*x3_3 + 4.56*x4_3 + 4.3*x5_3 + 4.46*x6_3 + 3.84*x7_3 + 4.57*x8_3 + 4.26*x9_3 + 4.37*x10_3 + 3.49*x11_3 + 4.43*x12_3 + 4.48*x13_3 + 4.01*x14_3 + 4.29*x15_3 + 4.42*x16_3 + 4.23*x17_3 + 4.42*x18_3 + 4.23*x19_3 + 3.49*x20_3 - 17.1)* (4.37*x1_3 + 4.56*x2_3 + 4.26*x3_3 + 4.56*x4_3 + 4.3*x5_3 + 4.46*x6_3 + 3.84*x7_3 + 4.57*x8_3 + 4.26*x9_3 + 4.37*x10_3 + 3.49*x11_3 + 4.43*x12_3 + 4.48*x13_3 + 4.01*x14_3 + 4.29*x15_3 + 4.42*x16_3 + 4.23*x17_3 + 4.42*x18_3 + 4.23*x19_3 + 3.49*x20_3 - 17.1) + (5.23*x1_3 + 5.74*x2_3 + 4.93*x3_3 + 5.74*x4_3 + 5.19*x5_3 + 5.46*x6_3 + 4.65*x7_3 + 5.27*x8_3 + 5.57*x9_3 + 5.12*x10_3 + 5.73*x11_3 + 5.45*x12_3 + 5.42*x13_3 + 4.05*x14_3 + 4.26*x15_3 + 4.58*x16_3 + 3.94*x17_3 + 4.18*x18_3 + 4.18*x19_3 + 5.89*x20_3 - 20.1)* (5.23*x1_3 + 5.74*x2_3 + 4.93*x3_3 + 5.74*x4_3 + 5.19*x5_3 + 5.46*x6_3 + 4.65*x7_3 + 5.27*x8_3 + 5.57*x9_3 + 5.12*x10_3 + 5.73*x11_3 + 5.45*x12_3 + 5.42*x13_3 + 4.05*x14_3 + 4.26*x15_3 + 4.58*x16_3 + 3.94*x17_3 + 4.18*x18_3 + 4.18*x19_3 + 5.89*x20_3 - 20.1) + (4.37*x1_4 + 4.56*x2_4 + 4.26*x3_4 + 4.56*x4_4 + 4.3*x5_4 + 4.46*x6_4 + 3.84*x7_4 + 4.57*x8_4 + 4.26*x9_4 + 4.37*x10_4 + 3.49*x11_4 + 4.43*x12_4 + 4.48*x13_4 + 4.01*x14_4 + 4.29*x15_4 + 4.42*x16_4 + 4.23*x17_4 + 4.42*x18_4 + 4.23*x19_4 + 3.49*x20_4 - 17.1)* (4.37*x1_4 + 4.56*x2_4 + 4.26*x3_4 + 4.56*x4_4 + 4.3*x5_4 + 4.46*x6_4 + 3.84*x7_4 + 4.57*x8_4 + 4.26*x9_4 + 4.37*x10_4 + 3.49*x11_4 + 4.43*x12_4 + 4.48*x13_4 + 4.01*x14_4 + 4.29*x15_4 + 4.42*x16_4 + 4.23*x17_4 + 4.42*x18_4 + 4.23*x19_4 + 3.49*x20_4 - 17.1) + (5.23*x1_4 + 5.74*x2_4 + 4.93*x3_4 + 5.74*x4_4 + 5.19*x5_4 + 5.46*x6_4 + 4.65*x7_4 + 5.27*x8_4 + 5.57*x9_4 + 5.12*x10_4 + 5.73*x11_4 + 5.45*x12_4 + 5.42*x13_4 + 4.05*x14_4 + 4.26*x15_4 + 4.58*x16_4 + 3.94*x17_4 + 4.18*x18_4 + 4.18*x19_4 + 5.89*x20_4 - 20.1)* (5.23*x1_4 + 5.74*x2_4 + 4.93*x3_4 + 5.74*x4_4 + 5.19*x5_4 + 5.46*x6_4 + 4.65*x7_4 + 5.27*x8_4 + 5.57*x9_4 + 5.12*x10_4 + 5.73*x11_4 + 5.45*x12_4 + 5.42*x13_4 + 4.05*x14_4 + 4.26*x15_4 + 4.58*x16_4 + 3.94*x17_4 + 4.18*x18_4 + 4.18*x19_4 + 5.89*x20_4 - 20.1) + (4.37*x1_5 + 4.56*x2_5 + 4.26*x3_5 + 4.56*x4_5 + 4.3*x5_5 + 4.46*x6_5 + 3.84*x7_5 + 4.57*x8_5 + 4.26*x9_5 + 4.37*x10_5 + 3.49*x11_5 + 4.43*x12_5 + 4.48*x13_5 + 4.01*x14_5 + 4.29*x15_5 + 4.42*x16_5 + 4.23*x17_5 + 4.42*x18_5 + 4.23*x19_5 + 3.49*x20_5 - 17.1)* (4.37*x1_5 + 4.56*x2_5 + 4.26*x3_5 + 4.56*x4_5 + 4.3*x5_5 + 4.46*x6_5 + 3.84*x7_5 + 4.57*x8_5 + 4.26*x9_5 + 4.37*x10_5 + 3.49*x11_5 + 4.43*x12_5 + 4.48*x13_5 + 4.01*x14_5 + 4.29*x15_5 + 4.42*x16_5 + 4.23*x17_5 + 4.42*x18_5 + 4.23*x19_5 + 3.49*x20_5 - 17.1) + (5.23*x1_5 + 5.74*x2_5 + 4.93*x3_5 + 5.74*x4_5 + 5.19*x5_5 + 5.46*x6_5 + 4.65*x7_5 + 5.27*x8_5 + 5.57*x9_5 + 5.12*x10_5 + 5.73*x11_5 + 5.45*x12_5 + 5.42*x13_5 + 4.05*x14_5 + 4.26*x15_5 + 4.58*x16_5 + 3.94*x17_5 + 4.18*x18_5 + 4.18*x19_5 + 5.89*x20_5 - 20.1)* (5.23*x1_5 + 5.74*x2_5 + 4.93*x3_5 + 5.74*x4_5 + 5.19*x5_5 + 5.46*x6_5 + 4.65*x7_5 + 5.27*x8_5 + 5.57*x9_5 + 5.12*x10_5 + 5.73*x11_5 + 5.45*x12_5 + 5.42*x13_5 + 4.05*x14_5 + 4.26*x15_5 + 4.58*x16_5 + 3.94*x17_5 + 4.18*x18_5 + 4.18*x19_5 + 5.89*x20_5 - 20.1); x1_1.up = 1.0; x1_2.up = 1.0; x1_3.up = 1.0; x1_4.up = 1.0; x1_5.up = 1.0; x2_1.up = 1.0; x2_2.up = 1.0; x2_3.up = 1.0; x2_4.up = 1.0; x2_5.up = 1.0; x3_1.up = 1.0; x3_2.up = 1.0; x3_3.up = 1.0; x3_4.up = 1.0; x3_5.up = 1.0; x4_1.up = 1.0; x4_2.up = 1.0; x4_3.up = 1.0; x4_4.up = 1.0; x4_5.up = 1.0; x5_1.up = 1.0; x5_2.up = 1.0; x5_3.up = 1.0; x5_4.up = 1.0; x5_5.up = 1.0; x6_1.up = 1.0; x6_2.up = 1.0; x6_3.up = 1.0; x6_4.up = 1.0; x6_5.up = 1.0; x7_1.up = 1.0; x7_2.up = 1.0; x7_3.up = 1.0; x7_4.up = 1.0; x7_5.up = 1.0; x8_1.up = 1.0; x8_2.up = 1.0; x8_3.up = 1.0; x8_4.up = 1.0; x8_5.up = 1.0; x9_1.up = 1.0; x9_2.up = 1.0; x9_3.up = 1.0; x9_4.up = 1.0; x9_5.up = 1.0; x10_1.up = 1.0; x10_2.up = 1.0; x10_3.up = 1.0; x10_4.up = 1.0; x10_5.up = 1.0; x11_1.up = 1.0; x11_2.up = 1.0; x11_3.up = 1.0; x11_4.up = 1.0; x11_5.up = 1.0; x12_1.up = 1.0; x12_2.up = 1.0; x12_3.up = 1.0; x12_4.up = 1.0; x12_5.up = 1.0; x13_1.up = 1.0; x13_2.up = 1.0; x13_3.up = 1.0; x13_4.up = 1.0; x13_5.up = 1.0; x14_1.up = 1.0; x14_2.up = 1.0; x14_3.up = 1.0; x14_4.up = 1.0; x14_5.up = 1.0; x15_1.up = 1.0; x15_2.up = 1.0; x15_3.up = 1.0; x15_4.up = 1.0; x15_5.up = 1.0; x16_1.up = 1.0; x16_2.up = 1.0; x16_3.up = 1.0; x16_4.up = 1.0; x16_5.up = 1.0; x17_1.up = 1.0; x17_2.up = 1.0; x17_3.up = 1.0; x17_4.up = 1.0; x17_5.up = 1.0; x18_1.up = 1.0; x18_2.up = 1.0; x18_3.up = 1.0; x18_4.up = 1.0; x18_5.up = 1.0; x19_1.up = 1.0; x19_2.up = 1.0; x19_3.up = 1.0; x19_4.up = 1.0; x19_5.up = 1.0; x20_1.up = 1.0; x20_2.up = 1.0; x20_3.up = 1.0; x20_4.up = 1.0; x20_5.up = 1.0; x1_1.l = 1.0 ; x2_1.l = 1.0 ; x3_1.l = 1.0 ; x4_1.l = 1.0 ; x5_2.l = 1.0; x6_2.l = 1.0 ; x7_2.l = 1.0 ; x8_2.l = 1.0 ; x9_3.l = 1.0 ; x10_3.l = 1.0; x11_3.l = 1.0 ; x12_3.l = 1.0 ; x13_4.l = 1.0 ; x14_4.l = 1.0 ; x15_4.l = 1.0; x16_4.l = 1.0 ; x17_5.l = 1.0 ; x18_5.l = 1.0 ; x19_5.l = 1.0 ; x20_5.l = 1.0; model grouping /all/; solve grouping using nlp minimize obj ; display x1_1.l;display x1_2.l;display x1_3.l;display x1_4.l;display x1_5.l; display x2_1.l;display x2_2.l;display x2_3.l;display x2_4.l;display x2_5.l; display x3_1.l;display x3_2.l;display x3_3.l;display x3_4.l;display x3_5.l; display x4_1.l;display x4_2.l;display x4_3.l;display x4_4.l;display x4_5.l; display x5_1.l;display x5_2.l;display x5_3.l;display x5_4.l;display x5_5.l; display x6_1.l;display x6_2.l;display x6_3.l;display x6_4.l;display x6_5.l; display x7_1.l;display x7_2.l;display x7_3.l;display x7_4.l;display x7_5.l; display x8_1.l;display x8_2.l;display x8_3.l;display x8_4.l;display x8_5.l; display x9_1.l;display x9_2.l;display x9_3.l;display x9_4.l;display x9_5.l; display x10_1.l;display x10_2.l;display x10_3.l;display x10_4.l;display x10_5.l; display x11_1.l;display x11_2.l;display x11_3.l;display x11_4.l;display x11_5.l; display x12_1.l;display x12_2.l;display x12_3.l;display x12_4.l;display x12_5.l; display x13_1.l;display x13_2.l;display x13_3.l;display x13_4.l;display x13_5.l; display x14_1.l;display x14_2.l;display x14_3.l;display x14_4.l;display x14_5.l; display x15_1.l;display x15_2.l;display x15_3.l;display x15_4.l;display x15_5.l; display x16_1.l;display x16_2.l;display x16_3.l;display x16_4.l;display x16_5.l; display x17_1.l;display x17_2.l;display x17_3.l;display x17_4.l;display x17_5.l; display x18_1.l;display x18_2.l;display x18_3.l;display x18_4.l;display x18_5.l; display x19_1.l;display x19_2.l;display x19_3.l;display x19_4.l;display x19_5.l; display x20_1.l;display x20_2.l;display x20_3.l;display x20_4.l;display x20_5.l; display obj.l;