Hi I am working on building an LP model of an electricity market. I had a model that ran in about 20 seconds. After changing some of the input data, I ran it again, and this time GLPK kept giving the message: 'spx_simplex: numerical instability (primal simplex, phase II)' and took much longer to run.
What does this message mean, and is there anything I can do about it to make my model run faster? I am using GLPK 4.8. A copy of some of the output from GLPK is attached. -- Andrew Walbran website: http://user.interface.org.nz/~andrew/ blog: http://qwandor.wordpress.com/
0: objval = 0.000000000e+00 infeas = 1.000000000e+00 (4760)
200: objval = 0.000000000e+00 infeas = 9.285714286e-01 (4635)
400: objval = 0.000000000e+00 infeas = 8.495238095e-01 (4518)
600: objval = 0.000000000e+00 infeas = 7.761904762e-01 (4395)
800: objval = 0.000000000e+00 infeas = 6.990476190e-01 (4276)
1000: objval = 0.000000000e+00 infeas = 6.276190476e-01 (4151)
1200: objval = 0.000000000e+00 infeas = 5.514285714e-01 (4031)
1400: objval = -1.067320000e+05 infeas = 4.885714286e-01 (3897)
1600: objval = -1.067320000e+05 infeas = 4.209523810e-01 (3768)
1800: objval = -1.067320000e+05 infeas = 3.438095238e-01 (3649)
2000: objval = -1.067320000e+05 infeas = 2.666666667e-01 (3530)
2200: objval = -1.125400000e+05 infeas = 1.971428571e-01 (3403)
2400: objval = -1.604280000e+05 infeas = 1.352380952e-01 (3268)
2600: objval = -2.218360000e+05 infeas = 6.380952381e-02 (3143)
2770: objval = -2.218360000e+05 infeas = 0.000000000e+00 (3040)
* 2770: objval = -2.218360000e+05 infeas = 0.000000000e+00 (3040)
* 2800: objval = -2.218360000e+05 infeas = 0.000000000e+00 (3016)
* 3000: objval = -2.218360000e+05 infeas = 0.000000000e+00 (2848)
* 3200: objval = -2.218360000e+05 infeas = 0.000000000e+00 (2840)
* 3400: objval = -2.218360000e+05 infeas = 0.000000000e+00 (2812)
* 3600: objval = -2.218360000e+05 infeas = 0.000000000e+00 (2614)
* 3800: objval = -2.218360000e+05 infeas = 0.000000000e+00 (2463)
* 3850: objval = -2.104749715e+05 infeas = 1.545625961e-05 (2431)
spx_simplex: numerical instability (primal simplex, phase II)
3850: objval = -2.104749715e+05 infeas = 1.000000000e+00 (2431)
3852: objval = -2.104899764e+05 infeas = 0.000000000e+00 (2431)
* 3852: objval = -2.104899764e+05 infeas = 0.000000000e+00 (2431)
* 4000: objval = -2.027960010e+05 infeas = 0.000000000e+00 (2325)
* 4200: objval = -2.027960010e+05 infeas = 0.000000000e+00 (2131)
* 4400: objval = -1.817560020e+05 infeas = 0.000000000e+00 (1974)
* 4600: objval = -1.385647655e+05 infeas = 1.167201132e-17 (1851)
* 4800: objval = -1.385647655e+05 infeas = 1.022719740e-16 (1673)
* 5000: objval = -1.182145462e+05 infeas = 8.312175542e-19 (1567)
* 5200: objval = -1.181936887e+05 infeas = 9.760128180e-19 (1494)
* 5400: objval = -6.024188358e+04 infeas = 9.760128180e-19 (1452)
* 5600: objval = -6.024188358e+04 infeas = 9.760128180e-19 (1393)
* 5800: objval = -6.024188358e+04 infeas = 9.760128180e-19 (1240)
* 6000: objval = -6.024188358e+04 infeas = 9.760128180e-19 (1189)
* 6200: objval = -5.974162677e+04 infeas = 2.713796019e-05 (1129)
* 6241: objval = -5.973727129e+04 infeas = 1.089093582e-06 (1129)
spx_simplex: numerical instability (primal simplex, phase II)
6241: objval = -5.973727129e+04 infeas = 1.000000000e+00 (1129)
6273: objval = -5.977393357e+04 infeas = 6.224386775e-13 (1128)
* 6273: objval = -5.977393357e+04 infeas = 6.778939689e-19 (1128)
* 6400: objval = -4.408167396e+03 infeas = 1.116595321e-17 (1127)
* 6448: objval = 1.467293667e+04 infeas = 1.234802645e-05 (1125)
spx_simplex: numerical instability (primal simplex, phase II)
6448: objval = 1.467293667e+04 infeas = 1.000000000e+00 (1125)
6450: objval = 1.465459360e+04 infeas = 1.012469054e-12 (1125)
* 6450: objval = 1.465459360e+04 infeas = 1.250199466e-17 (1125)
* 6600: objval = 2.712762785e+04 infeas = 1.023956800e-17 (1094)
* 6635: objval = 4.142800162e+04 infeas = 1.383921078e-05 (1092)
spx_simplex: numerical instability (primal simplex, phase II)
6635: objval = 4.142800162e+04 infeas = 1.000000000e+00 (1092)
6650: objval = 4.091423576e+04 infeas = 3.522889062e-12 (1092)
* 6650: objval = 4.091423576e+04 infeas = 4.875400428e-17 (1092)
* 6800: objval = 4.144166671e+04 infeas = 4.630515260e-17 (1089)
* 6854: objval = 4.178153969e+04 infeas = 6.125667318e-07 (1081)
spx_simplex: numerical instability (primal simplex, phase II)
6854: objval = 4.178153969e+04 infeas = 1.000000000e+00 (1081)
6855: objval = 4.178071147e+04 infeas = 6.282247448e-02 (1081)
* 6855: objval = 4.178071147e+04 infeas = 3.848295788e-08 (1081)
* 6923: objval = 5.775901320e+04 infeas = 1.757007070e-07 (1081)
spx_simplex: numerical instability (primal simplex, phase II)
6923: objval = 5.775901320e+04 infeas = 1.000000000e+00 (1081)
6925: objval = 5.775707787e+04 infeas = 2.928661479e-08 (1081)
* 6925: objval = 5.775707787e+04 infeas = 5.145678924e-15 (1081)
* 7000: objval = 6.565918031e+04 infeas = 1.593601934e-05 (1075)
* 7039: objval = 6.836728403e+04 infeas = 3.797430285e-05 (1069)
spx_simplex: numerical instability (primal simplex, phase II)
7039: objval = 6.836728403e+04 infeas = 1.000000000e+00 (1069)
7110: objval = 6.836064051e+04 infeas = 1.540055113e-11 (1069)
* 7110: objval = 6.836064051e+04 infeas = 5.848251927e-16 (1069)
* 7200: objval = 6.845804622e+04 infeas = 6.389592533e-16 (1069)
* 7400: objval = 8.355675131e+04 infeas = 1.749627951e-15 (1026)
* 7600: objval = 9.850668561e+04 infeas = 2.882826372e-14 (983)
* 7785: objval = 1.102691911e+05 infeas = 1.281523628e-06 (952)
spx_simplex: numerical instability (primal simplex, phase II)
7785: objval = 1.102691911e+05 infeas = 1.000000000e+00 (952)
7791: objval = 1.102285924e+05 infeas = 3.897958138e-10 (952)
* 7791: objval = 1.102285924e+05 infeas = 4.995325454e-16 (952)
* 7800: objval = 1.102289169e+05 infeas = 1.120809444e-09 (952)
* 7838: objval = 1.302813724e+05 infeas = 8.219175570e-06 (952)
spx_simplex: numerical instability (primal simplex, phase II)
7838: objval = 1.302813724e+05 infeas = 1.000000000e+00 (952)
7861: objval = 1.301260637e+05 infeas = 3.526325240e-11 (952)
* 7861: objval = 1.301260637e+05 infeas = 2.898348627e-16 (952)
* 7895: objval = 1.440006435e+05 infeas = 7.597997903e-07 (952)
spx_simplex: numerical instability (primal simplex, phase II)
7895: objval = 1.440006435e+05 infeas = 1.000000000e+00 (952)
7897: objval = 1.440003185e+05 infeas = 3.757066771e-10 (952)
* 7897: objval = 1.440003185e+05 infeas = 2.854618545e-16 (952)
* 7960: objval = 1.577276739e+05 infeas = 1.542108122e-06 (940)
spx_simplex: numerical instability (primal simplex, phase II)
7960: objval = 1.577276739e+05 infeas = 1.000000000e+00 (940)
7965: objval = 1.551342596e+05 infeas = 9.596750653e-11 (940)
* 7965: objval = 1.551342596e+05 infeas = 1.479922713e-16 (940)
* 8000: objval = 1.558562507e+05 infeas = 1.349003015e-16 (940)
* 8014: objval = 1.593749692e+05 infeas = 8.266211652e-07 (940)
spx_simplex: numerical instability (primal simplex, phase II)
8014: objval = 1.593749692e+05 infeas = 1.000000000e+00 (940)
8018: objval = 1.573225378e+05 infeas = 4.069235137e-10 (940)
* 8018: objval = 1.573225378e+05 infeas = 3.363715890e-16 (940)
* 8065: objval = 1.622893943e+05 infeas = 1.372972332e-04 (940)
spx_simplex: numerical instability (primal simplex, phase II)
8065: objval = 1.622893943e+05 infeas = 1.000000000e+00 (940)
8066: objval = 1.605101428e+05 infeas = 6.826752520e-05 (940)
* 8066: objval = 1.605101428e+05 infeas = 9.372942329e-09 (940)
* 8200: objval = 1.804962802e+05 infeas = 3.817291701e-16 (940)
* 8261: objval = 1.843583648e+05 infeas = 8.999891551e-07 (939)
spx_simplex: numerical instability (primal simplex, phase II)
8261: objval = 1.843583648e+05 infeas = 1.000000000e+00 (939)
8263: objval = 1.843581728e+05 infeas = 4.425420640e-10 (939)
* 8263: objval = 1.843581728e+05 infeas = 3.982830583e-16 (939)
* 8400: objval = 2.058503059e+05 infeas = 6.818637691e-16 (937)
* 8484: objval = 2.088968757e+05 infeas = 6.873728204e-07 (932)
spx_simplex: numerical instability (primal simplex, phase II)
8484: objval = 2.088968757e+05 infeas = 1.000000000e+00 (932)
8489: objval = 2.088514344e+05 infeas = 5.856782746e-10 (932)
* 8489: objval = 2.088514344e+05 infeas = 4.025793274e-16 (932)
* 8600: objval = 2.691227618e+05 infeas = 2.315862918e-16 (932)
* 8800: objval = 2.814827296e+05 infeas = 8.659814955e-16 (928)
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