Currently they are:
LPSolve (LGPL) - requires lpsolve + Python bindings installations (all mentioned is available in here)
cvxopt_lp (GPL) - requires CVXOPT
cvxopt_glpk(GPL2) - requires CVXOPT & glpk
cvxopt_mosek(non-free) - requires CVXOPT & mosek
However, I have some problems with mosek (even with trial license), it don't want to run in my AMD 64 + Linux, yielding 'inner mosek error'. Maybe, you will be more lucky:)
So, that report showed LPSolve to be much more better than other solvers.
Now I found the matter (and it's not my bug).
So, this is due to handling of lb-ub bounds: they are absent in CVXOPT (hence in glpk, mosek), and I used a routine that translated lb-ub bounds to Ax
BTW, I think that LP solvers by themself should handle lines with single non-zero, but these ones involved don't. So, in future (but I guess not nearest) I intend to add the handling to the OpenOpt Kernel.
However, it has disadvantage: no correct duals will be returned, or it will require restart LP solver with unchanged LP problem from x_opt once again.
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See whole LP bench results in my comment.
***********************************************
ReplyDeletedensity = 1
-----------------------------------------------
func trig : nVars = 100 nConstraints = 200 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 0.17 0.09
glpk 0.11 0.1
lpsolve 0.13 0.12
-----------------------------------------------
func trig : nVars = 100 nConstraints = 1100 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 0.83 0.71
glpk 1.69 1.61
lpsolve 0.87 0.83
-----------------------------------------------
func trig : nVars = 1000 nConstraints = 1100 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 40.92 40.42
glpk 46.83 46.17
lpsolve 47.45 46.56
-----------------------------------------------
func trig : nVars = 500 nConstraints = 1500 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 19.09 18.6
glpk 19.65 19.42
lpsolve 16.64 16.43
-----------------------------------------------
func trig : nVars = 1000 nConstraints = 1500 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 71.12 70.29
glpk 55.65 53.87
lpsolve 63.32 62.5
-----------------------------------------------
func trig : nVars = 100 nConstraints = 5100 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 4.45 4.14
glpk 26.34 25.89
lpsolve 8.01 7.81
-----------------------------------------------
func trig : nVars = 100 nConstraints = 10100 density = 1
Solver TimeElapsed CPUTimeElapsed
cvxopt 9.01 8.58
glpk 99.77 95.76
lpsolve 25.94 25.59
whole timeElapsed = 560.718302011
whole cpuTimeElapsed = 548.01
***********************************************
density = 0.1
-----------------------------------------------
func trig : nVars = 100 nConstraints = 200 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 0.09 0.07
glpk 0.05 0.02
lpsolve 0.03 0.03
-----------------------------------------------
func trig : nVars = 100 nConstraints = 1100 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 0.72 0.68
glpk 0.3 0.29
lpsolve 0.13 0.12
-----------------------------------------------
func trig : nVars = 1000 nConstraints = 1100 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 10.73 10.42
glpk 1.93 1.91
lpsolve 3.91 3.84
-----------------------------------------------
func trig : nVars = 500 nConstraints = 1500 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 6.89 6.68
glpk 1.56 1.56
lpsolve 1.69 1.58
-----------------------------------------------
func trig : nVars = 1000 nConstraints = 1500 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 15.87 15.38
glpk 3.0 2.77
lpsolve 5.14 5.06
-----------------------------------------------
func trig : nVars = 100 nConstraints = 5100 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 14.7 14.49
glpk 3.77 3.55
lpsolve 0.97 0.93
-----------------------------------------------
func trig : nVars = 100 nConstraints = 10100 density = 0.1
Solver TimeElapsed CPUTimeElapsed
cvxopt 61.2 60.8
glpk 8.69 8.55
lpsolve 2.44 2.42
whole timeElapsed = 149.099064827
whole cpuTimeElapsed = 146.06
***********************************************
density = 0.02
-----------------------------------------------
func trig : nVars = 100 nConstraints = 200 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 0.04 0.04
glpk 0.02 0.02
lpsolve 0.02 0.02
-----------------------------------------------
func trig : nVars = 100 nConstraints = 1100 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 0.2 0.16
glpk 0.24 0.23
lpsolve 0.08 0.08
-----------------------------------------------
func trig : nVars = 1000 nConstraints = 1100 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 1.26 1.23
glpk 0.91 0.89
lpsolve 1.53 1.51
-----------------------------------------------
func trig : nVars = 500 nConstraints = 1500 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 1.25 1.12
glpk 0.75 0.74
lpsolve 0.74 0.74
-----------------------------------------------
func trig : nVars = 1000 nConstraints = 1500 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 2.09 2.03
glpk 1.32 1.29
lpsolve 2.07 2.02
-----------------------------------------------
func trig : nVars = 100 nConstraints = 5100 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 2.18 2.08
glpk 2.59 2.56
lpsolve 0.58 0.54
-----------------------------------------------
func trig : nVars = 100 nConstraints = 10100 density = 0.02
Solver TimeElapsed CPUTimeElapsed
cvxopt 8.92 8.59
glpk 6.84 6.78
lpsolve 1.2 1.19
whole timeElapsed = 39.8548879623
whole cpuTimeElapsed = 38.67
***********************************************