TomSym compared to the Symbolic Toolbox - Revision history

Per: /* tomSym code */

2015-01-21T12:34:09Z

tomSym code

← Older revision		Revision as of 08:34, 21 January 2015
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	options = struct;		options = struct;
	options.solver = 'knitro';		options.solver = 'knitro'; % also try: 'snopt'
	options.Prob.KNITRO.options.ALG=3;		options.Prob.KNITRO.options.ALG=3;
	options.scale = 'auto'		options.scale = 'auto'

Per: /* tomSym code */ KNITRO works with ALG=2 or 3.

2015-01-21T12:31:41Z

tomSym code: KNITRO works with ALG=2 or 3.

← Older revision		Revision as of 08:31, 21 January 2015
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	options = struct;		options = struct;
	options.solver = '~~snopt~~';		options.solver = 'knitro';
			options.Prob.KNITRO.options.ALG=3;
	options.scale = 'auto'		options.scale = 'auto'

Per at 16:50, 20 January 2015

2015-01-20T16:50:26Z

← Older revision		Revision as of 12:50, 20 January 2015
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	We look at the optimization problem of maximizing the revenue of a hydroelectric dam.		We look at the optimization problem of maximizing the revenue of a hydroelectric dam.
	This problem was published by By Seth DeLand of the MathWorks, as an example of how to combine their optimization and symbolic toolboxes. [http://www.mathworks.com/company/newsletters/articles/solving-large-scale-optimization-problems-with-matlab-a-hydroelectric-flow-example.html]		This problem was published by By Seth DeLand of the MathWorks, as an example of how to combine their optimization and symbolic toolboxes. [http://www.mathworks.com/company/newsletters/articles/solving-large-scale-optimization-problems-with-matlab-a-hydroelectric-flow-example.html]
	We solve the same probem using [[tomSym]] and the TOMLAB solvers, noting a significant speed difference, with tomSym running thousands of times faster than the Symbolic Toolbox ~~on a problem with 960 decision variables~~.		We solve the same probem using [[tomSym]] and the TOMLAB solvers, noting a significant speed difference, with tomSym running thousands of times faster than the Symbolic Toolbox.

	== Problem description ==		== Problem description ==

Per: /* tomSym code */ some versionsn of KNITRO seem to have problems?

2015-01-20T15:48:32Z

tomSym code: some versionsn of KNITRO seem to have problems?

← Older revision		Revision as of 11:48, 20 January 2015
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	options = struct;		options = struct;
	options.solver = '~~knitro~~';		options.solver = 'snopt';
	options.scale = 'auto'		options.scale = 'auto'

Per: bugfix (transpose was lost in copying code into wiki)

2015-01-20T13:31:38Z

bugfix (transpose was lost in copying code into wiki)

← Older revision		Revision as of 09:31, 20 January 2015
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	electricity = turbineFlow.(0.5k1*(storage + [stor0; storage(1:end-1)]) + k2)./MW2kW;		electricity = turbineFlow.(0.5k1*(storage + [stor0; storage(1:end-1)]) + k2)./MW2kW;

	revenue = price*electricity;		revenue = price'*electricity;

	objective = -revenue; % Minimization objective		objective = -revenue; % Minimization objective
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	[[File:Hydroelectric plots a.png\|thumb\|Plots of the result, when the approximate indata is used.]]		[[File:Hydroelectric plots a.png\|thumb\|Plots of the result, when the approximate indata is used.]]

	Although the Hessian is ~~numeric~~, this is <em>not</em> a quadratic programming.		Although the Hessian is constant, this is <em>not</em> a quadratic programming.
	The Hessian is not positive semidefinite, and the objective is therefore not convex. There may exist		The Hessian is not positive semidefinite, and the objective is therefore not convex. There may exist
	local optima that are not as good as the global one. For this reason, the QP solvers in the		local optima that are not as good as the global one. For this reason, the QP solvers in the

Per: /* Comparing tomSym to the symbolic toolbox */

2013-11-25T09:28:22Z

Comparing tomSym to the symbolic toolbox

← Older revision		Revision as of 05:28, 25 November 2013
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	The symbolic toolbox, on the other hand, only handles scalar symbols. This means that both the number of		The symbolic toolbox, on the other hand, only handles scalar symbols. This means that both the number of
	expressions and their sizes increase as the size of symbolic matrices increase.		symbolic expressions and their sizes increase as the size of symbolic matrices increase.
	The matlab code generated by the symbolic toolbox also becomes quite lengthy because of the use of multiple		The matlab code generated by the symbolic toolbox also becomes quite lengthy because of the use of multiple
	scalar operations instead of vector/matrix operations.		scalar operations instead of vector/matrix operations.

Per: /* Comparing tomSym to the symbolic toolbox */

2013-11-25T09:27:47Z

Comparing tomSym to the symbolic toolbox

← Older revision		Revision as of 05:27, 25 November 2013
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	The main reason why tomSym is so much faster than the symbolic toolbox is that it can handle vector and matrix symbols.		The main reason why tomSym is so much faster than the symbolic toolbox is that it can handle vector and matrix symbols.
	This means that symbolic manipulations of matrix expressions are handled at approximately the same speed, regardless of the sizes of the symbolic matrices involved (until the matrices become so large that the time for numeric computations ~~begin~~ to matter.)		This means that symbolic manipulations of matrix expressions are handled at approximately the same speed, regardless of the sizes of the symbolic matrices involved (until the matrices become so large that the time for numeric computations begins to matter.)

	The symbolic toolbox, on the other hand, only handles scalar symbols. This means that both the number of		The symbolic toolbox, on the other hand, only handles scalar symbols. This means that both the number of

Per: /* Comparing tomSym to the symbolic toolbox */

2013-11-25T09:27:35Z

Comparing tomSym to the symbolic toolbox

← Older revision		Revision as of 05:27, 25 November 2013
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	The main reason why tomSym is so much faster than the symbolic toolbox is that it can handle vector and matrix symbols.		The main reason why tomSym is so much faster than the symbolic toolbox is that it can handle vector and matrix symbols.
	This means that symbolic manipulations of matrix expressions are handled at approximately the same speed, regardless of the sizes of the symbolic matrices involved.		This means that symbolic manipulations of matrix expressions are handled at approximately the same speed, regardless of the sizes of the symbolic matrices involved (until the matrices become so large that the time for numeric computations begin to matter.)

	The symbolic toolbox, on the other hand, only handles scalar symbols. This means that both the number of		The symbolic toolbox, on the other hand, only handles scalar symbols. This means that both the number of

Per: /* Timing measurments */

2013-11-25T09:19:24Z

Timing measurments

← Older revision		Revision as of 05:19, 25 November 2013
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	\|}		\|}

	KNITRO runs at about the same speed as quadprog on the smallest problem sizes, and about 2.5 times faster for larger problems. In every case, the time for the numeric solver is much smaller than the time for symbolic processing.		KNITRO runs at about the same speed as quadprog on the smallest problem sizes, and about 2.5 times faster for larger problems. (This is perhaps not a fair comparison, because quadprog has to do its own pre-scaling, while KNITRO gets a pre-scaled problem from tomSym.) In every case, the time for the numeric solver is much smaller than the time for symbolic processing.

	== Comparing tomSym to the symbolic toolbox ==		== Comparing tomSym to the symbolic toolbox ==

Per: /* Solution */

2013-11-25T09:16:39Z

Solution

← Older revision		Revision as of 05:16, 25 November 2013
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	The solution for the approximate input data is very similar to the one presented by DeLand.		The solution for the approximate input data is very similar to the one presented by DeLand.
	With identical input data, the solutions are of course nearly identical. (~~The TOMLAB~~ solvers		With identical input data, the solutions are of course nearly identical (within the tolerances of the solvers).
	~~give a slightly worse~~ objective value due to ~~slightly better constraint adherence~~.)
			Interestingly, the objective value reported by the quadprog solver does not match the value obtained from substituting
			the solution back into the objective function. The command
			<source lang="matlab">
			(subs(Rtot,X,x3)-fval3)./fval3
			</source>
			computes the relative error. This error should be zero, or on the order of machine precision: 1e-16,
			but it is on the order of 1e-4. This seems to be due to rounding errors in the gradient and Hessian as computed by the Symbolic Toolbox.
			The value obtained by "subs(Rtot,X,x3)" is very close to the optimum value returned by the TOMLAB solvers (within 1e-10 or so).

	== Code comparison ==		== Code comparison ==