Hi

I have a quadratic obj linear constraint NLP we are solving using

PATHNLP.

I have 3 questions here (bear with me ). The first two are strange

outcomes I don’t really understand, and the 3rd is a more generalised

advice question on techniques for getting our problem to solve (as I

have never tried solving NLPs or used PATH before).

We solve each year individually in a big loop, ie something like

loop (y) do

solve my_model using NLP maximising z;

endloop

## Question 1:

For year 2007 the model solved. I worked out that some constraints

are not required in all cases, and so eliminated this constraint for

some items (ie the problem is now less constrained). However where

the model used to solve with the full constraint set, it now reports

back as infeasible.(?!) Solving the full constraint set takes a few

mins, solving the optimised constraint set concludes it is infeasible

much quicker.

I have posted the output from the full and restricted constraint set

below in case it helps.

Can someone suggest why this is? Is it hitting some limit somewhere

perhaps which it reaches in the less constrained version but doesnt

hit in the fully constrained version?

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#### FULL CONSTRAINT SET

L O O P S scen Scen1

y 2007

s FullYr

S O L V E S U M M A R Y

MODEL TCONE OBJECTIVE Z

TYPE NLP DIRECTION MAXIMIZE

SOLVER PATHNLP FROM LINE 2206

**** SOLVER STATUS 1 NORMAL COMPLETION

**** MODEL STATUS 2 LOCALLY OPTIMAL

**** OBJECTIVE VALUE 11034141.0678

RESOURCE USAGE, LIMIT 80.314 100000000.000

ITERATION COUNT, LIMIT 34433 10000000

EVALUATION ERRORS 0 0

PATH-NLP Nov 27, 2006 WIN.PT.PT 22.3 016.035.041.VIS Path 4.6.07

NLP size: 16195 rows, 20241 cols, 60155 non-zeros, 0.02% dense.

MCP size: 36434 rows/cols, 100028 non-zeros, 0.01% dense.

**** REPORT SUMMARY : 0 NONOPT

0 INFEASIBLE

0 UNBOUNDED

0 ERRORS

### OPTIMISED (ie fewer) CONSTRAINTS

S O L V E S U M M A R Y

MODEL TCONE OBJECTIVE Z

TYPE NLP DIRECTION MAXIMIZE

SOLVER PATHNLP FROM LINE 2207

**** SOLVER STATUS 2 ITERATION INTERRUPT

**** MODEL STATUS 6 INTERMEDIATE INFEASIBLE

**** OBJECTIVE VALUE 11033991.5615

RESOURCE USAGE, LIMIT 32.141 100000000.000

ITERATION COUNT, LIMIT 13367 10000000

EVALUATION ERRORS 0 0

PATH-NLP Nov 27, 2006 WIN.PT.PT 22.3 016.035.041.VIS Path 4.6.07

## NLP size: 16181 rows, 20241 cols, 59595 non-zeros, 0.02% dense.

MCP size: 36420 rows/cols, 98908 non-zeros, 0.01% dense.

**** REPORT SUMMARY : 123 NONOPT ( NOPT)

4 INFEASIBLE (INFES)

SUM 8.4338869E-5

MAX 3.4079636E-5

MEAN 2.1084717E-5

0 UNBOUNDED

0 ERRORS

Question 2:

For some solve years we are not getting a feasible solution back, even

though I would imagine that one exists - and I have explicit slack

variables (at a very high cost) added to the constraints I thought

might cause trouble to try and reduce this issue.

Strangely however if I solve *just that year on its own*, i get a

feasible solution.

ie if for example year 2009 does not solve during the full loop, and I

change my loop to be as follows I get a feasible solution for 2009.

loop (y)$(SameAs(y,“2009”)) do

endloop;

Its possible we are hitting some limit, or do not have well tweaked

PATHNLP settings and so PATH is struggling for some reason.

Perhaps we have some previous solution’s residue floating around which

PATHNLP is picking up and its causing it issues? However I didnt see

a PATH option to turn this off…?

To add to the confusion, I can get a solution for 2009 if I have:

loop (y)(SameAs(y,"2009")) do [ie solve 2009 only]
or
loop (y)(SameAs(y,“2008”) OR SameAs(y,“2009”)) do [ie solve 2008

and 2009]

but not if I have

loop (y)(SameAs(y,"2007") OR SameAs(y,"2008") OR SameAs(y,"2009"))
do [ie solve 2007 and 2008 and 2009]
or
loop (y)(SameAs(y,“2007”) OR SameAs(y,“2009”)) do [ie solve 2007 and

2009]

## I have looked hard at the constraints via the .lst file and cannot see

any differences between the 2009 constraint listing for one which

works and one which doesn’t - so I don’t believe I am screwing up some

data value within the model during the data processing stage within

the loop.

Question 3:

Can someone advise as to a good set of PATHNLP or GAMS settings to try

first when trying to get PATHNLP to solve, and or what limits I should

be looking at. I am new to NLPs and PATH. Basically - are there any

good settings which increase the changes of PATHNLP solving even it it

slows things down, and we can wind them back as we get comfortable

that the model is finding solutions and the solutions are sensible.

Thanks in advance

Andy C

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