RELAX4 solves linear minimum-cost flow problems and returns to the
user information about the optimization problem, the solution process,
and the solution.

The NEOS Server interface to RELAX4 will accept inputs in either the DIMACS
minimum-cost flow format or the RELAX4 format. The code can be used for any
non-commercial research purposes and for comparative test purposes but
cannot be used to satisfy commercial deliverables to government or industry
without prior agreement with the authors.

RELAX4 is a solver for minimum cost flow problems that combines the RELAX
code (see two papers by Bertsekas and Tseng (1988)) with an initialization
based on an auction/sequential shortest path algorithm. This initialization
is shown to be extremely helpful in speeding up the solution of difficult
problems, involving for example long augmenting paths, for which the
relaxation method has been known to be slow. On the other hand, this
initialization procedure does not significantly deteriorate the performance
of the relaxation method for the types of problems where it has been known
to be very fast.

Bertsekas, D. P., and Tseng, P. 1988.
Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems.
Operations Research36: 93-114.

Bertsekas, D. P., and Tseng, P. 1988.
RELAX: A Computer Code for Minimum Cost Network Flow Problems.
Annals of Operations Research13: 127-190.

Using the NEOS Server for RELAX4/DIMACS

To use RELAX4 to solve a minimum-cost network flow problem, the user
must submit a problem in DIMACS standard format.

Web Submission Form

DIMACS File

Enter the location of the DIMACS input file

INIT:

Select the method for the initial solution. Relax-IV is the default
initialization. The auction/shortest path subroutine, which is used
for getting the initial price-flow pair, is recommended for difficult
problems where the default initialization yields long solution
times.

Relax-IV Auction/Shortest

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Additional Settings

Dry run: generate job XML instead of submitting it to NEOS
Short Priority: submit to higher priority queue with maximum CPU time
of 5 minutes
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