Commit 0ce66249 authored by Gregor Hendel's avatar Gregor Hendel
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Add MIP starts and README of Irv Lustig submission

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The 3 problems enclosed represent a set of sequential solves using 
hierarchical optimization, via 3 objectives.

The problem seqsolve.1.mps is the first problem to solve.  The objective 
is called "shortage".  The best known solution has an objective of 4288.

The problem seqsolve.2.short4288.mps is the second problem to solve. 
The objective is called "excess". It has a constraint called shortageBound 
that adds 0.25 to the objective of the first problem, so that the 
new objective is minimized without making the first objective worse. 
In the RHS section of the MPS file is the line:
    RHS1      shortageBound  4.28825e+03

If a better objective value than 4288 is found for seqsolve.1.mps, 
then the above line should be changed.

The best known solution for the second problem (given the objective 
bound derived from the first problem) is 384.

The problem seqsolve.3.short4288.excess384.mps is the third problem 
to solve. The objective is called "preference". It has 2 constraints, 
shortageBound and excessBound that each add 0.25 to the objectives 
of the first and second problem, respectively, so that the new 
objective is minimized without making either of the first two 
objectives worse. In the RHS section of the MPS file are the lines:
    RHS1      shortageBound  4.28825e+03
    RHS1      excessBound  3.8425e+02

If a better objective value is obtained for the first or second 
problems, then these values should be modified.

Note that the last feasible solution for the first problem should be 
used as a MIP start for the second problem.  Similarly, the last 
known feasible solution for the second problem should be used as a 
MIP start for the third problem.  For convenience, the Gurobi MST 
files first.mst and second.mst are supplied, representing the MIP 
start to use for seqsolve.2.short4288.mps and 
seqsolve.3.short4288.excess384.mps, respectively.

Each of the problems were solved with Gurobi 7.0.0 on a Intel Core 
i7-4800MQ CPU @ 2.70GHz, with 4 physical cores, and a total of 8 
logical processors.  The solver was stopped after 10 hours of 
computation for each run.  Here is a summary of the results:

Problem                         Objective          Bound              Gap
seqsolve.1                      4.288000000000e+03 4.275000000000e+03 0.3032%
seqsolve.2.short4288            3.840000000000e+02 1.771829204207e+01 95.3859%
seqsolve.3.short4288.excess384 -3.061900000000e+04 4.245900000000e+04 38.6688%

The gurobi.log file for the 3 solves is also included.

Submitted by Irv Lustig, Princeton Consultants, 11/22/16
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