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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 210
The following Solver Dialogue box shows the set of 5 Decision Variables
(Cells C10 to C14) subject collectively to the Alldifferent Constraint.
Step 5 – Test the Excel Spreadsheet
This spreadsheet can be very easily tested by varying the integer values
in the Decision Variable cells (cells C10 to C14). The city names and
distances between cities should correctly change to match the new
Decision Variable integer values corresponding to different rows.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 211
Step 6 – Insert All Data into the Solver Dialogue
Box
Once again here is the completed Solver dialogue box:
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 212
The  Travelling Salesman Problem provides an excellent opportunity to
demonstrate the use of the Evolutionary method. The Evolutionary
method must be used if the Mathematical Path to the Objective contains
any cells holding non-smooth or discontinuous formulas.
Common non-smooth Excel functions are MIN, MAX, and ABS.
Common discontinuous Excel functions are INDEX , HLOOKUP,
VLOOKUP, LOOKUP, INT, ROUND, COUNT,  CEILING, FLOOR, IF,
CHOOSE, NOT AND, OR, GREATER THAN, LESS THAN, and EQUAL
TO.
The INDEX function in this problem appears in cells that are part of the
Clear Mathematical Path to the Objective. We therefore must select the
Evolutionary method to solve this problem.
After we have selected the Evolutionary method, we hit Solve and
solution shown in several pages is reached.
This solution could be interpreted as follows:
The salesman stars in his home town of Chicago. He then visits Denver,
LA, Dallas, Boston, and finally back to Chicago in that order. The total
miles travelled on this route are 6,447 miles. This is the shortest route
that will cover all 5 cities starting and ending in Chicago.
Note that no special provision has to be made to ensure that the starting
point is Chicago.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 213
Following are views of the Excel model before solving and then after
solving with Excel Solver’s Evolutionary method:
Before Running Solver
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 214
After Running Solver
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 215
Part 1
Note:
The Solver Result
How long Solver took to solve the problem (especially
important in this case – This time could be reduced by several of
the Options settings.)
The Solver Engine that was used and the Solver Options settings
Where the Objective Cell was labeled in the Excel model for its
name to appear as it does in Part 1 of the Answer Report
Note the solution time of 164 seconds. This could have been reduced by
limiting the maximum allowable run time, iterations, or subproblems
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Page 216
Part 2 – Variable Cells
Note that the Variable Cells contain the Decision Variables
Note where the labels for each Decision Variable are placed in
the Excel model so that the Decision Variable’s name will appear
here in Part 2 of the Answer Report as it does
Note the type of variable  - Either Continuous or Integer (Integer,
Binary, or Alldifferent
Note the Before and After values of each Decision Variable
Part 3 - Constraints
Note how each Constraint is labeled in the Excel model in order
for the Constraint’s name to appear here in Part 3 of the Answer
Report as it does
Note which Constraints are binding (had their limits hit) and which
aren’t.
Note how much slack is still available in any Constraint that has
Note any Integer Constraints (Integer, Binary, Alldifferent)
Note that Cells C10 to C14 were set to AllDiff simultaneously as a group.
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master