Usually Cplex behaves very predictable with LP’s that have an advanced basis to start from. But now I have something that puzzles me. Basically I do a solve from an optimal solution. This should normally run in just a few iterations. But with the default setting I see:
First model  Iteration log . . . Iteration: 1 Dual objective = 1.005320 Iteration: 581 Dual objective = 296.751221 Iteration: 1247 Dual objective = 511.623938 Iteration: 1681 Dual objective = 514.072257 LP status(1): optimal 
Restart  Iteration log . . . Iteration: 1 Objective = 515.104554 Perturbation started. Iteration: 402 Objective = 515.104554 Iteration: 806 Objective = 515.104088 Iteration: 1107 Objective = 515.103794 Iteration: 1406 Objective = 515.103557 Iteration: 1684 Objective = 515.103314 Iteration: 1939 Objective = 515.103216 Iteration: 2186 Objective = 515.103124 Iteration: 2434 Objective = 515.103037 Iteration: 2672 Objective = 515.102875 Iteration: 2951 Objective = 515.102790 Iteration: 3210 Objective = 515.102730 Iteration: 3472 Objective = 515.102670 Iteration: 3709 Objective = 515.102630 Iteration: 3943 Objective = 515.102592 Iteration: 4199 Objective = 515.102525 Iteration: 4445 Objective = 515.102493 Iteration: 4692 Objective = 515.102468 Iteration: 4933 Objective = 515.102448 Iteration: 5181 Objective = 515.102428 Iteration: 5431 Objective = 515.102411 Iteration: 5689 Objective = 515.102395 Iteration: 5962 Objective = 515.102379 Iteration: 6224 Objective = 515.102362 Iteration: 6487 Objective = 515.102353 Iteration: 6765 Objective = 515.102342 Iteration: 7041 Objective = 515.102335 Removing perturbation. LP status(1): optimal

The restart from an optimal basis takes more iterations than solving from scratch. This is with a default setting of LPMETHOD=0 (automatic). When I use LPMETHOD=1 (Primal Simplex) or LPMETHOD=2 (Dual Simplex) I see:
Restart with LPMETHOD=1  Primal crossover. Primal: Fixed no variables. Dual: Fixing 993 variables. 992 DMoves: Infeasibility 6.76704726e+000 Objective 5.15104554e+002 394 DMoves: Infeasibility 1.33823843e+000 Objective 5.15104554e+002 0 DMoves: Infeasibility 7.17019911e001 Objective 5.15104554e+002 Dual: Pushed 0, exchanged 993. Iteration log . . . Iteration: 1 Objective = 515.104554 LP status(1): optimal 
Restart with LPMETHOD=2  Dual crossover. Dual: Fixing 994 variables. 993 DMoves: Infeasibility 2.07167616e013 Objective 5.15104554e+002 414 DMoves: Infeasibility 7.97140132e014 Objective 5.15104554e+002 0 DMoves: Infeasibility 0.00000000e+000 Objective 5.15104554e+002 Dual: Pushed 1, exchanged 993. Primal: Fixed no variables. LP status(1): optimal 
These seem indeed to take fewer iterations to solve the restarted model. I always assumed LPMETHOD=0 would just choose primal or dual simplex, but apparently it also does other things, and in this case that is not helping.
Update
I did some more experiments. With LPMETHOD=0 I can now also achieve a restart if I set all variable levels to zero. I.e.
solve m minimizing z using lp;
solve m minimizing z using lp;
gives a bad restart, while:
solve m minimizing z using lp;
x.l(i,j) = 0;
z.l=0;
solve m minimizing z using lp;
gives me zero iterations for the restart. Something is not completely right. As Bo suggested in his comments, the reason may be related to Cplex trying to do a presolve on an advanced basis. (I have heard about some ancient solvers that tried a basis preserving presolve, may be more limited than what current presolvers do). The difference between LPMETHOD=0 and both LPMETHOD=1 and LPMETHOD=2 is still a mystery to me. Update 2
The behavior can be partially explained by looking at the Cplex documentation describing the Advind parameter:
For continuous models solved with simplex, setting 1 (one) will use the currently loaded basis. If a basis is available only for the original, unpresolved model, or if CPLEX has a start vector rather than a simplex basis, then the simplex algorithm will proceed on the unpresolved model. With setting 2, CPLEX will first perform presolve on the model and on the basis or start vector, and then proceed with optimization on the presolved problem.
I was using the model from a GAMS environment. There the default is 2. The documentation for GAMS/Cplex is somewhat more limited than the above paragraph:
Advind (Integer)
Use an Advanced Basis. GAMS/Cplex will automatically use an advanced basis from a previous solve
statement. The GAMS Bratio option can be used to specify when not to use an advanced basis. The Cplex
option advind can be used to ignore a basis passed on by GAMS (it overrides Bratio).
(default = determined by GAMS Bratio)
0 Do not use advanced basis
1 Use advanced basis if available
2 Crash an advanced basis if available (use basis with presolve)
Looks like 1 is better for a very good basis, 2 may be better for models with a basis that is not very good (in that case presolving will pay off even when destroying some basis information).