Implementing Lazy Constraints (Java)

With the Xpress-Optimizer, you could implement "lazy constraints" as "delayed rows" (see XPRSloaddelayedrows; or if you are using a modelling tool for stating your problem: Mosel: defdelayedrows, BCL C: XPRBsetdelayed) - however, this means that you need to state all constraints upfront which certainly is impractical in the context of TSP.

Regarding the use of Optimizer callbacks from Java, please take a look at the examples FICO Xpress Examples Repository: Demonstrates setting up and using callbacks (http://examples.xpress.fico.com/example.pl?id=optimizer_java_1) and FICO Xpress Examples Repository: Els - An economic lot-sizing problem solved by cut-and-branch and branch-and-cut heuris… (http://examples.xpress.fico.com/example.pl?id=bcl_java_12_2)

One of the Mosel examples implements a subtour elimination algorithm for TSP, looping over complete MIP solves: FICO Xpress Examples Repository: Air transport (http://examples.xpress.fico.com/example.pl?id=mosel_book_6_11)

which is extended to a heuristic for larger instances in this version of the example: FICO Xpress Examples Repository: Solving the TSP problem by a series of optimization subproblems. (http://examples.xpress.fico.com/example.pl?id=mosel_solv_11)

Below I am attaching an alternative Mosel implementation of the TSP subproblem solving that uses MIP callbacks: if your initial problem statement does not correspond to the full problem and you wish to use the cut manager to add further constraints during the MIP search you need to configure the solver correspondingly (in particular, disable dual reductions).

See PDF attached.