To better understand how goals are executed, consider the concept of the goal stack. Every node has its own goal stack. When calling cplex.solve(goal), the goal stack of the root node is simply initialized with goal and then calls the regular cplex.solve method.

When IloCplex processes a node, it pops the first goal from the node's goal stack and calls method execute. If a nonempty goal is returned, it is simply pushed back on the stack. IloCplex keeps doing this until the node becomes inactive or the node's goal stack becomes empty. When the node stack is empty, IloCplex continues with its built-in search strategy for the subtree rooted at this node.

In light of the goal stack, here are the different types of goals:

With this understanding, consider further what really goes on when a goal returns

return AndGoal(OrGoal(var <= IloFloor(val), var >= IloFloor(val)+1), this);

The And goal is pushed onto the current node's goal stack, only to be immediately popped back off of it. When it is executed, it will push this on the goal stack and then the Or goal. Thus, the Or goal is the next goal that IloCplex pops and executes. The Or goal creates two subnodes, and initializes their goal stacks with copies of the goal stack of the current node. At this point both subnodes will have this on top of their goal stacks. Next, the Or goal will push a local cut goal for (where denotes the floor of val) on the goal stack of the first subnode. Similarly, it pushes a local cut goal for var on the goal stack of the second subnode. Finally, the current node is deactivated and IloCplex continues its search with a new active node from the tree.

When IloCplex processes one of the subnodes that have been created by the Or goal, it will pop and execute the first goal from the node's goal stack. As you just saw, this will be a local cut goal. Thus IloCplex adds the constraint to the node problem and re-solves the relaxation. Next, this will be popped from the goal stack and executed. This means that the same search strategy as implemented in the original goal is applied at that node.