Incumbent solutions in branch-and-bound algorithms: Setting the record straight

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

“…symmetry in the problem imposed a significant burden on the solver that could not be alleviated by even incorporating f ≤ f * at the root node of the B&B process. Furthermore, it is observed that enforcing such tight upper bound constraints induced limited computational speed-ups and sometimes had adverse computational effects, which resonates with the findings of Ragsdale and Shapiro (1996; as further echoed by Proll (2007) in the context of the blockmodel problem). Likewise, Table 4 reports the computational performance of DTP ("sym = 5"), DTP-S, and DTP µ -S to which we have appended the constraint f ≤ f * .…”

“…For the noise dosage and the wagon load-balancing problems, the formulations COP µ -S and COP-S strongly dominated COP ("sym = 5", f ≤ f * ), which suggests that jointly employing the two symmetry-defeating paradigms (objective perturbations and hierarchical constraints) provides a far more decisive factor in enhancing problem solvability than relying on the CPLEX-enabled symmetrydefeating feature, even when the objective function is subjected to a very tight bound. In fact, imposing such strong upper bound constraints yielded limited computational improvements and often had adverse effects on the solver for the applications we investigated, which echoes the findings of Ragsdale and Shapiro (1996) and Proll (2007).…”