Split algorithms for multiobjective integer programming problems

We consider split algorithms that partition the objective function space into p or p−1 dimensional regions so as to search for nondominated points of multiobjective integer programming problems, where p is the number of objectives. We provide a unified approach that allows different split strategies to be used within the same algorithmic framework with minimum change. We also suggest an effective way of making use of the information on subregions when setting the parameters of the scalarization problems used in the p-split structure. We compare the performances of variants of these algorithms both as exact algorithms and as solution approaches under time restriction, considering the fact that finding the whole set may be computationally infeasible or undesirable in practice. We demonstrate through computational experiments that while the (p−1)-split structure is superior in terms of overall computational time, the p-split structure provides significant advantage under time/cardinality limited settings in terms of representativeness, especially with adaptive parameter setting and/or a suitably chosen order for regions to be explored.