Split algorithms for multiobjective integer programming problems

We consider split algorithms that partition the objective function space into - 1 dimensional regions so as to search for nondominated points of multiobjective integer programming problems, where 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 -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 (-1)-split structure is superior in terms of overall computational time, the-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.

Automated summary

This paper investigates split algorithms for partitioning the objective function space in multiobjective integer programming problems. A unified approach is proposed to allow different split strategies within the same algorithmic framework with minimal changes. The performance of these algorithms is compared in terms of exact computation and solution approaches under time restriction, with a focus on representativeness. Experimental results show that the (-1)-split structure is superior in computational time, while the-split structure has significant advantages in terms of representativeness under time/cardinality limited settings, especially with adaptive parameter setting and/or a suitable region exploration order.