A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

Multiobjective Optimization by Decision Diagrams

“…Our key performance metric is the time to enumerate the complete set of nondominated solutions. We compare our approach with another general-purpose MODO solver developed by Kirlik and Sayın [23], an -constraint scalarization method which is currently regarded as one of the state of the art approaches for MODOs. We note in passing that we have also investigated other MODO solvers, such as the one proposed byÖzlen et al [29], but the method by Kirlik and Sayın was the best performing and numerically stable method across all solvers tested in our empirical setting.…”

“…We generated 10 instances per pair (n, p). Table 1 presents the average cardinalities of the nondominated sets (|Y N |) and average solution times (within solved instances) for p = 3, 4, 5, where Kirlik and BDD denotes the method by Kirlik and Sayın [23] and the BDD technique, respectively. Figure 2(a) depicts a scatter plot comparing solution times for all instances, where the size of a point is proportional to n. The BDD method is substantially faster and more robust than Kirlik, in particular when p is large.…”

“…We generated random MKP instances following the procedure by Kirlik and Sayın [23]. The values v j i and w i were drawn uniformly at random from the set {1, .…”

“…The -constraint method was first used by Laumanns et al [24], where an adaptive search over weighted objectives was proposed.Özlen et al [27,29] and Kirlik and Sayın [23] provide algorithmic improvements and are the basis for the comparison in the computational results presented in this paper. Other utilized scalarization techniques include Benson's method [3] (a combination of the weight-sum technique and theconstraint method) and the augmented weighted Chebychev method [32].…”

A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions

“…Laumanns et al (2006) as well as the follow-up work of Dhaenens et al (2010), Kirlik and Sayın (2014) and Boland et al (2014a) do not compute a representation of the nondominated set but aim at finding the exact nondominated set. Their method fixes one coordinate, projects the p-dimensional outcome space onto the remaining (p − 1)-dimensional space and partitions the projection by means of boxes into a grid.…”