Reference points and approximation algorithms in multicriteria discrete optimization

Bi-objective short-term scheduling in a rolling horizon framework: a priori approaches with alternative operational objectives

“…2 ), and 1NM (f 4 1 , f 2 2 ). In Figure 6, one non-dominated approach is observed: 1NM-ε Inc (f 4 1 , f 1 2 ). These results demonstrate that the a priori multi-objective scalarization methods can be used to improve TTP and AMS over a rolling horizon compared to a single-objective approach.…”

“…In contrast to a posteriori methods, the DM's preferences are selected in advance in a priori methods; hence, a single trade-off solution is obtained after a unique search [10,15], rather than a set of solutions for the DM to evaluate. Reference point methods, such as compromise programming [46], are very popular a priori methods that have been widely used in practice [16,4].…”

“…In general, the benefit of compromise programming lies in that it returns the compromise solution that best approximates an ideal unattainable solution [32,4]. The ε-constraint method [21] is another method that has enjoyed popularity due to its relative simplicity [10,8].…”

Dynamic programming bi-criteria combinatorial optimization

“…Our results belong to the fast-growing study of multi-criteria optimization [5,6,13]. Since 2011, we looked at the relationships between different parameters of decision trees and the construction of Pareto optimal points [7,9,22].…”

Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

“…The hypervolume scalarization shows some similarities with other reference point based methods like, e.g., compromise programming techniques which were introduced by Bowman (1976) and Yu (1973); Freimer and Yu (1976) in the context of group decisions. See also Büsing et al (2017) for recent research on reference point methods in the context of approximations of discrete multiobjective optimization problems.While compromise programming models typically aim at the minimization of the distance of an outcome vector from a given (utopian) reference point, e.g., based on p -norms, the hypervolume scalarization aims at maximizing the volume dominated by an outcome vector w.r.t. a given reference point.…”