Browsing by Subject "Convex cones"

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Open Access
Interactive algorithms to solve biobjective and triobjective decision making problems
(2021-05) Denktaş, Tuğba
We propose interactive algorithms to ﬁnd the most preferred solution of biobjec-tive and triobjective integer programming problems. The algorithms can be used in any setting where the decision-maker has a general monotone utility function. They divide the image space of the problems into boxes and search them by solv-ing Pascoletti-Seraﬁni scalarizations, asking questions to the decision-maker so as to eliminate boxes whenever possible. We also propose a cone based approach that can be incorporated into both algorithms if the decision-maker is assumed to have a non-decreasing quasiconcave utility function. We demonstrate the performances of the algorithms and their cone based extensions with computational experiments. The results of the experiments show that interactive algorithms are very useful in terms of solution time compared to a posteriori algorithms that ﬁnd the whole Pareto set. The results of the experiments also show that the cone based approach leads to less interaction with the decision-maker.
Open Access
Solution approaches for equitable multiobjective integer programming problems
(Springer, 2022-04) Bashir, Bashir; Karsu, Özlem
We consider multi-objective optimization problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse preferences, namely the equitably nondominated solutions. We discuss two algorithms for finding good subsets of equitably nondominated solutions. The first approach is an extension of an interactive approach developed for finding the most preferred nondominated solution when the utility function is assumed to be quasiconcave. We find the most preferred equitably nondominated solution when the utility function is assumed to be symmetric quasiconcave. In the second approach we generate an evenly distributed subset of the set of equitably nondominated solutions to be considered further by the DM. We show the computational feasibility of the two algorithms on equitable multi-objective knapsack problem, in which projects in different categories are to be funded subject to a limited budget. We perform experiments to show and discuss the performances of the algorithms. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.