Browsing by Subject "Multiobjective integer programming"

Now showing 1 - 4 of 4

Open Access
Finding all equitably non-dominated points of multiobjective integer programming problems
(2023-09) Ulutaş, Seyit
Equitable multiobjective programming (E-MOP) problems are multiobjective programming problems of a special type. In E-MOP, the decision-maker has equity concerns and hence has an equitable rational preference model. In line with this, our aim is to find all equitably non-dominated points (EN) of the multi-objective integer problems. There are different approaches to solving E-MOP problems. We use equitable aggregation functions and develop two different algorithms; one for equitable biobjective integer programming (E-BOIP) problems and one for equitable multiobjective integer programming (E-MOIP) problems with more than two objectives. In the first algorithm, we solve Pascoletti Serafini (PS) scalarization models iteratively while ensuring getting a weakly equitably non-dominated point in each iteration. In the second algorithm, we use cumulative ordered weighted average in the ExA algorithm of Özpeynirci and Köksalan [1] to find all extreme supported equitably non-dominated points (ESN) first. After finding all ESNs, we use them to define the regions that could contain EN. Then we use split algorithm and find all the remaining ENs. We also provide a split only version of the algorithm since the process of finding all ESNs could be time consuming. We compare two versions in multiobjective assignment and knapsack problem instances. Although the split only version is quicker, the original version of the algorithm is useful since it gives information about the weight space decomposition of ESNs. The weight space decomposition discussion is also provided.
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.
Open Access
Split algorithms for multiobjective integer programming problems
(Elsevier, 2022-04) Karsu, Özlem; Ulus, Firdevs
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.