An interactive approach for biobjective integer programs under quasiconvex preference functions

Date

2016-09-01

Author

Ozturk, Diclehan Tezcaner
Köksalan, Mustafa Murat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

264
views

0
downloads

We develop an interactive algorithm for biobjective integer programs that finds the most preferred solution of a decision maker whose preferences are consistent with a quasiconvex preference function to be minimized. During the algorithm, preference information is elicited from the decision maker. Based on this preference information and the properties of the underlying quasiconvex preference function, the algorithm reduces the search region and converges to the most preferred solution progressively. Finding the most preferred solution requires searching both supported and unsupported nondominated points, where the latter is harder. We develop theory to further restrict the region where unsupported nondominated points may lie. We demonstrate the algorithm on the generalized biobjective traveling salesperson problem where there are multiple efficient edges between node pairs and show its performance on a number of randomly generated instances.

Subject Keywords

Biobjective traveling salesperson problem, Interactive method, Combinatorial optimization, Multiobjective decision making

URI

https://hdl.handle.net/11511/56920

Journal

ANNALS OF OPERATIONS RESEARCH

DOI

https://doi.org/10.1007/s10479-016-2149-9

Collections

Department of Industrial Engineering, Article

Suggestions

OpenMETU
Core

An interactive approximation algorithm for multi-objective integer programs Lokman, Banu; Korhonen, Pekka J.; Wallenius, Jyrki (2018-08-01) We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences are consistent with a nondecreasing quasiconcave value function. Using pairwise comparisons of the DM, we construct convex cones and eliminate the inferior regions that are close to being dominated by the cones in addition to the regions dominated by the cones. The algorithm allows the DM to change th...
An Interactive partitioning approach for multiobjective decision making under a general monotone utility function Karasakal, Esra (2013-09-01) We develop an interactive partitioning approach for solving the multiobjective decision making problem of a decision maker (DM) who has an implicit general monotone utility function. The approach reduces feasible solution space using the DM's preferences. Hypothetical solutions called partition ideals (PIs) that dominate portions of the efficient frontier are generated and those that are inferior to a feasible solution are used to eliminate the dominated regions. We investigate the issues in representation ...
An interactive algorithm to find the most preferred solution of multi-objective integer programs LOKMAN, BANU; Köksalan, Mustafa Murat; Korhonen, Pekka J.; Wallenius, Jyrki (Springer Science and Business Media LLC, 2016-10-01) In this paper, we develop an interactive algorithm that finds the most preferred solution of a decision maker (DM) for multi-objective integer programming problems. We assume that the DM's preferences are consistent with a quasiconcave value function unknown to us. Based on the properties of quasiconcave value functions and pairwise preference information obtained from the DM, we generate constraints to restrict the implied inferior regions. The algorithm continues iteratively and guarantees to find the mos...
An evolutionary approach to generalized biobjective traveling salesperson problem Köksalan, Mustafa Murat; Ozturk, Diclehan Tezcaner (2017-03-01) We consider the generalized biobjective traveling salesperson problem, where there are a number of nodes to be visited and each node pair is connected by a set of edges. The final route requires finding the order in which the nodes are visited (tours) and finding edges to follow between the consecutive nodes of the tour. We exploit the characteristics of the problem to develop an evolutionary algorithm for generating an approxiMation of nondominated points. For this, we approximate the efficient tours using...
An interactive ranking-based multi-criteria choice algorithm with filtering: Applications to university selection Karakaya, Gülşah (Orta Doğu Teknik Üniversitesi (Ankara, Turkey), 2019-6) In this study, we develop an interactive algorithm to converge to the most preferred alternative of a decision maker (DM) among a set of discrete alternatives. The algorithm presents a limited number of alternatives to the DM and collects preference ranking of them iteratively. The preferences are modeled by a flexible and realistic preference function. To improve the performance, the alternatives presented are determined by a filtering method. We compare our algorithm with benchmark algorithms on nume...

Citation Formats

D. T. Ozturk and M. M. Köksalan, “An interactive approach for biobjective integer programs under quasiconvex preference functions,” ANNALS OF OPERATIONS RESEARCH, pp. 677–696, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56920.