Evaluating solutions and solution sets under multiple objectives

Date

2021-10-01

Author

Köksalan, M.
Karakaya, Gülşah

Metadata

Show full item record

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

Item Usage Stats

577
views

0
downloads

In this study we address evaluating solutions and solution sets that are defined by multiple objectives based on a function. Although any function can be used, we focus on mostly weighted Tchebycheff functions that can be used for a variety of purposes when multiple objectives are considered. One such use is to approximate a decision maker's preferences with a Tchebycheff utility function. Different solutions can be evaluated in terms of expected utility conditional on weight values. Another possible use is to evaluate a set of solutions that approximate a Pareto set. It is not straightforward to find the Pareto set, especially for large-size multi-objective combinatorial optimization problems. To measure the representation quality of approximate Pareto sets and to compare such sets with each other, there are some performance indicators such as the hypervolume measure, the ε indicator, and the integrated preference functional (IPF) measure. A Tchebycheff function based IPF measure can be used to estimate how well a set of solutions represents the Pareto set. We develop the necessary theory to practically evaluate solutions and solution sets. We develop a general algorithm and demonstrate it for two, three, and four objectives.

Subject Keywords

Multiple objective programming, Tchebycheff function, Weight set partitioning

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85100436170&origin=inward
https://hdl.handle.net/11511/90810

Journal

European Journal of Operational Research

DOI

https://doi.org/10.1016/j.ejor.2021.01.021

Collections

Department of Business Administration, Article

Suggestions

OpenMETU
Core

Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs Karakaya, Gülşah; Köksalan, M. (2023-07-01) Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the pre...
An adaptive simulated annealing algorithm-based approach for assembly line balancing and a real-life case study Guden, H.; Meral, Fatma Sedef (2016-05-01) In this study, we address the deterministic assembly line balancing problem (ALBP) in a multiple product-models environment with multiple objectives. We have been motivated by the assembly line balancing problem of a white goods product production line that is a multi-model type line with 68 stations through which four product-models are assembled, each with approximately 400 precedence relations and 300 tasks. In the plant, to cope with the increasing demand in the medium term, the efficiency of the line i...
Optimising a nonlinear utility function in multi-objective integer programming Ozlen, Melih; Azizoğlu, Meral; Burton, Benjamin A. (2013-05-01) In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective i...
Interactive Approaches to Multiple Criteria Sorting Problems: Entropy-Based Question Selection Methods Özarslan, Ali; Karakaya, Gülşah (2022-08-01) In this study, interactive approaches for sorting alternatives evaluated on multiple criteria are developed. The possible category ranges of alternatives are defined by mathematical models iteratively under the assumption that the preferences of the decision maker (DM) are consistent with an additive utility function. Simulation-based and model-based parameter generation methods are proposed to hypothetically assign the alternatives to categories. A practical approach to solve the incompatibility problem of...
Reducing inconsistencies in intuitionistic 2-way adaptive fuzzy control systems Gurkan, E; Erkmen, Aydan Müşerref; Erkmen, İsmet (2000-08-30) Our objective in this paper is to model and reduce inconsistency in expert knowledge for our proposed 2-way adaptive fuzzy system that makes use of intuitionistic fuzzy sets. Intuitionistic fuzzy sets model an interval valued distribution of information in the adaptive control architecture with the necessity at the lower bound as the degree of membership functions and the possibility at the upper bound as the complement of the degree of nonmembership functions. Uncertainty is modelled as the width of this i...

Citation Formats

M. Köksalan and G. Karakaya, “Evaluating solutions and solution sets under multiple objectives,” European Journal of Operational Research, pp. 16–28, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85100436170&origin=inward.