A Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization

TL;DR

This paper presents a computational method to identify nonessential objective functions in linear multicriteria optimization, simplifying decision-making by reducing the number of criteria without changing the set of optimal solutions.

Contribution

It combines two methods for determining nonessential functions and implements them computationally using a computer algebra system, advancing the analysis of multicriteria problems.

Findings

Effective identification of nonessential objectives

Reduction of criteria without altering efficient solutions

Implementation in a computer algebra system

Abstract

The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function is called nonessential if the set of efficient solutions is the same both with or without that objective function. In this paper we put together two methods for determining nonessential objective functions. A computational implementation is done using a computer algebra system.