Redundant objective functions in linear vector maximum problems and their determination

TL;DR: This study investigates how adding or omitting objectives affects the problem characteristics and proposes a general notion of conflict between objective sets as a theoretical foundation for objective reduction.

TL;DR: In this paper, a multiparametric method based on earlier works of the author is presented, where efficient vertices and efficient edges are generated via one subprogram, which works as a simple linear programming problem, and just by inspection of these results higher dimensional efficient faces are determined.

TL;DR: The results underline that the use of a population of solutions that is characteristic of MOEAs is a powerful concept if the goal is to obtain a good Pareto set, i.e., instead of only a single solution.

TL;DR: An objective extraction method (OEM) for MaOPs that formulates the reduced objective as a linear combination of the original objectives to maximize the conflict between the reduced objectives and can thus preserve the dominance structure as much as possible.

TL;DR: Five options within this revised simplex algorithm for the enumeration of the set of efficient extreme points were tested on a variety of problems, providing indications for effective use of the algorithm.

TL;DR: In this article, it was shown that each efficient solution of a linear vector maximum problem is also properly efficient, and the notion of proper efficiency has been proposed to exclude efficient solutions of a certain anomalous type.

TL;DR: In this paper, a simplex method of linear programming is used to determine the frame and the lineality space of a convex hull of a finite set H(S) spanned by a set S. The problem of finding the frame can be successively reduced to problems in lower dimensions.