Biobjective Optimization Problems on Matroids with Binary Costs

08/02/2021
by   Jochen Gorski, et al.
0

Like most multiobjective combinatorial optimization problems, biobjective optimization problems on matroids are in general NP-hard and intractable. In this paper, we consider biobjective optimization problems on matroids where one of the objective functions is restricted to binary cost coefficients. We show that in this case the problem has a connected efficient set with respect to a natural definition of a neighborhood structure and hence, can be solved efficiently using a neighborhood search approach. This is, to the best of our knowledge, the first non-trivial problem on matroids where connectedness of the efficient set can be established. The theoretical results are validated by numerical experiments with biobjective minimum spanning tree problems (graphic matroids) and with biobjective knapsack problems with a cardinality constraint (uniform matroids). In the context of the minimum spanning tree problem, coloring all edges with cost 0 green and all edges with cost 1 red leads to an equivalent problem where we want to simultaneously minimize one general objective and the number of red edges (which defines the second objective) in a Pareto sense.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/30/2019

Deleting to Structured Trees

We consider a natural variant of the well-known Feedback Vertex Set prob...
research
10/02/2017

Network Optimization on Partitioned Pairs of Points

Given n pairs of points, S = {{p_1, q_1}, {p_2, q_2}, ..., {p_n, q_n}}, ...
research
12/19/2019

Imposing edges in Minimum Spanning Tree

We are interested in the consequences of imposing edges in T a minimum s...
research
10/22/2022

NeuroPrim: An Attention-based Model for Solving NP-hard Spanning Tree Problems

Spanning tree problems with special constraints are widely applied in re...
research
05/26/2019

Taxonomization of Combinatorial Optimization Problems in Fourier Space

We propose and develop a novel framework for analyzing permutation-based...
research
04/05/2018

Structural cost-optimal design of sensor networks for distributed estimation

In this letter we discuss cost optimization of sensor networks monitorin...
research
12/12/2012

A constraint satisfaction approach to the robust spanning tree problem with interval data

Robust optimization is one of the fundamental approaches to deal with un...

Please sign up or login with your details

Forgot password? Click here to reset