Randomized Local Search Heuristics for Submodular Maximization and Covering Problems: Benefits of Heavy-tailed Mutation Operators

05/28/2018
by   Tobias Friedrich, et al.
0

A core feature of evolutionary algorithms is their mutation operator. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this line of work, we propose a new mutation operator and analyze its performance on the (1+1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1+1) EA on classes of problems for which results on the other mutation operators are available. We present a "jump" function for which the performance of the (1+1) EA using any static uniform mutation and any restart strategy can be worse than the performance of the (1+1) EA using our mutation operator with no restarts. We show that the (1+1) EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve this problem. Finally, we evaluate experimentally the performance of the (1+1) EA using our operator, on real-world graphs of different origins with up to 37,000 vertices and 1.6 million edges. In comparison with uniform mutation and a recently proposed dynamic scheme our operator comes out on top on these instances.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/22/2012

Hybridizing PSM and RSM Operator for Solving NP-Complete Problems: Application to Travelling Salesman Problem

In this paper, we present a new mutation operator, Hybrid Mutation (HPRM...
research
01/28/2021

Stagnation Detection with Randomized Local Search

Recently a mechanism called stagnation detection was proposed that autom...
research
05/21/2013

Improving NSGA-II with an Adaptive Mutation Operator

The performance of a Multiobjective Evolutionary Algorithm (MOEA) is cru...
research
08/23/2022

A multiplicity-preserving crossover operator on graphs. Extended version

Evolutionary algorithms usually explore a search space of solutions by m...
research
06/05/2023

Representation-agnostic distance-driven perturbation for optimizing ill-conditioned problems

Locality is a crucial property for efficiently optimising black-box prob...
research
06/16/2020

Evolutionary Algorithms with Self-adjusting Asymmetric Mutation

Evolutionary Algorithms (EAs) and other randomized search heuristics are...
research
06/01/2018

Fast Artificial Immune Systems

Various studies have shown that characteristic Artificial Immune System ...

Please sign up or login with your details

Forgot password? Click here to reset