Runtime Performances of Randomized Search Heuristics for the Dynamic Weighted Vertex Cover Problem

01/24/2020
by   Feng Shi, et al.
3

Randomized search heuristics such as evolutionary algorithms are frequently applied to dynamic combinatorial optimization problems. Within this paper, we present a dynamic model of the classic Weighted Vertex Cover problem and analyze the runtime performances of the well-studied algorithms Randomized Local Search and (1+1) EA adapted to it, to contribute to the theoretical understanding of evolutionary computing for problems with dynamic changes. In our investigations, we use an edge-based representation based on the dual form of the Linear Programming formulation for the problem and study the expected runtime that the adapted algorithms require to maintain a 2-approximate solution when the given weighted graph is modified by an edge-editing or weight-editing operation. Considering the weights on the vertices may be exponentially large with respect to the size of the graph, the step size adaption strategy is incorporated, with or without the 1/5-th rule that is employed to control the increasing/decreasing rate of the step size. Our results show that three of the four algorithms presented in the paper can recompute 2-approximate solutions for the studied dynamic changes in polynomial expected runtime, but the (1+1) EA with 1/5-th Rule requires pseudo-polynomial expected runtime.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/23/2015

On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling

Evolutionary algorithms have been frequently used for dynamic optimizati...
research
03/06/2019

Runtime Analysis of RLS and (1+1) EA for the Dynamic Weighted Vertex Cover Problem

In this paper, we perform theoretical analyses on the behaviour of an ev...
research
01/15/2020

Parameterized Complexity Analysis of Randomized Search Heuristics

This chapter compiles a number of results that apply the theory of param...
research
05/26/2021

Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem

We contribute to the theoretical understanding of randomized search heur...
research
02/04/2020

The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics

Several important optimization problems in the area of vehicle routing c...
research
05/28/2020

More Effective Randomized Search Heuristics for Graph Coloring Through Dynamic Optimization

Dynamic optimization problems have gained significant attention in evolu...
research
07/28/2022

Analysis of Quality Diversity Algorithms for the Knapsack Problem

Quality diversity (QD) algorithms have been shown to be very successful ...

Please sign up or login with your details

Forgot password? Click here to reset