A First Runtime Analysis of the NSGA-II on a Multimodal Problem

04/28/2022
by   Zhongdi Qu, et al.
0

Very recently, the first mathematical runtime analyses of the multi-objective evolutionary optimizer NSGA-II have been conducted (AAAI 2022, GECCO 2022 (to appear), arxiv 2022). We continue this line of research with a first runtime analysis of this algorithm on a benchmark problem consisting of two multimodal objectives. We prove that if the population size N is at least four times the size of the Pareto front, then the NSGA-II with four different ways to select parents and bit-wise mutation optimizes the OneJumpZeroJump benchmark with jump size 2 ≤ k ≤ n/4 in time O(N n^k). When using fast mutation, a recently proposed heavy-tailed mutation operator, this guarantee improves by a factor of k^Ω(k). Overall, this work shows that the NSGA-II copes with the local optima of the OneJumpZeroJump problem at least as well as the global SEMO algorithm.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/16/2021

A First Mathematical Runtime Analysis of the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

The non-dominated sorting genetic algorithm II (NSGA-II) is the most int...
research
04/20/2023

How the Move Acceptance Hyper-Heuristic Copes With Local Optima: Drastic Differences Between Jumps and Cliffs

In recent work, Lissovoi, Oliveto, and Warwicker (Artificial Intelligenc...
research
03/09/2017

Fast Genetic Algorithms

For genetic algorithms using a bit-string representation of length n, th...
research
10/07/2022

The (1+(λ,λ)) Global SEMO Algorithm

The (1+(λ,λ)) genetic algorithm is a recently proposed single-objective ...
research
08/18/2022

The First Mathematical Proof That Crossover Gives Super-Constant Performance Gains For the NSGA-II

Very recently, the first mathematical runtime analyses for the NSGA-II, ...
research
05/21/2013

Improving NSGA-II with an Adaptive Mutation Operator

The performance of a Multiobjective Evolutionary Algorithm (MOEA) is cru...
research
07/09/2018

Evolving Multimodal Robot Behavior via Many Stepping Stones with the Combinatorial Multi-Objective Evolutionary Algorithm

An important challenge in reinforcement learning, including evolutionary...

Please sign up or login with your details

Forgot password? Click here to reset