Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives

Authors: Benjamin Doerr, Weijie Zheng12293-12301

AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We prove that the simple evolutionary multi-objective optimizer (SEMO) cannot compute the full Pareto front. In contrast, for all problem sizes n and all jump sizes k [4.. n 2 1], the global SEMO (GSEMO) covers the Pareto front in Θ((n 2k)nk) iterations in expectation. To improve the performance, we combine the GSEMO with two approaches, a heavy-tailed mutation operator and a stagnation detection strategy, that showed advantages in singleobjective multi-modal problems. Runtime improvements of asymptotic order at least kΩ(k) are shown for both strategies. Our experiments verify the substantial runtime gains already for moderate problem sizes.
Researcher Affiliation Academia 1Laboratoire d Informatique (LIX), Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France 2 Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China
Pseudocode Yes Algorithm 1 SEMO, Algorithm 2 GSEMO, Algorithm 3 The GSEMO-HTM algorithm with power-law exponent β > 1, Algorithm 4 SD-GSEMO with safety parameter R
Open Source Code No The paper does not provide any statement or link indicating the release of open-source code for the described methodology.
Open Datasets No The paper defines a new theoretical problem ONEJUMPZEROJUMPn,k for analysis and experimentation, rather than using a publicly available dataset in the traditional sense.
Dataset Splits No The paper performs theoretical analyses and simulations on a defined function; it does not mention training/validation/test dataset splits as commonly used for machine learning models.
Hardware Specification No The paper describes its experimental settings for the defined problem but does not specify any hardware details like GPU/CPU models or memory used.
Software Dependencies No The paper does not list specific software components with version numbers needed to replicate the experiments.
Experiment Setup Yes Our experimental settings are the same for all algorithms. ONEJUMPZEROJUMPn,k: jump size k = 4 and problem size n = 10, 14, . . . , 50. β = 1.5 as suggested in (Doerr et al. 2017) for the powerlaw distribution in GSEMO-HTM. R = n for SD-GSEMO and SD-GSEMO-Ind as suggested in (Rajabi and Witt 2020). 20 independent runs for each setting.