Stochastic Population Update Provably Needs An Archive in Evolutionary Multi-objective Optimization

• URL: http://arxiv.org/abs/2501.16735v1
• Date: Tue, 28 Jan 2025 06:21:38 GMT
• Title: Stochastic Population Update Provably Needs An Archive in Evolutionary Multi-objective Optimization
• Authors: Shengjie Ren, Zimin Liang, Miqing Li, Chao Qian,
• Abstract summary: We show that using an archive can allow a small population and accelerate the search of SPU-based MOEAs substantially. Specifically, we analyze the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II for solving a commonly studied bi-objective problem OneJumpZero.
• Score: 20.883780207120783
• License:
• Abstract: Evolutionary algorithms (EAs) have been widely applied to multi-objective optimization, due to their nature of population-based search. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. However, recent studies have questioned this practice and shown that stochastic population update (SPU), which allows inferior solutions have a chance to be preserved, can help MOEAs jump out of local optima more easily. While introducing randomness in the population update process boosts the exploration of MOEAs, there is a drawback that the population may not always preserve the very best solutions found, thus entailing a large population. Intuitively, a possible solution to this issue is to introduce an archive that stores the best solutions ever found. In this paper, we theoretically show that using an archive can allow a small population and accelerate the search of SPU-based MOEAs substantially. Specifically, we analyze the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, with SPU for solving a commonly studied bi-objective problem OneJumpZeroJump, and prove that using an archive can bring (even exponential) speedups. The comparison between SMS-EMOA and NSGA-II also suggests that the $(\mu+\mu)$ update mode may be more suitable for SPU than the $(\mu+1)$ update mode. Furthermore, our derived running time bounds for using SPU alone are significantly tighter than previously known ones. Our theoretical findings are also empirically validated on a well-known practical problem, the multi-objective traveling salesperson problem. We hope this work may provide theoretical support to explore different ideas of designing algorithms in evolutionary multi-objective optimization.

Related papers

• Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs [76.43407125275202]
  o1-like models can emulate human-like long-time thinking during inference. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models. We propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy.
  arXiv  Detail & Related papers  (2024-12-30T18:55:12Z)
• A Pairwise Comparison Relation-assisted Multi-objective Evolutionary Neural Architecture Search Method with Multi-population Mechanism [58.855741970337675]
  Neural architecture search (NAS) enables re-searchers to automatically explore vast search spaces and find efficient neural networks. NAS suffers from a key bottleneck, i.e., numerous architectures need to be evaluated during the search process. We propose the SMEM-NAS, a pairwise com-parison relation-assisted multi-objective evolutionary algorithm based on a multi-population mechanism.
  arXiv  Detail & Related papers  (2024-07-22T12:46:22Z)
• An Archive Can Bring Provable Speed-ups in Multi-Objective Evolutionary Algorithms [22.123838452178585]
  We show for the first time, that using an archive can guarantee speed-ups for MOEAs. We prove that for two well-established MOEAs, using an archive brings a acceleration on the expected running time.
  arXiv  Detail & Related papers  (2024-06-04T08:59:16Z)
• Quality-Diversity Algorithms Can Provably Be Helpful for Optimization [24.694984679399315]
  Quality-Diversity (QD) algorithms aim to find a set of high-performing, yet diverse solutions. This paper tries to shed some light on the optimization ability of QD algorithms via rigorous running time analysis.
  arXiv  Detail & Related papers  (2024-01-19T07:40:24Z)
• Towards Running Time Analysis of Interactive Multi-objective Evolutionary Algorithms [23.815981112784552]
  This paper provides the first running time analysis (the essential theoretical aspect of EAs) for practical iMOEAs. We prove that the expected running time of the well-developed interactive NSGA-II for solving the OneMinMax and OneJumpZeroJump problems is $O(n log n)$ and $O(nk)$, respectively.
  arXiv  Detail & Related papers  (2023-10-12T14:57:47Z)
• Bidirectional Looking with A Novel Double Exponential Moving Average to Adaptive and Non-adaptive Momentum Optimizers [109.52244418498974]
  We propose a novel textscAdmeta (textbfADouble exponential textbfMov averagtextbfE textbfAdaptive and non-adaptive momentum) framework. We provide two implementations, textscAdmetaR and textscAdmetaS, the former based on RAdam and the latter based on SGDM.
  arXiv  Detail & Related papers  (2023-07-02T18:16:06Z)
• Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms [23.248796792928204]
  Population update is a key component in multi-objective Evolutionary algorithms (MOEAs) In this paper, we analytically present that population update can be beneficial for the search of MOEAs. Specifically, we prove that the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, for solving two bi-objective problems, OneJumpZero and bi-RoyalRoad, can be exponentially decreased if replacing its deterministic population update mechanism with a randomness one.
  arXiv  Detail & Related papers  (2023-06-05T05:54:56Z)
• Enhancing MAP-Elites with Multiple Parallel Evolution Strategies [8.585387103144825]
  We propose a novel Quality-Diversity (QD) algorithm based on Evolution Strategies (ES) MEMES maintains multiple (up to 100) simultaneous ES processes, each with its own independent objective and reset mechanism designed for QD optimisation. We show that MEMES outperforms both gradient-based and mutation-based QD algorithms on black-box optimisation and QD-Reinforcement-Learning tasks.
  arXiv  Detail & Related papers  (2023-03-10T18:55:02Z)
• Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees [94.72461292387146]
  We propose to reformulate the result diversification problem as a bi-objective search problem, and solve it by a multi-objective evolutionary algorithm (EA) We theoretically prove that the GSEMO can achieve the optimal-time approximation ratio, $1/2$. When the objective function changes dynamically, the GSEMO can maintain this approximation ratio in running time, addressing the open question proposed by Borodin et al.
  arXiv  Detail & Related papers  (2021-10-18T14:00:22Z)
• Harnessing Heterogeneity: Learning from Decomposed Feedback in Bayesian Modeling [68.69431580852535]
  We introduce a novel GP regression to incorporate the subgroup feedback. Our modified regression has provably lower variance -- and thus a more accurate posterior -- compared to previous approaches. We execute our algorithm on two disparate social problems.
  arXiv  Detail & Related papers  (2021-07-07T03:57:22Z)
• Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments [55.24895403089543]
  Domain generalization aims at performing well on unseen test environments with data from a limited number of training environments. We present a new algorithm based on performing iterative feature matching that is guaranteed with high probability to yield a predictor that generalizes after seeing only $O(logd_s)$ environments.
  arXiv  Detail & Related papers  (2021-06-18T04:39:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.