Maintaining Diversity Provably Helps in Evolutionary Multimodal Optimization

• URL: http://arxiv.org/abs/2406.02658v1
• Date: Tue, 4 Jun 2024 17:52:14 GMT
• Title: Maintaining Diversity Provably Helps in Evolutionary Multimodal Optimization
• Authors: Shengjie Ren, Zhijia Qiu, Chao Bian, Miqing Li, Chao Qian,
• Abstract summary: We show that a simple method that considers diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs) We prove that the proposed method, working with crossover, can help enhance the exploration, leading to multimodal or even exponential acceleration on the expected running time.
• Score: 20.621635722585502
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal problems, a simple method that considers the diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs). Specifically, we prove that the proposed method, working with crossover, can help enhance the exploration, leading to polynomial or even exponential acceleration on the expected running time. This result is derived by rigorous running time analysis in both single-objective and multi-objective scenarios, including $(\mu+1)$-GA solving the widely studied single-objective problem, Jump, and NSGA-II and SMS-EMOA (two well-established multi-objective EAs) solving the widely studied bi-objective problem, OneJumpZeroJump. Experiments are also conducted to validate the theoretical results. We hope that our results may encourage the exploration of diversity maintenance in the solution space for multi-objective optimization, where existing EAs usually only consider the diversity in the objective space and can easily be trapped in local optima.

Related papers

• UCB-driven Utility Function Search for Multi-objective Reinforcement Learning [75.11267478778295]
  In Multi-objective Reinforcement Learning (MORL) agents are tasked with optimising decision-making behaviours. We focus on the case of linear utility functions parameterised by weight vectors w. We introduce a method based on Upper Confidence Bound to efficiently search for the most promising weight vectors during different stages of the learning process.
  arXiv  Detail & Related papers  (2024-05-01T09:34:42Z)
• Achieving Diversity in Objective Space for Sample-efficient Search of Multiobjective Optimization Problems [4.732915763557618]
  We introduce the Likelihood of Metric Satisfaction (LMS) acquisition function, analyze its behavior and properties, and demonstrate its viability on various problems. This method presents decision makers with a robust pool of promising design decisions and helps them better understand the space of good solutions.
  arXiv  Detail & Related papers  (2023-06-23T20:42:22Z)
• Multi-Objective GFlowNets [59.16787189214784]
  We study the problem of generating diverse candidates in the context of Multi-Objective Optimization. In many applications of machine learning such as drug discovery and material design, the goal is to generate candidates which simultaneously optimize a set of potentially conflicting objectives. We propose Multi-Objective GFlowNets (MOGFNs), a novel method for generating diverse optimal solutions, based on GFlowNets.
  arXiv  Detail & Related papers  (2022-10-23T16:15:36Z)
• Multi-Objective Quality Diversity Optimization [2.4608515808275455]
  We propose an extension of the MAP-Elites algorithm in the multi-objective setting: Multi-Objective MAP-Elites (MOME) Namely, it combines the diversity inherited from the MAP-Elites grid algorithm with the strength of multi-objective optimizations. We evaluate our method on several tasks, from standard optimization problems to robotics simulations.
  arXiv  Detail & Related papers  (2022-02-07T10:48:28Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• 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)
• Runtime Analysis of Single- and Multi-Objective Evolutionary Algorithms for Chance Constrained Optimization Problems with Normally Distributed Random Variables [11.310502327308575]
  We study the scenario of components that are independent and normally distributed. We introduce a multi-objective formulation of the problem which trades off the expected cost and its variance. We prove that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem.
  arXiv  Detail & Related papers  (2021-09-13T09:24:23Z)
• An Analysis of Phenotypic Diversity in Multi-Solution Optimization [118.97353274202749]
  We show that multiobjective optimization does not always produce much diversity, multimodal optimization produces higher fitness solutions, and quality diversity is not sensitive to genetic neutrality. An autoencoder is used to discover phenotypic features automatically, producing an even more diverse solution set with quality diversity.
  arXiv  Detail & Related papers  (2021-05-10T10:39:03Z)
• Niching Diversity Estimation for Multi-modal Multi-objective Optimization [9.584279193016522]
  Niching is an important and widely used technique in evolutionary multi-objective optimization. In MMOPs, a solution in the objective space may have multiple inverse images in the decision space, which are termed as equivalent solutions. A general niching mechanism is proposed to make standard diversity estimators more efficient when handling MMOPs.
  arXiv  Detail & Related papers  (2021-01-31T05:23:31Z)
• Hybrid Adaptive Evolutionary Algorithm for Multi-objective Optimization [0.0]
  This paper proposed a new Multi-objective Algorithm as an extension of the Hybrid Adaptive Evolutionary algorithm (HAEA) called MoHAEA. MoHAEA is compared with four states of the art MOEAs, namely MOEA/D, pa$lambda$-MOEA/D, MOEA/D-AWA, and NSGA-II.
  arXiv  Detail & Related papers  (2020-04-29T02:16:49Z)
• Pareto Multi-Task Learning [53.90732663046125]
  Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. It is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other. Recently, a novel method is proposed to find one single Pareto optimal solution with good trade-off among different tasks by casting multi-task learning as multiobjective optimization.
  arXiv  Detail & Related papers  (2019-12-30T08:58:40Z)

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.