An Efficient Multi-Indicator and Many-Objective Optimization Algorithm based on Two-Archive

• URL: http://arxiv.org/abs/2201.05435v1
• Date: Fri, 14 Jan 2022 13:09:50 GMT
• Title: An Efficient Multi-Indicator and Many-Objective Optimization Algorithm based on Two-Archive
• Authors: Ziming Wang, Xin Yao
• Abstract summary: This paper proposes an indicator-based multi-objective optimization algorithm based on two-archive (SRA3) It can efficiently select good individuals in environment selection based on indicators performance and uses an adaptive parameter strategy for parental selection without setting additional parameters. Experiments on the DTLZ and WFG problems show that SRA3 has good convergence and diversity while maintaining high efficiency.
• Score: 7.7415390727490445
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Indicator-based algorithms are gaining prominence as traditional multi-objective optimization algorithms based on domination and decomposition struggle to solve many-objective optimization problems. However, previous indicator-based multi-objective optimization algorithms suffer from the following flaws: 1) The environment selection process takes a long time; 2) Additional parameters are usually necessary. As a result, this paper proposed an multi-indicator and multi-objective optimization algorithm based on two-archive (SRA3) that can efficiently select good individuals in environment selection based on indicators performance and uses an adaptive parameter strategy for parental selection without setting additional parameters. Then we normalized the algorithm and compared its performance before and after normalization, finding that normalization improved the algorithm's performance significantly. We also analyzed how normalizing affected the indicator-based algorithm and observed that the normalized $I_{\epsilon+}$ indicator is better at finding extreme solutions and can reduce the influence of each objective's different extent of contribution to the indicator due to its different scope. However, it also has a preference for extreme solutions, which causes the solution set to converge to the extremes. As a result, we give some suggestions for normalization. Then, on the DTLZ and WFG problems, we conducted experiments on 39 problems with 5, 10, and 15 objectives, and the results show that SRA3 has good convergence and diversity while maintaining high efficiency. Finally, we conducted experiments on the DTLZ and WFG problems with 20 and 25 objectives and found that the algorithm proposed in this paper is more competitive than other algorithms as the number of objectives increases.

Related papers

• Provably Faster Algorithms for Bilevel Optimization via Without-Replacement Sampling [96.47086913559289]
  gradient-based algorithms are widely used in bilevel optimization. We introduce a without-replacement sampling based algorithm which achieves a faster convergence rate. We validate our algorithms over both synthetic and real-world applications.
  arXiv  Detail & Related papers  (2024-11-07T17:05:31Z)
• Equitable and Fair Performance Evaluation of Whale Optimization Algorithm [4.0814527055582746]
  It is essential that all algorithms are exhaustively, somewhat, and intelligently evaluated. evaluating the effectiveness of optimization algorithms equitably and fairly is not an easy process for various reasons.
  arXiv  Detail & Related papers  (2023-09-04T06:32:02Z)
• Preference Inference from Demonstration in Multi-objective Multi-agent Decision Making [0.0]
  We propose an algorithm to infer linear preference weights from either optimal or near-optimal demonstrations. Empirical results demonstrate significant improvements compared to the baseline algorithms. In future work, we plan to evaluate the algorithm's effectiveness in a multi-agent system.
  arXiv  Detail & Related papers  (2023-04-27T12:19:28Z)
• An Effective and Efficient Evolutionary Algorithm for Many-Objective Optimization [2.5594423685710814]
  We develop an effective evolutionary algorithm (E3A) that can handle various many-objective problems. In E3A, inspired by SDE, a novel population maintenance method is proposed. We conduct extensive experiments and show that E3A performs better than 11 state-of-the-art many-objective evolutionary algorithms.
  arXiv  Detail & Related papers  (2022-05-31T15:35:46Z)
• A Simple Evolutionary Algorithm for Multi-modal Multi-objective Optimization [0.0]
  We introduce a steady-state evolutionary algorithm for solving multi-modal, multi-objective optimization problems (MMOPs) We report its performance on 21 MMOPs from various test suites that are widely used for benchmarking using a low computational budget of 1000 function evaluations.
  arXiv  Detail & Related papers  (2022-01-18T03:31:11Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• Solving Large-Scale Multi-Objective Optimization via Probabilistic Prediction Model [10.916384208006157]
  An efficient LSMOP algorithm should have the ability to escape the local optimal solution from the huge search space. Maintaining the diversity of the population is one of the effective ways to improve search efficiency. We propose a probabilistic prediction model based on trend prediction model and generating-filtering strategy, called LT-PPM, to tackle the LSMOP.
  arXiv  Detail & Related papers  (2021-07-16T09:43:35Z)
• Unified Convergence Analysis for Adaptive Optimization with Moving Average Estimator [75.05106948314956]
  We show that an increasing large momentum parameter for the first-order moment is sufficient for adaptive scaling. We also give insights for increasing the momentum in a stagewise manner in accordance with stagewise decreasing step size.
  arXiv  Detail & Related papers  (2021-04-30T08:50:24Z)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Adaptivity of Stochastic Gradient Methods for Nonconvex Optimization [71.03797261151605]
  Adaptivity is an important yet under-studied property in modern optimization theory. Our algorithm is proved to achieve the best-available convergence for non-PL objectives simultaneously while outperforming existing algorithms for PL objectives.
  arXiv  Detail & Related papers  (2020-02-13T05:42:27Z)

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.