Decomposition in Decision and Objective Space for Multi-Modal Multi-Objective Optimization

• URL: http://arxiv.org/abs/2006.02628v3
• Date: Wed, 3 Feb 2021 16:01:04 GMT
• Title: Decomposition in Decision and Objective Space for Multi-Modal Multi-Objective Optimization
• Authors: Monalisa Pal and Sanghamitra Bandyopadhyay
• Abstract summary: Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set. Prevalent multi-objective evolutionary algorithms are not purely designed to search for multiple solution subsets, whereas, algorithms designed for MMMOPs demonstrate degraded performance in the objective space. This motivates the design of better algorithms for addressing MMMOPs.
• Score: 15.681236469530397
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to the same Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely designed to search for multiple solution subsets, whereas, algorithms designed for MMMOPs demonstrate degraded performance in the objective space. This motivates the design of better algorithms for addressing MMMOPs. The present work identifies the crowding illusion problem originating from using crowding distance globally over the entire decision space. Subsequently, an evolutionary framework, called graph Laplacian based Optimization using Reference vector assisted Decomposition (LORD), is proposed, which uses decomposition in both objective and decision space for dealing with MMMOPs. Its filtering step is further extended to present LORD-II algorithm, which demonstrates its dynamics on multi-modal many-objective problems. The efficacies of the frameworks are established by comparing their performance on test instances from the CEC 2019 multi-modal multi-objective test suite and polygon problems with the state-of-the-art algorithms for MMMOPs and other multi- and many-objective evolutionary algorithms. The manuscript is concluded by mentioning the limitations of the proposed frameworks and future directions to design still better algorithms for MMMOPs. The source code is available at https://worksupplements.droppages.com/lord.

Related papers

• LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning [56.273799410256075]
  The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability.
  arXiv  Detail & Related papers  (2024-10-03T18:12:29Z)
• 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)
• 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 Policy Gradients with Topological Constraints [108.10241442630289]
  We present a new algorithm for a policy gradient in TMDPs by a simple extension of the proximal policy optimization (PPO) algorithm. We demonstrate this on a real-world multiple-objective navigation problem with an arbitrary ordering of objectives both in simulation and on a real robot.
  arXiv  Detail & Related papers  (2022-09-15T07:22:58Z)
• Late Fusion Multi-view Clustering via Global and Local Alignment Maximization [61.89218392703043]
  Multi-view clustering (MVC) optimally integrates complementary information from different views to improve clustering performance. Most of existing approaches directly fuse multiple pre-specified similarities to learn an optimal similarity matrix for clustering. We propose late fusion MVC via alignment to address these issues.
  arXiv  Detail & Related papers  (2022-08-02T01:49:31Z)
• 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)
• A novel multiobjective evolutionary algorithm based on decomposition and multi-reference points strategy [14.102326122777475]
  Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been regarded as a significantly promising approach for solving multiobjective optimization problems (MOPs) We propose an improved MOEA/D algorithm by virtue of the well-known Pascoletti-Serafini scalarization method and a new strategy of multi-reference points.
  arXiv  Detail & Related papers  (2021-10-27T02:07:08Z)
• Manifold Interpolation for Large-Scale Multi-Objective Optimization via Generative Adversarial Networks [12.18471608552718]
  Large-scale multiobjective optimization problems (LSMOPs) are characterized as involving hundreds or even thousands of decision variables and multiple conflicting objectives. Previous research has shown that these optimal solutions are uniformly distributed on the manifold structure in the low-dimensional space. In this work, a generative adversarial network (GAN)-based manifold framework is proposed to learn the manifold and generate high-quality solutions.
  arXiv  Detail & Related papers  (2021-01-08T09:38:38Z)
• A Framework to Handle Multi-modal Multi-objective Optimization in Decomposition-based Evolutionary Algorithms [7.81768535871051]
  decomposition-based evolutionary algorithms have good performance for multi-objective optimization. They are likely to perform poorly for multi-modal multi-objective optimization due to the lack of mechanisms to maintain the solution space diversity. This paper proposes a framework to improve the performance of decomposition-based evolutionary algorithms for multi-modal multi-objective optimization.
  arXiv  Detail & Related papers  (2020-09-30T14:32:57Z)
• Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems [59.804810122136345]
  We propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed. An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed. We show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.
  arXiv  Detail & Related papers  (2020-06-15T02:57:57Z)
• A Decomposition-based Large-scale Multi-modal Multi-objective Optimization Algorithm [9.584279193016522]
  We propose an efficient multi-modal multi-objective optimization algorithm based on the widely used MOEA/D algorithm. Experimental results show that our proposed algorithm can effectively preserve the diversity of solutions in the decision space.
  arXiv  Detail & Related papers  (2020-04-21T09:18:54Z)

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.