Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems

• URL: http://arxiv.org/abs/2306.03409v1
• Date: Tue, 6 Jun 2023 05:13:29 GMT
• Title: Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems
• Authors: Anh Viet Do, Aneta Neumann, Frank Neumann, Andrew M. Sutton
• Abstract summary: We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. We show that the MOEA/D algorithm, given an appropriate setting, finds all extreme points within expected fixed-objective time in the oracle model.
• Score: 16.803653908913514
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. Using these properties, we give the first run-time analysis of the MOEA/D algorithm for this problem, an evolutionary algorithm that effectively optimizes by decomposing the objectives into single-objective components. We show that the MOEA/D, given an appropriate decomposition setting, finds all extreme points within expected fixed-parameter polynomial time in the oracle model, the parameter being the number of objectives. Experiments are conducted on random bi-objective minimum spanning tree instances, and the results agree with our theoretical findings. Furthermore, compared with a previously studied evolutionary algorithm for the problem GSEMO, MOEA/D finds all extreme points much faster across all instances.

Related papers

• A Simulated Annealing-Based Multiobjective Optimization Algorithm for Minimum Weight Minimum Connected Dominating Set Problem [0.0]
  We propose a simulated algorithm based on a greedy for tackling a variant of the minimum connected dominating set problem. Experimental results compared to those obtained by a recent proposed research show the superiority of our approach.
  arXiv  Detail & Related papers  (2023-12-13T13:36:04Z)
• On Single-Objective Sub-Graph-Based Mutation for Solving the Bi-Objective Minimum Spanning Tree Problem [0.0]
  We contribute to the efficient approximation of the $mathcalNP$-hard multi-objective minimum spanning tree problem (moMST) adopting evolutionary computation. We design several highly biased sub-graph-based mutation operators founded on the gained insights. Our results confirm that the sub-graph based operators beat baseline algorithms from the literature.
  arXiv  Detail & Related papers  (2023-05-31T22:35:17Z)
• Finite-Sum Coupled Compositional Stochastic Optimization: Theory and Applications [43.48388050033774]
  This paper provides a comprehensive analysis of a simple algorithm for both non- and convex objectives. Our analysis also exhibits new insights for improving the practical implementation by sampling batches of equal size for the outer and inner levels.
  arXiv  Detail & Related papers  (2022-02-24T22:39:35Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• 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)
• Analysis of Truncated Orthogonal Iteration for Sparse Eigenvector Problems [78.95866278697777]
  We propose two variants of the Truncated Orthogonal Iteration to compute multiple leading eigenvectors with sparsity constraints simultaneously. We then apply our algorithms to solve the sparse principle component analysis problem for a wide range of test datasets.
  arXiv  Detail & Related papers  (2021-03-24T23:11:32Z)
• Provable Multi-Objective Reinforcement Learning with Generative Models [98.19879408649848]
  We study the problem of single policy MORL, which learns an optimal policy given the preference of objectives. Existing methods require strong assumptions such as exact knowledge of the multi-objective decision process. We propose a new algorithm called model-based envelop value (EVI) which generalizes the enveloped multi-objective $Q$-learning algorithm.
  arXiv  Detail & Related papers  (2020-11-19T22:35:31Z)
• Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization [98.0595480384208]
  We propose a generalization extraient spaces which converges to a stationary point. The algorithm applies not only to general $p$-normed spaces, but also to general $p$-dimensional vector spaces.
  arXiv  Detail & Related papers  (2020-10-31T21:35:42Z)
• Optimizing Monotone Chance-Constrained Submodular Functions Using Evolutionary Multi-Objective Algorithms [11.807734722701786]
  Here the constraint involves components and the constraint can only be violated with a small probability of alpha. We show that the algorithm GSEMO obtains the same worst case performance guarantees for monotone submodular functions. Our experimental results show that the use of evolutionary multi-objective algorithms leads to significant performance improvements.
  arXiv  Detail & Related papers  (2020-06-20T00:17:44Z)
• Convergence of Meta-Learning with Task-Specific Adaptation over Partial Parameters [152.03852111442114]
  Although model-agnostic metalearning (MAML) is a very successful algorithm meta-learning practice, it can have high computational complexity. Our paper shows that such complexity can significantly affect the overall convergence performance of ANIL.
  arXiv  Detail & Related papers  (2020-06-16T19:57:48Z)
• Fast Objective & Duality Gap Convergence for Non-Convex Strongly-Concave Min-Max Problems with PL Condition [52.08417569774822]
  This paper focuses on methods for solving smooth non-concave min-max problems, which have received increasing attention due to deep learning (e.g., deep AUC)
  arXiv  Detail & Related papers  (2020-06-12T00:32:21Z)

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.