Local Optima Correlation Assisted Adaptive Operator Selection

• URL: http://arxiv.org/abs/2305.02805v1
• Date: Wed, 3 May 2023 13:25:41 GMT
• Title: Local Optima Correlation Assisted Adaptive Operator Selection
• Authors: Jiyuan Pei, Hao Tong, Jialin Liu, Yi Mei, Xin Yao
• Abstract summary: We propose to empirically analyse the relationship between operators in terms of the correlation between their local optima. Based on this newly proposed local optima correlation metric, we propose a novel approach for adaptively selecting among the operators during the search process.
• Score: 4.983846689106013
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between operators for various purposes, e.g., adaptively deciding when to use which operator to find optimal solutions efficiently. However, it is difficult to theoretically analyse this relationship, especially in the complex solution space of combinatorial optimisation problems. In this paper, we propose to empirically analyse the relationship between operators in terms of the correlation between their local optima and develop a measure for quantifying their relationship. The comprehensive analyses on a wide range of capacitated vehicle routing problem benchmark instances show that there is a consistent pattern in the correlation between commonly used operators. Based on this newly proposed local optima correlation metric, we propose a novel approach for adaptively selecting among the operators during the search process. The core intention is to improve search efficiency by preventing wasting computational resources on exploring neighbourhoods where the local optima have already been reached. Experiments on randomly generated instances and commonly used benchmark datasets are conducted. Results show that the proposed approach outperforms commonly used adaptive operator selection methods.

Related papers

• Feature-Based Interpretable Surrogates for Optimization [0.8437187555622164]
  In this work, we investigate how we can use more general optimization rules to increase interpretability. The proposed rules do not map to a concrete solution but to a set of solutions characterized by common features. In particular, we demonstrate the improvement in solution quality that our approach offers compared to existing interpretable surrogates for optimization.
  arXiv  Detail & Related papers  (2024-09-03T13:12:49Z)
• Modeling Local Search Metaheuristics Using Markov Decision Processes [0.0]
  We introduce a theoretical framework based on Markov Decision Processes (MDP) for analyzing local search metaheuristics. This framework not only helps in providing convergence results for individual algorithms, but also provides an explicit characterization of the exploration-exploitation tradeoff.
  arXiv  Detail & Related papers  (2024-07-29T11:28:30Z)
• Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems [61.580419063416734]
  A recent stream of structured learning approaches has improved the practical state of the art for a range of optimization problems. The key idea is to exploit the statistical distribution over instances instead of dealing with instances separately. In this article, we investigate methods that smooth the risk by perturbing the policy, which eases optimization and improves the generalization error.
  arXiv  Detail & Related papers  (2024-07-24T12:00:30Z)
• Distributed Fractional Bayesian Learning for Adaptive Optimization [7.16937736207894]
  This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter. We aim to provide valuable insights for addressing parameter uncertainty in distributed optimization problems and simultaneously find the optimal solution.
  arXiv  Detail & Related papers  (2024-04-17T13:09:33Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Optimizer Amalgamation [124.33523126363728]
  We are motivated to study a new problem named Amalgamation: how can we best combine a pool of "teacher" amalgamations into a single "student" that can have stronger problem-specific performance? First, we define three differentiable mechanisms to amalgamate a pool of analyticals by gradient descent. In order to reduce variance of the process, we also explore methods to stabilize the process by perturbing the target.
  arXiv  Detail & Related papers  (2022-03-12T16:07:57Z)
• 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)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems [9.015720257837575]
  We consider the regression between spaces, aiming to infer high-quality optimization solutions from samples of input-solution pairs. For learning foundations, we present learning-error analysis under the PAC-Bayesian framework. We obtain highly encouraging experimental results for several classic problems on both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-07-15T17:59:08Z)
• Local policy search with Bayesian optimization [73.0364959221845]
  Reinforcement learning aims to find an optimal policy by interaction with an environment. Policy gradients for local search are often obtained from random perturbations. We develop an algorithm utilizing a probabilistic model of the objective function and its gradient.
  arXiv  Detail & Related papers  (2021-06-22T16:07:02Z)
• Multi-layer local optima networks for the analysis of advanced local search-based algorithms [0.6299766708197881]
  Local Optima Network (LON) is a graph model that compresses the fitness landscape of a particular optimization problem based on a specific neighborhood operator and a local search algorithm. This paper proposes the concept of multi-layer LONs as well as a methodology to explore these models aiming at extracting metrics for fitness landscape analysis.
  arXiv  Detail & Related papers  (2020-04-29T03:20:01Z)

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.