Learning Combined Set Covering and Traveling Salesman Problem

• URL: http://arxiv.org/abs/2007.03203v1
• Date: Tue, 7 Jul 2020 05:11:28 GMT
• Title: Learning Combined Set Covering and Traveling Salesman Problem
• Authors: Yuwen Yang, Jayant Rajgopal
• Abstract summary: We study a combined Set Covering and Traveling Salesman problem and provide a mixed integer programming formulation to solve the problem. Motivated by applications where the optimal policy needs to be updated on a regular basis, we propose a machine learning approach to effectively deal with this problem.
• Score: 2.0407204637672893
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it raises even more issues related to tractability and scalability. We study a combined Set Covering and Traveling Salesman problem and provide a mixed integer programming formulation to solve the problem. Motivated by applications where the optimal policy needs to be updated on a regular basis and repetitively solving this via MIP can be computationally expensive, we propose a machine learning approach to effectively deal with this problem by providing an opportunity to learn from historical optimal solutions that are derived from the MIP formulation. We also present a case study using the vaccine distribution chain of the World Health Organization, and provide numerical results with data derived from four countries in sub-Saharan Africa.

Related papers

• Autoformulation of Mathematical Optimization Models Using LLMs [50.030647274271516]
  We develop an automated approach to creating optimization models from natural language descriptions for commercial solvers. We identify the three core challenges of autoformulation: (1) defining the vast, problem-dependent hypothesis space, (2) efficiently searching this space under uncertainty, and (3) evaluating formulation correctness.
  arXiv  Detail & Related papers  (2024-11-03T20:41:38Z)
• Problem Categorization Can Help Large Language Models Solve Math Problems [0.0]
  We show the effectiveness of using the classification of problems into different categories to facilitate problem-solving. We also optimize the classification of problems into categories by creating an accurate dataset.
  arXiv  Detail & Related papers  (2024-10-29T16:06:26Z)
• AI-Copilot for Business Optimisation: A Framework and A Case Study in Production Scheduling [3.522755287096529]
  We propose an AI-Copilot for business optimisation problem formulation. For token limitations, we introduce modularization and prompt engineering techniques. We design performance evaluation metrics that are better suited for assessing the accuracy and quality of problem formulations.
  arXiv  Detail & Related papers  (2023-09-22T23:45:21Z)
• A Survey for Solving Mixed Integer Programming via Machine Learning [76.04988886859871]
  This paper surveys the trend of machine learning to solve mixed integer (MIP) problems. In this paper, we first introduce the formulation and preliminaries of MIP and several traditional algorithms to solve MIP. Then, we advocate further promoting the different integration of machine learning and MIP algorithms.
  arXiv  Detail & Related papers  (2022-03-06T05:03:37Z)
• The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights [59.93939636422896]
  The ML4CO aims at improving state-of-the-art optimization solvers by replacing key components. The competition featured three challenging tasks: finding the best feasible solution, producing the tightest optimality certificate, and giving an appropriate routing configuration.
  arXiv  Detail & Related papers  (2022-03-04T17:06:00Z)
• Minimizing Entropy to Discover Good Solutions to Recurrent Mixed Integer Programs [0.0]
  Current solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. Recent works have shown that machine learning (ML) can be integrated with an MIP solver to inject domain knowledge and efficiently close the optimality gap. This paper proposes an online solver that uses the notion of entropy to efficiently build a model with minimal training data and tuning.
  arXiv  Detail & Related papers  (2022-02-07T18:52:56Z)
• 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)
• Learning Mixed-Integer Linear Programs from Contextual Examples [37.56298025474654]
  Mixed-integer linear programs (MILPs) are widely used in artificial intelligence and operations research. In this paper, we study the problem of acquiring MILPs from contextual examples. We also contribute MISSLE, an algorithm for learning MILPs from contextual examples.
  arXiv  Detail & Related papers  (2021-07-15T05:45:52Z)
• A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems [54.61091936472494]
  We develop a two-stage framework, in which reinforcement learning (RL) and traditional operations research (OR) algorithms are combined together. The scheduling problem is solved in two stages, including a finite Markov decision process (MDP) and a mixed-integer programming process, respectively. Results show that the proposed algorithms could stably and efficiently obtain satisfactory scheduling schemes for agile Earth observation satellite scheduling problems.
  arXiv  Detail & Related papers  (2021-03-10T03:16:12Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

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.