Accelerating the Branch-and-Price Algorithm Using Machine Learning

Václavík, Roman; Novák, Antonín; Šůcha, Přemysl; Hanzálek, Zdeněk

doi:10.1016/j.ejor.2018.05.046

Cited by 42 publications

(13 citation statements)

References 25 publications

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“…Traditional algorithms for scheduling problems can be summarised into three categories: mathematical programming, heuristic algorithms, and metaheuristic algorithms. Mathematical programming such as branch-and-bound [24], branch-and-price [25], and dynamic programming [26] guarantee the optimal solution under certain assumptions, but the time complexity of these algorithms is usually exponential. Therefore, they are usually time-consuming and space-consuming in dealing with large scale problems.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In the above model, the objective function is to maximize the sum of the profit of all scheduled tasks, which as (22). Inequality (23) to (25) affiliate to constraints in the prior stage, while (26) to (30) belong to that of the rear stage.…”

Section: A Definition Of Aeos Scheduling Problemmentioning

confidence: 99%

“…Constraints (23) refers that a task is scheduled at most once; (24) and (25) shows the capacity constraints of the AEOSs with respect to energy and storage. (26) and (27) indicate that all tasks should be executed in one of their ETWs.…”

Section: A Definition Of Aeos Scheduling Problemmentioning

confidence: 99%

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A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems

He,

Wu,

Chen

et al. 2021

Preprint

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There hardly exists a general solver that is efficient for scheduling problems due to their diversity and complexity. In this study, we develop a two-stage framework, in which reinforcement learning (RL) and traditional operations research (OR) algorithms are combined together to efficiently deal with complex scheduling problems. The scheduling problem is solved in two stages, including a finite Markov decision process (MDP) and a mixed-integer programming process, respectively. This offers a novel and general paradigm that combines RL with OR approaches to solving scheduling problems, which leverages the respective strengths of RL and OR: The MDP narrows down the search space of the original problem through an RL method, while the mixed-integer programming process is settled by an OR algorithm. These two stages are performed iteratively and interactively until the termination criterion has been met. Under this idea, two implementation versions of the combination methods of RL and OR are put forward. The agile Earth observation satellite scheduling problem is selected as an example to demonstrate the effectiveness of the proposed scheduling framework and methods. The convergence and generalization capability of the methods are verified by the performance of training scenarios, while the efficiency and accuracy are tested in 50 untrained scenarios. The results show that the proposed algorithms could stably and efficiently obtain satisfactory scheduling schemes for agile Earth observation satellite scheduling problems. In addition, it can be found that RL-based optimization algorithms have stronger scalability than non-learning algorithms. This work reveals the advantage of combining reinforcement learning methods with heuristic methods or mathematical programming methods for solving complex combinatorial optimization problems.

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Section: Literature Reviewmentioning

confidence: 99%

Section: A Definition Of Aeos Scheduling Problemmentioning

confidence: 99%

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A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems

He,

Wu,

Chen

et al. 2021

Preprint

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“…[50] demonstrated the use of a constraint programming solver on the pricing problem in their approach but again the maximum sized problems they solved was four weeks. Other ways of speeding up branch and price methods include stabilisation in the column generation such as demonstrated in [23], or using a regression model to try and predict upper bounds in the pricing problem [51]. Another possible improvement is to combine branch and price with a metaheuristic.…”

Section: Literature Reviewmentioning

confidence: 99%

First-order linear programming in a column generation-based heuristic approach to the nurse rostering problem

Strandmark¹,

Curtois²

2020

Computers & Operations Research

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Highlights A fast, column generation based heuristic method for the nurse rostering problem.  It is effective on large instances and found best known solutions on benchmark tests.  A low-accuracy but fast, first-order linear programming method is used.  It is compared against the state-of-the-art, previously published methods.  The source code for the algorithms is available on-line.

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“…If the size is changed, a new neural network must be trained. Another method, which does not directly predict a solution to the given instance, is proposed in (Václavík et al, 2018). In this case, an online ML technique is integrated into an exact algorithm where it acts as a heuristic.…”

Section: Machine Learning Integration To Combinatorial Optimization Pmentioning

confidence: 99%

Data-driven Algorithm for Scheduling with Total Tardiness

Bouška

Novák

Šůcha

et al. 2020

Proceedings of the 9th International Conference on Operations Research and Enterprise Systems

Self Cite

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In this paper, we investigate the use of deep learning for solving a classical N P -hard single machine scheduling problem where the criterion is to minimize the total tardiness. Instead of designing an end-to-end machine learning model, we utilize well known decomposition of the problem and we enhance it with a data-driven approach. We have designed a regressor containing a deep neural network that learns and predicts the criterion of a given set of jobs. The network acts as a polynomial-time estimator of the criterion that is used in a singlepass scheduling algorithm based on Lawler's decomposition theorem. Essentially, the regressor guides the algorithm to select the best position for each job. The experimental results show that our data-driven approach can efficiently generalize information from the training phase to significantly larger instances (up to 350 jobs) where it achieves an optimality gap of about 0.5%, which is four times less than the gap of the state-of-the-art NBR heuristic. d https://orcid.org/0000-0003-4692-1625 e https://orcid.org/0000-0002-8135-1296 jobs, which is significantly more than, e.g., an end-toend approach (Vinyals et al., 2015) that solves Traveling Salesman Problem with about 50 nodes. Our proposed approach outperforms the state-of-the-art heuristic for SMTTP.

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Accelerating the Branch-and-Price Algorithm Using Machine Learning

Cited by 42 publications

References 25 publications

A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems

A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems

First-order linear programming in a column generation-based heuristic approach to the nurse rostering problem

Data-driven Algorithm for Scheduling with Total Tardiness

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