With the rapid development of artificial intelligence in recent years,applying various learning techniques to solve mixed-integer linear programming(MILP)problems has emerged as a burgeoning research domain.Apart from...With the rapid development of artificial intelligence in recent years,applying various learning techniques to solve mixed-integer linear programming(MILP)problems has emerged as a burgeoning research domain.Apart from constructing end-to-end models directly,integrating learning approaches with some modules in the traditional methods for solving MILPs is also a promising direction.The cutting plane method is one of the fundamental algorithms used in modern MILP solvers,and the selection of appropriate cuts from the candidate cuts subset is crucial for enhancing efficiency.Due to the reliance on expert knowledge and problem-specific heuristics,classical cut selection methods are not always transferable and often limit the scalability and generalizability of the cutting plane method.To provide a more efficient and generalizable strategy,we propose a reinforcement learning(RL)framework to enhance cut selection in the solving process of MILPs.Firstly,we design feature vectors to incorporate the inherent properties of MILP and computational information from the solver and represent MILP instances as bipartite graphs.Secondly,we choose the weighted metrics to approximate the proximity of feasible solutions to the convex hull and utilize the learning method to determine the weights assigned to each metric.Thirdly,a graph convolutional neural network is adopted with a self-attention mechanism to predict the value of weighting factors.Finally,we transform the cut selection process into a Markov decision process and utilize RL method to train the model.Extensive experiments are conducted based on a leading open-source MILP solver SCIP.Results on both general and specific datasets validate the effectiveness and efficiency of our proposed approach.展开更多
Many important integer and mixed-integer programming problems are difficult to solve.A representative example is unit commitment with combined cycle units and transmission capacity constraints.Complicated transitions ...Many important integer and mixed-integer programming problems are difficult to solve.A representative example is unit commitment with combined cycle units and transmission capacity constraints.Complicated transitions within combined cycle units are difficult to follow,and system-wide coupling transmission capacity constraints are difficult to handle.Another example is the quadratic assignment problem.The presence of cross-products in the objective function leads to nonlinearity.In this study,building upon the novel integration of surrogate Lagrangian relaxation and branch-and-cut,such problems will be solved by relaxing selected coupling constraints.Monotonicity of the relaxed problem will be assumed and exploited and nonlinear terms will be dynamically linearised.The linearity of the resulting problem will be exploited using branch-and-cut.To achieve fast convergence,guidelines for selecting stepsizing parameters will be developed.The method opens up directions for solving nonlinear mixed-integer problems,and numerical results indicate that the new method is efficient.展开更多
基金supported by the National Key R&D Program of China(Grant No.2022YFB2403400)National Natural Science Foundation of China(Grant Nos.11991021 and 12021001)。
文摘With the rapid development of artificial intelligence in recent years,applying various learning techniques to solve mixed-integer linear programming(MILP)problems has emerged as a burgeoning research domain.Apart from constructing end-to-end models directly,integrating learning approaches with some modules in the traditional methods for solving MILPs is also a promising direction.The cutting plane method is one of the fundamental algorithms used in modern MILP solvers,and the selection of appropriate cuts from the candidate cuts subset is crucial for enhancing efficiency.Due to the reliance on expert knowledge and problem-specific heuristics,classical cut selection methods are not always transferable and often limit the scalability and generalizability of the cutting plane method.To provide a more efficient and generalizable strategy,we propose a reinforcement learning(RL)framework to enhance cut selection in the solving process of MILPs.Firstly,we design feature vectors to incorporate the inherent properties of MILP and computational information from the solver and represent MILP instances as bipartite graphs.Secondly,we choose the weighted metrics to approximate the proximity of feasible solutions to the convex hull and utilize the learning method to determine the weights assigned to each metric.Thirdly,a graph convolutional neural network is adopted with a self-attention mechanism to predict the value of weighting factors.Finally,we transform the cut selection process into a Markov decision process and utilize RL method to train the model.Extensive experiments are conducted based on a leading open-source MILP solver SCIP.Results on both general and specific datasets validate the effectiveness and efficiency of our proposed approach.
基金supported by the United States National Science Foundation[grant numbers ECCS-1028870 and ECCS-1509666]and Southern California Edison.
文摘Many important integer and mixed-integer programming problems are difficult to solve.A representative example is unit commitment with combined cycle units and transmission capacity constraints.Complicated transitions within combined cycle units are difficult to follow,and system-wide coupling transmission capacity constraints are difficult to handle.Another example is the quadratic assignment problem.The presence of cross-products in the objective function leads to nonlinearity.In this study,building upon the novel integration of surrogate Lagrangian relaxation and branch-and-cut,such problems will be solved by relaxing selected coupling constraints.Monotonicity of the relaxed problem will be assumed and exploited and nonlinear terms will be dynamically linearised.The linearity of the resulting problem will be exploited using branch-and-cut.To achieve fast convergence,guidelines for selecting stepsizing parameters will be developed.The method opens up directions for solving nonlinear mixed-integer problems,and numerical results indicate that the new method is efficient.
