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Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot…
Most combinatorial optimization problems can be formulated as mixed integer linear programming (MILP), in which branch-and-bound (B\&B) is a general and widely used method. Recently, learning to branch has become a hot research topic in the…
Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
Network adaptation is essential for the efficient operation of Cloud-RANs. Unfortunately, it leads to highly intractable mixed-integer nonlinear programming problems. Existing solutions typically rely on convex relaxation, which yield…
Mixed integer linear programs are commonly solved by Branch and Bound algorithms. A key factor of the efficiency of the most successful commercial solvers is their fine-tuned heuristics. In this paper, we leverage patterns in real-world…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
Deriving a good variable selection strategy in branch-and-bound is essential for the efficiency of modern mixed-integer programming (MIP) solvers. With MIP branching data collected during the previous solution process, learning to branch…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
This paper proposes Branch & Learn, a framework for Predict+Optimize to tackle optimization problems containing parameters that are unknown at the time of solving. Given an optimization problem solvable by a recursive algorithm satisfying…
Branch-and-bound is a systematic enumerative method for combinatorial optimization, where the performance highly relies on the variable selection strategy. State-of-the-art handcrafted heuristic strategies suffer from relatively slow…
While Branch and Bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective Branch and Bound methods are only rarely applied compared to the predominant objective space…
There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…
Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern…
Data and knowledge representation are fundamental concepts in machine learning. The quality of the representation impacts the performance of the learning model directly. Feature learning transforms or enhances raw data to structures that…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
Due to the significant increase in the size of spatial data, it is essential to use distributed parallel processing systems to efficiently analyze spatial data. In this paper, we first study learned spatial data partitioning, which…
In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…