Using Statistical Measures and Machine Learning for Graph Reduction to Solve Maximum Weight Clique Problems

Sun, Yuan; Li, Xiaodong; Ernst, Andreas T.

doi:10.1109/tpami.2019.2954827

Cited by 23 publications

(34 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly, machine learning algorithms can be used to reduce the size of an optimization problem before being tackled. For examples, some recent work on employing machine learning techniques to learn from known instances that contain optimal solutions in order to reduce the problem first, without losing the optimal solutions [247,248].…”

Section: B Potential Areas For Future Researchmentioning

confidence: 99%

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part II

Omidvar

Yao

2022

IEEE Trans. Evol. Computat.

Self Cite

View full text Add to dashboard Cite

This paper is the second part of a two-part survey series on large-scale global optimization. The first part covered two major algorithmic approaches to large-scale optimization, namely decomposition methods and hybridization methods such as memetic algorithms and local search. In this part we focus on sampling and variation operators, approximation and surrogate modeling, initialization methods, and parallelization. We also cover a range of problem areas in relation to large-scale global optimization, such as multi-objective optimization, constraint handling, overlapping components, the component imbalance issue, and benchmarks, and applications. The paper also includes a discussion on pitfalls and challenges of current research and identifies several potential areas of future research.

show abstract

Section: B Potential Areas For Future Researchmentioning

confidence: 99%

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part II

Omidvar

Yao

2022

IEEE Trans. Evol. Computat.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Those hints include warm start information, additional constraints to the problem and identified admissible regions that may contain the optimal solution. A similar principle based on Support Vector Machines is also applied by Sun et al (2019). A very interesting approach has been proposed by the authors of Lodi et al (2019).…”

Section: And Optimizationmentioning

confidence: 99%

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

et al. 2021

View full text Add to dashboard Cite

Planning of operations, such as routing of vehicles, is often performed repetitively in rea-world settings, either by humans or algorithms solving mathematical problems. While humans build experience over multiple executions of such planning tasks and are able to recognize common patterns in different problem instances, classical optimization algorithms solve every instance independently. Machine learning (ML) can be seen as a computational counterpart to the human ability to recognize patterns based on experience. We consider variants of the classical Vehicle Routing Problem with Time Windows and Capacitated Vehicle Routing Problem, which are based on the assumption that problem instances follow specific common patterns. For this problem, we propose a ML-based branch and price framework which explicitly utilizes those patterns. In this context, the ML models are used in two ways: (a) to predict the value of binary decision variables in the optimal solution and (b) to predict branching scores for fractional variables based on full strong branching. The prediction of decision variables is then integrated in a node selection policy, while a predicted branching score is used within a variable selection policy. These ML-based approaches for node and variable selection are integrated in a reliability-based branching algorithm that assesses their quality and allows for replacing ML approaches by other (classical) better performing approaches at the level of specific variables in each specific instance. Computational results show that our algorithms outperform benchmark branching strategies. Further, we demonstrate that our approach is robust with respect to small changes in instance sizes.

show abstract

“…We describe those features in Appendix A. Given the training data, an ML model can be trained by minimising the crossentropy loss function [14] to separate the training examples with different class labels [10], [11].…”

Section: A Solution Predictionmentioning

confidence: 99%

“…Khalil et al [9] train an SVM model to select which primal heuristic to run at a certain sub-problem. More related to our work here, Sun et al [10] and Ding et al [11] leverage ML to predict values of decision variables in the optimal solution, which are then used to fix a proportion of decision variables to reduce the size of the original problem, in the hope that the reduced space still contains the optimal solution of the original problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Learning Primal Heuristics for Mixed Integer Programs

Shen

Sun

Eberhard

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper proposes a novel primal heuristic for Mixed Integer Programs, by employing machine learning techniques. Mixed Integer Programming is a general technique for formulating combinatorial optimization problems. Inside a solver, primal heuristics play a critical role in finding good feasible solutions that enable one to tighten the duality gap from the outset of the Branch-and-Bound algorithm (B&B), greatly improving its performance by pruning the B&B tree aggressively. In this paper, we investigate whether effective primal heuristics can be automatically learned via machine learning. We propose a new method to represent an optimization problem as a graph, and train a Graph Convolutional Network on solved problem instances with known optimal solutions. This in turn can predict the values of decision variables in the optimal solution for an unseen problem instance of a similar type. The prediction of variable solutions is then leveraged by a novel configuration of the B&B method, Probabilistic Branching with guided Depthfirst Search (PB-DFS) approach, aiming to find (near-)optimal solutions quickly. The experimental results show that this new heuristic can find better primal solutions at a much earlier stage of the solving process, compared to other state-of-the-art primal heuristics.

show abstract

Using Statistical Measures and Machine Learning for Graph Reduction to Solve Maximum Weight Clique Problems

Cited by 23 publications

References 44 publications

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part II

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part II

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

Learning Primal Heuristics for Mixed Integer Programs

Contact Info

Product

Resources

About