Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trends (original) (raw)

Learning to Branch in Mixed Integer Programming

Proceedings of the AAAI Conference on Artificial Intelligence

The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP.Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the MIP instance. Experiments...

Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm

Lecture Notes in Computer Science, 2020

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 instances to learn from scratch a new branching strategy optimised for a given problem and compare it with a commercial solver. We propose FMSTS, a novel Reinforcement Learning approach specifically designed for this task. The strength of our method lies in the consistency between a local value function and a global metric of interest. In addition, we provide insights for adapting known RL techniques to the Branch and Bound setting, and present a new neural network architecture inspired from the literature. To our knowledge, it is the first time Reinforcement Learning has been used to fully optimise the branching strategy. Computational experiments show that our method is appropriate and able to generalise well to new instances.

Improved branch and bound algorithm with a comparison between different LP solvers

2010 9th IEEE/IAS International Conference on Industry Applications, INDUSCON 2010, 2010

This paper presents a comparison of the effectiveness of different linear programming (LP) solvers when used with a branch-and-bound algorithm to find optimal solutions to mixed integer linear problems (MIP). We compare the performance of an improved implementation of the branch-and-bound algorithm with three different LP solvers in order to evaluate each one. We also compare our implementation with other available solvers, to obtain multiple optimal solutions when they exist. The comparison between those different situations was useful in order to prove the robustness and the efficiency of the developed algorithm.

Discovering Branching Rules for Mixed Integer Programming by Computational Intelligence

2015

This thesis introduces two novel search methods for automated design and discovery of heuristic branching rules, employed by the branch-and-bound algorithm for Mixed Integer Programming (MIP). For this experiment, SCIP, an open source MIP solver is used. The rules are specifically designed/trained to be effective at solving the 0-1 Multidimensional Knapsack Problem. A supervised approach is developed, utilizing data collected at the root node of the solution tree, where each instance is solved once for each branching candidate available at the root. Rules are then designed via feature selection with weights inferred through evolutionary search. The resulting branching rules are designed for use at the root node only where the most important branching decisions are made. Another, nonsupervised method, assigns weights to heuristic components selected beforehand. Weights are assigned using (1+1)CMA-ES which evaluates performance by solving every training instance with SCIP. For both me...

A method to improve integer linear programming problem with branch-and-bound procedure

Applied Mathematics and Computation, 2006

Integer linear programming (ILP) problems are harder to solve than linear programming (LP) problems. It doesn't work if try to round off the results of LP problems and claim they are the optimum solution. The branch-and-bound (B&B) is the popular method to solve ILP problems. In this paper, we propose a revised B&B, which is demonstrated to be more efficient most of time. This method is extraordinarily useful when facing ILP problems with large differences between constraints and variables. It could reduce the number of constraint and work efficiently when handling ILP problems with many constraints and less variables. Even if the ILP problems have fewer constraints but many variables, we suggest using duality concept to interchange variables with constraints. Then, the revised B&B could be used to compute results very quickly.

A Note on Branch and Bound Algorithm for Integer Linear Programming

Current Journal of Applied Science and Technology

In branch and bound algorithm for integer linear programming the usual approach is incorporating dual simplex method to achieve feasibility for each sub-problem. Although one can also employ the phase 1 simplex method but the simplicity and easy implementation of the dual simplex method bounds the users to use it. In this paper a new technique for handling sub-problems in branch and bound method has been presented, which is an efficient alternative of dual simplex method.

Adapted branch-and-bound algorithm using SVM with model selection

International Journal of Electrical and Computer Engineering (IJECE), 2019

Branch-and-Bound algorithm is the basis for the majority of solving methods in mixed integer linear programming. It has been proving its efficiency in different fields. In fact, it creates little by little a tree of nodes by adopting two strategies. These strategies are variable selection strategy and node selection strategy. In our previous work, we experienced a methodology of learning branch-and-bound strategies using regression-based support vector machine twice. That methodology allowed firstly to exploit information from previous executions of Branch-and-Bound algorithm on other instances. Secondly, it created information channel between node selection strategy and variable branching strategy. And thirdly, it gave good results in term of running time comparing to standard Branch-and-Bound algorithm. In this work, we will focus on increasing SVM performance by using cross validation coupled with model selection. 1. INTRODUCTION In real life, MILP has countless applications in different fields like logistics, finance and transportation. A very common solution technique of MILP framework is Branch-and-Bound. It continues to prove its relevance nowadays. Branch-and-Bound algorithm is an iterative algorithm, and at each iteration, we eventually get a feasible or optimal solution of an initial problem. Concretely, the algorithm constructs little by little a tree of nodes, where each node represents a modified version of the original problem. The construction of child nodes is conducted by a variable branching strategy. Another fundamental element in Branch-and-Bound algorithm is Node Selection Strategy that aims to choose among a nodes queue, one that will speed up the search. Recently, some works has been trying to identify an analytic approach that decide about strategies described above, given a set of problem features. Authors use likely machine learning techniques. The main remark is that few authors who deal with node selection strategy, and if so, they did not use machine learning framework. Our contribution is oriented towards learning efficient branch-and-bound strategies. This is the result of a consistent methodology beginning with the collection of the data set, and ending with the test of the final hypothesis. More explicitly, we:-Define features-Collect data set-Pick the optimal learning model-Learn the final hypothesis with the chosen model-Implement and test the final hypothesis

Information-based branching schemes for binary linear mixed integer problems

Mathematical Programming Computation, 2009

Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from an incomplete branch-and-bound tree. In particular, we use this information to define new branching rules that reduce the risk of incurring inappropriate branchings. We provide computational results that demonstrate the effectiveness of the new branching rules on various benchmark instances.