An Automatic Method of Solving Discrete Programming Problems

By A. Land, A. Doig. 1960

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Citations in the corpus

Optimal Generalized Decision Trees via Integer Programming (2016, methodology): “While ﬁnding an optimal DT (even without the generalized decisions) is known to be an NP-hard problem, that does not mean that it is always impractical to try to solve this problem using the modern techniques that have gone way beyond simple Branch & Bound (B & B) enumeration [7].”
Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization (2013, background): “A common approach to try to address bigger problems is to do an implicit enumeration via a branch-and-bound algorithm [24,25].”
Solving Mixed Integer Programs Using Neural Networks (2020, methodology): “MIP solvers use a form of tree search over integer variables called branch-and-bound (Land and Doig 1960) (see section 2), which progressively tightens the bound and helps find feasible assignments.”
Complete search in continuous global optimization and constraint satisfaction (2004, background): “The branch and bound principle is a general label (invented in Land and Doig (1960) and Little et al. (1963)) to denote methods to split a problem recursively into subproblems which are sooner or later eliminated by showing that the subproblem cannot lead to a point better than (or as least as good…”
State-Of-The-Art Review of Mathematical Optimisation Approaches for Synthesis of Energy Systems (2017, unknown): “On the other hand, MILP problems are solved via the branch-and-bound algorithm developed by Land and Doig (1960).”
Real-time loop closure in 2D LIDAR SLAM (2016, methodology): “This approach was first suggested in the context of mixed integer linear programs [17].”
Hyperparameter Search Space Pruning - A New Component for Sequential Model-Based Hyperparameter Optimization (2015, methodology): “Branch-and-Bound [18] is a pruning technique that is applied in the domain of operations research for discrete and combinatorial optimization problems and is very common for NP-hard optimization problems [17].”
Tree Species Classification in Boreal Forests With Hyperspectral Data (2013, background): “Among all of the search algorithms present in the literature, such as the branch and bound [26], the steepest ascent [27], and the sequential”
The Ant Lion Optimizer (2015, unknown): “A deterministic algorithm [5–7] reliably determines the same answer for a given problem with a similar initial starting point.”
A Computational Study of Search Strategies for Mixed Integer Programming (1999, methodology): “However, the idea of using a branch and bound algorithm for integer programming using linear programming relaxations was proposed somewhat earlier by Land and Doig 26].”
Primer3—new capabilities and interfaces (2012, background): “It uses ‘branch and bound’ techniques (23) to reduce the search space while still generating the optimal primer pairs according to the penalty function and constraints.”
Combinatorial optimization and reasoning with graph neural networks (2021, methodology): “4 Exact methods ILP models are generally solved to proven optimality (or proof of infeasibility) by variations of the branch-and-bound algorithm (Land and Doig, 1960; Lodi, 2010).”
Mixed-integer nonlinear optimization*† (2013, methodology): “Like depth-first search, this strategy has also been used since the very first branch-and-bound algorithms (Land and Doig, 1960; Lawler and Woods, 1966).”
A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2013, methodology): “This search can be based like in EGRA [5] on an optimisation method such as the branch-and-bound discrete technique [23] and the DIRECT algorithm [24].”