# Branch and bound algorithms

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A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set.

** Branch and bound algorithms -principles and examples**

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A large number of real-world planning problems called combinatorial optimization problems share the following properties: They are optimization problems, are easy to state, and have a finite but usually very large number of feasible solutions. While some of these as eg the

** Tree elaboration strategies in branch – and – bound algorithms for solving the quadratic assignment problem**

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This paper presents a new strategy for selecting nodes in a branch – and – bound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies had failed on larger-sized problems. The strategy is a variation

** Branch – and – bound algorithms for stochastic resource-constrained project scheduling**

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We study branch – and – bound algorithms for resource-constrained project scheduling where processing times of jobs are random. The objective is to find a so-called scheduling policy which minimizes the project makespan in expectation. The proposed procedures are based

** Bob: a uni ed platform for implementing branch – and – bound like algorithms **

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In this report, we propose the library BOB for an easy development of the Branch – and – Bound applications (min/maximization). This library has the double goal of allowing on the one hand the Combinatorial Optimization community to implement their applications without

** Branch and bound algorithms for highly constrained integer programs**

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In this paper we describe a new branch and bound algorithm for solving 0-1 integer linear programs (ILP). The algorithm is specifically targeted at ILP instances that are highly constrained, ie instances for which the constraints are hard to satisfy. Our approach is based

** Improved branch and bound algorithms for integer programming**

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I would like to take this opportunity to thank my advisor, John Mitchell, for introducing me to the whole eld of interior point methods and supervising the work that went into this thesis. I would also like to thank the members of the thesis committee, Joe Ecker, George Habetler

** Parallel and distributed branch – and – bound /A* algorithms **

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In this report, we propose new concurrent data structures and load balancing strategies for Branch – and – Bound (BB)/A* algorithms in two models of parallel programming: shared and distributed memory. For the shared memory model (SMM), we present a general

** Experimental comparison of branch – and – bound algorithms for the 1| rj| Lmax problem**

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We consider the problem 1| rj| Lmax. A set N={ , n} of jobs has to be scheduled on a single machine. Each job j∈ N has a processing time pj, a release date rj and a due date dj. Lateness Lj of a job j∈ N in a schedule π is the difference between its completion time and

** Parallel branch – and – bound and parallel PSO algorithms for job shop scheduling problem with blocking**

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In this paper, we deal with the resolution of the scheduling problem with blocking which is known to be non-polynomial-hard. The nature of the workshop defines the type of issue to treat: flow shop problem and job shop problem (JSP). A lot of researches are dedicated in

** Depthfirst search versus jurema search on gpu branch – and – bound algorithms : a case study**

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Abstract Branch – and – Bound (BB) is a general problem solving paradigm and it has been successfully used to prove optimality of combinatorial optimization problems. The development of GPU-based parallel Branch – and – Bound algorithm is a brandnew and

** Visualizing branch – and – bound algorithms **

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We present a suite of tools for visualizing the status and progress of branch – and – bound algorithms for mixed integer programming. By integrating these tools with the open-source codes CBC, SYMPHONY, and GLPK, we demonstrate the potential usefulness of visual

** Branch and bound algorithms for minimizing maximum lateness of trucks at a transshipment terminal**

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This paper focuses on the scheduling of trucks at a transshipment terminal with a single gate. Trucks deliver or pick up a single type of items at the gate and , therefore, increase or decrease, respectively, the inventory level. Naturally, pick up trucks can be served only if the

** A Review of Suboptimal Branch and Bound Algorithms **

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The branch and bound algorithm is an optimal feature selection method that is well-known for its computational efficiency. However, when the dimensionality of the original feature space is large, the execution time required by the branch and bound algorithm becomes

** Efficient algorithms based on branch and bound methods for multi floor facility layout problems**

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We consider multi floor facility layout problems where lmn machines (facility units) are assigned to lmn cells. These cells are arranged into a rectangular pattern with l floors, m rows and n columns. We consider material handling costs and adjacent factors between

** Parallelization of branch – and – bound algorithms in a functional programming environment**

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The referential transparancy of functional languages imposes restraints on the communication between parallel tasks. This seriously hampers the implementation of parallel branch – and – bound algorithms , because the parallel tasks cannot update a shared We consider the determination of a maximizing decision in a fuzzy environment, ie a sequence of controls u,(;,uj, . UN _ such that JlD(U(;, uN- d = max[min(JlcO(uo), , JlcN 1(UN_ d, JlGN(xN)]. The main idea applied is based on the fact that if we consider a sequence of controls

** Branch – and – bound algorithms for the problem of sorting by transpositions**

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In computational biology, genome rearrangements is a field in which we investigate the mutational event of transposition, that moves blocks of genes from a region to another inside a chromosome. This event generates the combinatorial problem of transposition distance

** Solving the school time tabling problem using tabu search, simulated annealing, genetic and branch bound algorithms **

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Using a real world School Time Tabling problem we compare the performance of different optimization algorithms , namely Tabu Search, Simulated Annealing, Genetic Algorithm and Branch Bound . All experiments are being executed using the same problem specification

** POLYNOMIAL TIME CLUSTERING ALGORITHMS DERIVED FROM BRANCH – AND – BOUND TECHNIQUE**

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Optimal clustering can be solved using branch – and – bound technique. The algorithm has exponential time complexity and , therefore, only very small size problem instances can be solved in practice. On the other hand, the branch – and – bound technique provides useful

** Improved branch and bound algorithms for Max-2-SAT and weighted Max-2-SAT**

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We present novel branch and bound algorithms for solving Max-SAT and weighted Max- SAT, and provide experimental evidence that outperform the algorithm of Borchers Furman on Max-2-SAT and weighted Max-2-SAT instances. Our algorithms decrease the