Solving set covering problems using heuristics with branch and bound
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Solving set covering problems using heuristics with branch and bound by Kook Jin Nam

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Published by Naval Postgraduate School in Monterey, California .
Written in English


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Open LibraryOL25487094M

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  This paper introduces new heuristic and exact methods to solve this problem. We present a new MIP model, propose a novel heuristic algorithm based on beam search, as well as a task-oriented branch-and-bound procedure which uses new reduction rules and lower bounds for solving the by: The post Use branch and bound to solve the partition problem in C# uses the branch and bound technique to solve larger instances of the problem. Branch and bound avoids visiting branches in a search tree if that branch cannot possibly improve the best solution found so far. However, the initial implementation of branch and bound begins by. In this article a branch‐and‐bound algorithm is proposed for solving the quadratic assignment problem. Using symmetric properties of the problem, the algorithm eliminates “mirror image” branches, thus reducing the search effort. Several routines that transform the procedure into an efficient heuristic are also by: We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5, rows.

We present an algorithm for a mixed set covering/partitioning model that includes as special cases the well-known set covering problem and set partitioning problem. The novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm. solve the bidirectional graph-search problem, giving a new unified view of existing solutions, both heuristic and non-heuristic. Finally the application of multiple branch-and-bound is further extended to cover the use of subgoals in graph search and problem solving. Graph searching as a problem area in artificial intelligence is important. Relaxation Heuristics for SCP approximation ratio for SCP have been shown. Feige [27] proved that, for any † > 0, it is impossible to achieve a polynomial time (1¡†)lnn approximation algorithm unless NP has nO(loglogn)-time deterministic algorithms, and Trevisan [46] showed that the problem is hard to approximate within a factor lnd¡O(lnlnd) unless P = NP, where d = maxj2N jSjj. BRANCH-AND-BOUND METHOD Heuristics. BnB choices to be made We are converting a minimum cost vertex cover computation to ILP. • Selection heuristics are best found by experimenting with a large set of problems from the domain.

  Abstract. We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The main characteristics of the algorithm we propose are (1) a dynamic pricing scheme for the variables, akin to that used for solving large-scale LP's, to be coupled with subgradient optimization and greedy algorithms, and (2) the systematic use of column fixing to obtain improved . We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5, rows and 1,, columns, arising from crew scheduling in . In this article we will briefly discuss about the travelling salesman problem and the branch and bound method to solve the same.. What is the problem statement? Travelling Salesman Problem is based on a real life scenario, where a salesman from a company has to start from his own city and visit all the assigned cities exactly once and return to his home till the end of the day. Set Covering Problem Cutting-planes Subgradient Optimization Computation Heuristics Algorithms Branch and Bound Research supported by the National Science Foundation under grant MCS A02 and the Office of Naval Research under contract NC NR