1. Basic idea of algorithmThe branch and bound method uses the width first to search the solution space tree, and the Slipknot point is stored in a special table. At the extension node, the husband becomes the node of all sons and discards those sons who lead to non-solvable or suboptimal solutions, and the remaining sons are added to the Slipknot point table. After that, a node is removed from the Slipknot point table as the current extension node in accordance with a rule, and the search continues.
2. ClassificationThe different ways of selecting the next extension node from the Slipknot point table result in different branching and bounding methods. The most common are the following two ways:
(1) Queue-type branching and clearance method
The Slipknot point table is organized into a queue, and the next node is selected as the current extension node according to the FIFO principle. The method of queue branching and clearance is similar to the search method of spatial tree, but the queue-type branch-bound method does not search for the sub-tree of the root of infeasible nodes (which are not likely to lead to feasible solution or optimal solution), so the nodes are not put into the Slipknot point table.
(2) Priority queue-type branch-and-gauge method
The Slipknot point table is organized into a priority queue, giving priority to nodes, and selecting the next node with the highest priority as the current expansion node. The search mode of the priority queue branching and clearance method determines the next extension node based on the priority of the Slipknot point. The priority of a node is usually represented by a value p associated with that node. The maximum priority queue specifies that nodes with large p-values have higher precedence and are typically implemented using a maximum heap. The minimum priority queue specifies that nodes with a lower p-value have higher precedence, typically using a minimal heap.
3, the search of the arrangement tree
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4. Subset Tree Search
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4. Travel Business issues
4.1 Queue-Type branch and gauge method
Process Description:
4.2 Priority queue-type branch and gauge method
Algorithm Description:
4.3 The priority queue-based branching and clearance algorithm for traveling quotient problem
Branching and clearance algorithm
