Show that the branch-and-bound method will always branch if seven or less variables have been branched on. (In fact, most of the branches have almost all the variables set.) This shows that branch-and-bound can take exponential time. For this problem, many solvers would catch what is happening in preprocessing and find the optimal solution almost immediately.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Solve the following problem and find the optimal solution.

Consider the problem
Minimize:
Subject to:
Y
2x1 +
2x15
2x2 +
+
x1, x2,..., T15, y = {0, 1}
+y< 15
Show that the branch-and-bound method will always branch if seven or less variables have been branched
on. (In fact, most of the branches have almost all the variables set.) This shows that branch-and-bound can
take exponential time. For this problem, many solvers would catch what is happening in preprocessing and
find the optimal solution almost immediately.
Transcribed Image Text:Consider the problem Minimize: Subject to: Y 2x1 + 2x15 2x2 + + x1, x2,..., T15, y = {0, 1} +y< 15 Show that the branch-and-bound method will always branch if seven or less variables have been branched on. (In fact, most of the branches have almost all the variables set.) This shows that branch-and-bound can take exponential time. For this problem, many solvers would catch what is happening in preprocessing and find the optimal solution almost immediately.
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