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Booth function

As explained in Grokking AI Algorithms, Second Edition

The Booth function is a two-variable mathematical benchmark function with a known global minimum used to evaluate optimization methods.

The Booth function is a two-variable benchmark with a known global minimum, making it a reliable target for checking whether an optimization method reaches the right solution. section 7.8

Particle swarm optimization (PSO) uses it as a visible search landscape: particles move through the space, converge on a region, and are checked against the known target at x=1, y=3. section 7.8

A known target for the drone problem

A drone design treats aluminum and plastic as two variables. The ratio 1:3 produces a fitness value of 0, the minimum, so the swarm's result can be verified rather than guessed. section 7.8

How Grokking AI Algorithms, Second Edition covers it

How deep it goes
Explains the benchmark's role and target point, but defers its mathematical formula and detailed surface construction.
Examples
Uses particle movement, convergence visualizations, and a drone-material ratio of one part aluminum to three parts plastic.
What it assumes
Assumes familiarity with optimization experiments and particle swarms while using a known answer to make correctness intuitive.
What you can do after
Evaluate optimization methods by comparing their discovered solution with the known minimum at x=1, y=3.
How it connects
Connects the Booth function with particle swarm optimization, global minimum, fitness function, search space, and convergence.
Cover of Grokking AI Algorithms, Second Edition
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Grokking AI Algorithms, Second Edition. The section links point to the parts of the book it draws on.