A global optimum is the best valid solution across an entire search space, not just the best one nearby. If the goal is to make a value as small as possible, it is a global minimum; if the goal is to make it as large as possible, it is a global maximum. section 1.9 section 7.2
The best restaurant nearby—or anywhere?
The best restaurant in your neighborhood may be a local best: it wins within the area you searched. To call a restaurant the global best, you would have to compare it with restaurants throughout the entire search space. section 1.9
Finding the least spicy pepper
Imagine plotting pepper size against spiciness and searching the resulting curve from left to right. You encounter several lower points, then a higher one. Stopping because the curve has risen would miss the lowest point, which lies farther to the right. That last point is the global minimum in this example. section 7.2
The distinction matters because real optimization problems can have enormous search spaces. Adding another property, such as pepper color, turns a simple curve into a surface; with more properties, inspecting every possibility becomes impractical. An algorithm’s best result so far is therefore not automatically the global optimum. section 1.9 section 7.2
A known global minimum can also serve as a test target. The Booth function has a known minimum at x = 1, y = 3, so it can be used to check whether a particle swarm optimization run converges on the correct target. In a separate drone example, a 1:3 aluminum-to-plastic ratio gives the fitness function its minimum value of 0. section 7.8
