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Deceptive function

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

An objective-function landscape whose local structure can mislead search away from the global optimum.

A deceptive function has a narrow global minimum and a broad, strong local minimum with a similar value. The local basin can mislead search algorithms away from the best solution. section 2.1.2

Distinguish deceptive landscapes from related optimization cases:

  • Unimodal functions have one clear global optimum. section 2.1.2
  • Multimodal functions contain more than one optimum. section 2.1.2
  • Deceptive functions add a wide attractive basin around a near-global local minimum, increasing the risk of search stagnation. section 2.1.2

Visualizing a deceptive landscape

A Python objective_deceptive(x, y) function combines a narrow trigonometric structure with a broader quadratic term. Plotting its values as a 3D surface alongside unimodal and multimodal functions makes the misleading basin visible.

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines the landscape pattern and visualizes it computationally, but does not develop a specific remedy for deception.
Examples
Uses a Python three-dimensional surface plot comparing unimodal, multimodal, and deceptive objective functions.
What you can do after
Evaluate optimization landscapes by recognizing when a broad local basin can conceal a narrow global optimum.
How it connects
Connects deceptive functions with objective functions, global minima, local minima, unimodal functions, multimodal functions, and search algorithms.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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