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To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:Calculate Effective Upstream Velocity:When the downstream gate closes, a hydraulic jump forms, traveling upstream at 2 meters per second. This wave speed combines with the initial channel flow velocity, creating an effective upstream velocity.Identify Flow Velocities Before and After the Hydraulic Jump:Upstream of the hydraulic jump, the effective flow velocity includes both the...
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Trigonometric and exponential functions are essential mathematical tools used to model distinct types of real-world behavior, particularly in periodic and growth-related phenomena. These functions extend the capabilities of basic algebraic models by capturing recurring cycles and rapid changes across various scientific and engineering contexts.Trigonometric functions, such as sine and cosine, are particularly effective for representing periodic phenomena. Their cyclic behavior makes them...
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Importance of Jumping Ability in Handball Throwing Speed and Accuracy
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Unbiased Black-Box Complexities of Jump Functions.

Benjamin Doerr1, Carola Doerr2, Timo Kötzing3

  • 1École Polytechnique, Palaiseau, France.

Evolutionary Computation
|July 3, 2015
PubMed
Summary

This study reveals that unbiased black-box optimization algorithms can efficiently solve complex jump functions, even those with large plateaus. Efficient algorithms exist even for extreme jump functions, challenging previous assumptions.

Keywords:
Black-box complexityruntime analysistheory

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Optimization

Background:

  • Black-box optimization problems often feature fitness plateaus, which can significantly hinder algorithm performance.
  • Understanding the complexity of these problems is crucial for developing efficient optimization strategies.

Purpose of the Study:

  • To analyze the unbiased black-box complexities of jump functions with varying fitness plateau sizes.
  • To investigate the existence and efficiency of optimization algorithms for challenging jump functions.

Main Methods:

  • Analysis of unbiased black-box complexities for jump functions.
  • Development of new analytical tools, including parent selection based on empirical expected offspring fitness.
  • Evaluation of algorithms on jump functions with small, medium, and large fitness plateaus.

Main Results:

  • Unbiased black-box complexities for jump functions with a (1/2 - ε) jump size are comparable to the OneMax function for arities 3 and higher.
  • Polynomial time mutation-based algorithms are shown to exist even for the extreme jump function.
  • The presence of large fitness plateaus does not necessarily preclude efficient optimization.

Conclusions:

  • Efficient unbiased black-box optimization is achievable for a wider range of jump functions than previously thought.
  • New analytical techniques provide deeper insights into the complexities of black-box optimization.
  • The findings challenge the notion that large fitness plateaus inherently lead to intractable optimization problems.