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Related Concept Videos

Pareto Chart00:52

Pareto Chart

5.9K
A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the lines represent the cumulative total values. In this chart, the longest bars are arranged on the left and the shortest bars on the right, which makes it easier to read and interpret the data. It can also be called a Pareto diagram or Pareto analysis.
The Pareto chart is named after the Italian economist Vilfredo Pareto, who described the Pareto...
5.9K
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

357
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
357
Response Surface Methodology01:16

Response Surface Methodology

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Response Surface Methodology (RSM) is a collection of statistical and mathematical techniques used to develop, improve, and optimize processes. It is particularly valuable when many input variables or factors potentially influence a response variable.
The process of RSM involves several key steps:
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Flat Belts: Problem Solving01:28

Flat Belts: Problem Solving

1.0K
Flat belts are crucial in many industrial applications as they help transmit power from one pulley to another. The concept of forces and moments is used to determine the maximum moment on a pulley. For instance, consider a flat belt that wraps around two pulleys, A and B, with radii of 30 cm and 10 cm, respectively. The angle between the belt and the horizontal is 20 degrees at the pulleys. As pulley B rotates clockwise and drives pulley A, tension T2 is caused at one end of the belt, while...
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Coplanar Forces01:25

Coplanar Forces

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Consider an object upon which multiple forces are acting. If the lines of action of each force lie within the same plane, the system can be considered coplanar. The Cartesian vector form can be used to resolve each force into its respective components. For a coplanar system, the system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. If the sum of the forces is not equal to zero, then the object will not be in equilibrium...
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Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
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Related Experiment Videos

Active learning of Pareto fronts.

Paolo Campigotto, Andrea Passerini, Roberto Battiti

    IEEE Transactions on Neural Networks and Learning Systems
    |May 9, 2014
    PubMed
    Summary

    This study presents the active learning of Pareto fronts (ALP) algorithm for multiobjective optimization. ALP accurately approximates Pareto fronts using machine learning with reduced computational effort compared to existing methods.

    Area of Science:

    • Multiobjective Optimization
    • Machine Learning
    • Computational Science

    Background:

    • Identifying the Pareto front is crucial for solving multiobjective optimization problems.
    • Existing methods like genetic algorithms can be computationally intensive.
    • Supervised machine learning offers a potential alternative for Pareto front approximation.

    Purpose of the Study:

    • Introduce a novel algorithm for Pareto front recovery: active learning of Pareto fronts (ALP).
    • Frame Pareto front identification as a supervised machine learning task to build an analytical model.
    • Reduce computational effort through an active learning strategy.

    Main Methods:

    • The active learning of Pareto fronts (ALP) algorithm is proposed.
    • ALP treats Pareto front identification as a supervised machine learning problem.

    Related Experiment Videos

  • An active learning strategy selects informative training objective vectors, approximated Pareto-optimal vectors from scalarized problems, to build the model.

    • Main Results:

    • ALP successfully builds an analytical model of the Pareto front.
    • The algorithm achieves accurate Pareto front approximation.
    • ALP demonstrates lower computational effort compared to state-of-the-art estimation of distribution algorithms and genetic techniques.

    Conclusions:

    • The active learning of Pareto fronts (ALP) algorithm is an effective approach for multiobjective optimization.
    • ALP offers a computationally efficient method for Pareto front recovery.
    • This machine learning-based approach provides a competitive alternative to traditional optimization techniques.