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Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
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Solving Generalized Vehicle Routing Problem With Occasional Drivers via Evolutionary Multitasking.

Liang Feng, Lei Zhou, Abhishek Gupta

    IEEE Transactions on Cybernetics
    |December 25, 2019
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    Summary
    This summary is machine-generated.

    Incorporating occasional drivers into delivery logistics significantly cuts routing costs. A new algorithm efficiently solves multiple complex delivery problems simultaneously, improving optimization through shared learning.

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    Area of Science:

    • Operations Research
    • Logistics Management
    • Computational Intelligence

    Background:

    • The rise of the sharing economy and crowdshipping necessitates new logistics models.
    • Existing vehicle routing problems (VRP) do not fully account for occasional drivers or vehicle heterogeneity.
    • The vehicle routing problem with occasional drivers (VRPOD) is a recent development addressing these gaps.

    Purpose of the Study:

    • To introduce a generalized variant, the vehicle routing problem with heterogeneous capacity, time window, and occasional driver (VRPHTO).
    • To develop an evolutionary multitasking algorithm (EMA) for simultaneously optimizing multiple VRPHTO instances, inspired by cloud computing's parallel processing needs.

    Main Methods:

    • A novel evolutionary multitasking algorithm (EMA) was designed to handle multiple VRPHTO tasks concurrently using a single population.
    • 56 new VRPHTO instances were created using established vehicle routing benchmarks.
    • Empirical studies compared the EMA's performance against a state-of-the-art single-task solver.

    Main Results:

    • The inclusion of occasional drivers demonstrably reduces overall routing costs.
    • The proposed EMA effectively solves multiple VRPHTO problems simultaneously.
    • EMA achieved superior optimization performance compared to the single-task solver due to inter-task knowledge transfer.

    Conclusions:

    • Occasional drivers offer a significant cost-saving potential in goods delivery.
    • The EMA provides an effective and efficient approach for multitasking in complex optimization problems.
    • Knowledge transfer in multitasking evolutionary algorithms enhances optimization outcomes.