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Related Concept Videos

Optimization Problems01:26

Optimization Problems

Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...
Lagrange Multipliers: One Constraint01:29

Lagrange Multipliers: One Constraint

In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
Sight Distance in a Vertical Curve01:29

Sight Distance in a Vertical Curve

Sight distance on vertical curves is critical in roadway design. It ensures drivers can see far enough ahead to identify and respond to hazards effectively. This directly impacts safety, driver comfort, and the overall efficiency of the transportation network.Vertical curves are classified into crest and sag curves based on their geometry. For crest curves, sight distance is determined by the line of sight between a driver's eye and a small object on the road's surface. Design parameters for...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

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...
Design Example: Measuring Distance Between Two Points with Obstructions01:10

Design Example: Measuring Distance Between Two Points with Obstructions

When measuring distances in areas with physical obstructions, such as a lake in a field, surveyors must employ techniques to calculate accurate lengths without direct line measurements. One effective method is the offset technique, which allows for precise distance estimation over inaccessible stretches.In this scenario, a surveyor must measure a side of an area that crosses a lake. Since the measuring tape cannot span the lake, the surveyor begins by establishing a baseline that aligns with...

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Related Experiment Video

Updated: Jun 8, 2026

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
11:41

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

Published on: February 1, 2020

Approximate solution of the multiple watchman routes problem with restricted visibility range.

Jan Faigl1

  • 1Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague 6, Czech Republic. xfaigl@labe.felk.cvut.cz

IEEE Transactions on Neural Networks
|September 15, 2010
PubMed
Summary

This study introduces a novel self-organizing map (SOM) method for the multiple watchman route problem with limited visibility. The approach effectively covers polygonal areas, offering a new solution for navigation and surveillance challenges.

Related Experiment Videos

Last Updated: Jun 8, 2026

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
11:41

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

Published on: February 1, 2020

Area of Science:

  • Robotics and Artificial Intelligence
  • Computational Geometry
  • Operations Research

Background:

  • The multiple watchman route problem (MWRP) is crucial for surveillance and exploration in complex environments.
  • Existing solutions often struggle with restricted visibility and dynamic obstacle avoidance.
  • The art gallery problem and traveling salesman problem are related but distinct challenges.

Purpose of the Study:

  • To propose a novel self-organizing map (SOM) based adaptation procedure for the MWRP.
  • To address the MWRP within a polygonal domain (W) under restricted visibility constraints.
  • To develop an efficient method for determining optimal watchman routes.

Main Methods:

  • A new SOM-based adaptation procedure is introduced.
  • Watchman routes are modeled as evolving rings of neuron weights within the domain W.
  • Obstacles are handled using shortest path approximations.
  • The procedure ensures coverage by attracting nodes to uncovered areas.

Main Results:

  • The proposed procedure was experimentally verified across various environments and visibility ranges.
  • Performance was compared against decoupled approaches using art gallery and traveling salesman problem solutions.
  • The SOM-based method demonstrated suitability using simple geometric structures.

Conclusions:

  • The proposed SOM-based adaptation procedure is effective for the MWRP with restricted visibility.
  • The method offers a viable alternative to existing decoupled approaches.
  • SOM principles can be successfully applied to complex watchman route problems.