Fast computation of optimal paths in two- and higher-dimension maps

doi:10.1016/0893-6080(90)90078-Y

Neural Networks

Volume 3, Issue 3, 1990, Pages 355-363

https://doi.org/10.1016/0893-6080(90)90078-Y Get rights and content

Abstract

Highly interconnected networks of relatively simple processing elements are shown to be very effective in solving difficult optimization problems. Problems that fall into the broad category of finding a least cost path between two points, given a distributed and sometimes complex cost map, are studied in this paper. A neural-like architecture and associated computational rules are proposed for the solution of this class of optimal path-finding problems in two- and higher-dimensional spaces.

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This paper presents the application of path planning in construction sites according to multiple objectives. It quantitatively evaluates the performance of three optimisation algorithms namely: Dijkstra, A^∗, and Genetic algorithms that are used to find multi-criteria paths in construction sites based on transportation and safety-related cost. During a construction project, site planners need to select paths for site operatives and vehicles, which are characterised by short distance, low risks and high visibility. These path evaluation criteria are combined using a multi-objective approach. The criteria can be optimised to present site planners with the shortest path, the safest path, the most visible path or a path that reflects a combination of short distance, low risk and high visibility. The accuracy of the path solutions and the time complexities of the optimisation algorithms are compared and critically analysed.
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We have developed a new optimal path algorithm in which the paths are subjected to turning constraints. The restriction which we have incorporated is the next link in the path must not make an angle exceeding 45 ° in magnitude with the preceeding link. This algorithm has a natural implementation as an artificial neural system with either synchronous or asynchronous weight updating, and as an automata executing on a massively parallel array processor. At a given step in the path solution process our path planning artificial neural system keeps track of all constrained optimal paths flowing into the nodes of the network. This new algorithm has applications to any path planning problem where the vehicle traveling the path is subject to a limited turning capability. The ability of the network to solve for constrained paths is illustrated with both a graph theoretic example and a scenario involving an unmanned vehicle that must travel a constrained path through a real terrain area containing artificially generated keep out zones.
Computer simulations of path generation and path form modification with local rules working on a parallel cell-based architecture
1994, Computers and Mathematics with Applications
Many mathematical and engineering algorithms are dealing with path finding and path planning problems which arise for a mobile navigating robot or the endeffector of a manipulator. Natural mobile systems, like animals navigating in their everyday surroundings, are faced with the same problems and normally generate adequate solutions. For this reason we performed psychometric experiments with human probands [1,2] to investigate both decision-making and path generation in the case of full information. In this paper we present several methods which can be used to generate path forms roughly comparable to those produced by the human probands. The computer simulations proposed here concentrate on algorithms which use local rules and work upon a parallel, cell-based architecture. On the basis of the ‘dynamic-system metaphor,’ we define a framework for the investigation of several algorithms. A diffusion-algorithm proposed in [3,4] is modified and combined with a so-called relative potential field. This diffusion in potential fields (DIP) provides a method to influence the smoothness of the forms of the path during the development of the gradient field. Once a path has been found, the relative potentials can also help to gradually modulate the first found path with a time-saving mechanism called Tube-Diffusion. In addition to the DIP-algorithm, we investigated two wave-spreading algorithms which generate cost-optimal paths. These are a further development of the path planning approach used in [5] and a new approach which we called Inclusive-Or-algorithm (IOR).
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Original contributionFast computation of optimal paths in two- and higher-dimension maps

Abstract

Journal of Mathematical Analysis and Applications

A note on two problems in connexion graphs

Numerische Mathematik

An appraisal of some short-path algorithms

Operations Research

Computers and intractability: A guide to the theory of NP-completeness

Neural computation of decisions in optimization problems

Biological Cybernetics

Original contribution
Fast computation of optimal paths in two- and higher-dimension maps