Automated map generation for the physical traveling salesman problem

Diego Perez, Julian Togelius, Spyridon Samothrakis, Philipp Rohlfshagen, Simon M. Lucas

    Research output: Contribution to journalArticle

    Abstract

    This paper presents a method for generating complex problems that allow multiple nonobvious solutions for the physical traveling salesman problem (PTSP). PTSP is a single-player game adaptation of the classical traveling salesman problem that makes use of a simple physics model: the player has to visit a number of waypoints as quickly as possible by navigating a ship in real time across an obstacle-filled 2-D map. The difficulty of this game depends on the distribution of waypoints and obstacles across the 2-D plane. Due to the physics of the game, the shortest route is not necessarily the fastest, as the ship's momentum makes it difficult to turn sharply at high speed. This paper proposes an evolutionary approach to obtaining maps where the optimal solution is not immediately obvious. In particular, any optimal route for these maps should differ distinctively from: 1) the optimal distance-based TSP route and 2) the route that corresponds to always approaching the nearest waypoint first. To achieve this, the evolutionary algorithm covariance matrix adaptation-evolutionary strategy (CMA-ES) is employed, where maps, indirectly represented as vectors of real numbers, are evolved to differentiate maximally between a game-playing agent that follows two or more different routes. The results presented in this paper show that CMA-ES is able to generate maps that fulfil the desired conditions.

    Original languageEnglish (US)
    Article number6605565
    Pages (from-to)708-720
    Number of pages13
    JournalIEEE Transactions on Evolutionary Computation
    Volume18
    Issue number5
    DOIs
    StatePublished - Oct 1 2014

    Fingerprint

    Traveling salesman problem
    Travelling salesman problems
    Game
    Covariance Matrix Adaptation
    Evolutionary Strategy
    Covariance matrix
    Ship
    Ships
    Physics
    Multiple Solutions
    Differentiate
    Evolutionary algorithms
    Immediately
    Evolutionary Algorithms
    Momentum
    High Speed
    Optimal Solution

    Keywords

    • Automated content generation
    • evolutionary computation
    • games

    ASJC Scopus subject areas

    • Software
    • Computational Theory and Mathematics
    • Theoretical Computer Science

    Cite this

    Perez, D., Togelius, J., Samothrakis, S., Rohlfshagen, P., & Lucas, S. M. (2014). Automated map generation for the physical traveling salesman problem. IEEE Transactions on Evolutionary Computation, 18(5), 708-720. [6605565]. https://doi.org/10.1109/TEVC.2013.2281508

    Automated map generation for the physical traveling salesman problem. / Perez, Diego; Togelius, Julian; Samothrakis, Spyridon; Rohlfshagen, Philipp; Lucas, Simon M.

    In: IEEE Transactions on Evolutionary Computation, Vol. 18, No. 5, 6605565, 01.10.2014, p. 708-720.

    Research output: Contribution to journalArticle

    Perez, D, Togelius, J, Samothrakis, S, Rohlfshagen, P & Lucas, SM 2014, 'Automated map generation for the physical traveling salesman problem', IEEE Transactions on Evolutionary Computation, vol. 18, no. 5, 6605565, pp. 708-720. https://doi.org/10.1109/TEVC.2013.2281508
    Perez, Diego ; Togelius, Julian ; Samothrakis, Spyridon ; Rohlfshagen, Philipp ; Lucas, Simon M. / Automated map generation for the physical traveling salesman problem. In: IEEE Transactions on Evolutionary Computation. 2014 ; Vol. 18, No. 5. pp. 708-720.
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