### 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 language | English (US) |
---|---|

Article number | 6605565 |

Pages (from-to) | 708-720 |

Number of pages | 13 |

Journal | IEEE Transactions on Evolutionary Computation |

Volume | 18 |

Issue number | 5 |

DOIs | |

State | Published - Oct 1 2014 |

### Fingerprint

### Keywords

- Automated content generation
- evolutionary computation
- games

### ASJC Scopus subject areas

- Software
- Computational Theory and Mathematics
- Theoretical Computer Science

### Cite this

*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.

Research output: Contribution to journal › Article

*IEEE Transactions on Evolutionary Computation*, vol. 18, no. 5, 6605565, pp. 708-720. https://doi.org/10.1109/TEVC.2013.2281508

}

TY - JOUR

T1 - Automated map generation for the physical traveling salesman problem

AU - Perez, Diego

AU - Togelius, Julian

AU - Samothrakis, Spyridon

AU - Rohlfshagen, Philipp

AU - Lucas, Simon M.

PY - 2014/10/1

Y1 - 2014/10/1

N2 - 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.

AB - 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.

KW - Automated content generation

KW - evolutionary computation

KW - games

UR - http://www.scopus.com/inward/record.url?scp=84907807481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907807481&partnerID=8YFLogxK

U2 - 10.1109/TEVC.2013.2281508

DO - 10.1109/TEVC.2013.2281508

M3 - Article

VL - 18

SP - 708

EP - 720

JO - IEEE Transactions on Evolutionary Computation

JF - IEEE Transactions on Evolutionary Computation

SN - 1089-778X

IS - 5

M1 - 6605565

ER -