### Abstract

This paper describes a method to solve Multi-objective Dynamic Travelling Salesman Problems. The problems are formulated as multi-objective hybrid optimal control problems, where the choice of the target destination for each phase is an integer variable. The resulting problem has thus a combinatorial nature in addition to being a multi-objective optimal control problem. The overall solution approach is based on a combination of the Multi Agent Collaborative Search, a population based memetic multi-objective optimisation algorithm, and the Direct Finite Elements Transcription, a direct method for optimal control problems. A relaxation approach is employed to transform the mixed integer problem into a purely continuous problem, and a set of smooth constraints is added in order to ensure that the relaxed variables of the final solution assume an integer value. A special set of smooth constraints is introduced in order to treat the mutually exclusive choices of the targets for each phase. The method is tested on two problems: the first is a motorised Travelling salesman problem described in the literature, the second is a space application where a satellite has to de-orbit multiple debris. For the first problem, the approach is generating better solutions than those reported in the literature.

Original language | English |
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Title of host publication | GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference Companion |

Editors | Manuel López-Ibáñez |

Place of Publication | New York |

Pages | 1999-2007 |

Number of pages | 9 |

DOIs | |

Publication status | Published - 13 Jul 2019 |

Event | GECCO 2019: The Genetic and Evolutionary Computation Conference - Prague Conress Centre, Prague, Czech Republic Duration: 13 Jul 2019 → 17 Jul 2019 https://gecco-2019.sigevo.org/index.html/HomePage |

### Conference

Conference | GECCO 2019 |
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Country | Czech Republic |

City | Prague |

Period | 13/07/19 → 17/07/19 |

Internet address |

### Keywords

- multi-objective optimisation
- global optimisation
- optimal control
- mixed integer nonlinear programming
- memetic algorithms
- aerospace

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## Cite this

Ricciardi, L. A., & Vasile, M. (2019). Solving multi-objective dynamic travelling salesman problems by relaxation. In M. López-Ibáñez (Ed.),

*GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference Companion*(pp. 1999-2007). New York. https://doi.org/10.1145/3319619.3326837