Solving multi-objective dynamic travelling salesman problems by relaxation

Ricciardi, Lorenzo A. and Vasile, Massimiliano; López-Ibáñez, Manuel, ed. (2019) Solving multi-objective dynamic travelling salesman problems by relaxation. In: GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference Companion. ACM, CZE, pp. 1999-2007. ISBN 9781450367486 (

[thumbnail of Ricciardi-Vasile-GECCO-2019-Solving-multi-objective-dynamic-travelling-salesman-problems-by-relaxation]
Text. Filename: Ricciardi_Vasile_GECCO_2019_Solving_multi_objective_dynamic_travelling_salesman_problems_by_relaxation.pdf
Accepted Author Manuscript

Download (1MB)| Preview


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.