ABSTRACT
The Traveling Salesman Problem (TSP) is a difficult permutation-based optimisation problem typically solved using heuristics or meta-heuristics which search the solution problem space. An alternative is to find sets of manipulations to a solution which lead to optimality. Hyper-heuristics search this space applying heuristics sequentially, similar to a program. Genetic Programming (GP) evolves programs typically for classification or regression problems. This paper hypothesizes that GP can be used to evolve heuristic programs to directly solve the TSP. However, evolving a full program to solve the TSP is likely difficult due to required length and complexity. Consequently, a phased GP method is proposed whereby after a phase of generations the best program is saved and executed. The subsequent generation phase restarts operating on this saved program output. A full program is evolved piecemeal. Experiments demonstrate that whilst pure GP cannot solve TSP instances when using simple operators, Phased-GP can obtain solutions within 4% of optimal for TSPs of several hundred cities. Moreover, Phased-GP operates up to nine times faster than pure GP.
- Peter John Angeline. 1994. Genetic programming and emergent intelligence. Advances in genetic programming 1 (1994), 75--98.Google Scholar
- David Applegate, William Cook, and André Rohe. 2003. Chained Lin-Kernighan for large traveling salesman problems. INFORMS Journal on Computing 15, 1 (2003), 82--92.Google ScholarDigital Library
- Markus Brameier and Wolfgang Banzhaf. 2001. A comparison of linear genetic programming and neural networks in medical data mining. IEEE Transactions on Evolutionary Computation 5, 1 (2001), 17--26.Google ScholarDigital Library
- Edmund K Burke, Michel Gendreau, Matthew Hyde, Graham Kendall, Gabriela Ochoa, Ender Özcan, and Rong Qu. 2013. Hyper-heuristics: A survey of the state of the art. Journal of the Operational Research Society 64, 12 (2013), 1695--1724.Google ScholarCross Ref
- Peter Cowling, Graham Kendall, and Eric Soubeiga. 2000. A hyperheuristic approach to scheduling a sales summit. In International conference on the practice and theory of automated timetabling. Springer, 176--190.Google ScholarDigital Library
- Christos Dimopoulos and Ali MS Zalzala. 2001. Investigating the use of genetic programming for a classic one-machine scheduling problem. Advances in engineering software 32, 6 (2001), 489--498.Google Scholar
- Marco Dorigo and Luca Maria Gambardella. 1997. Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on evolutionary computation 1, 1 (1997), 53--66.Google ScholarDigital Library
- Gabriel Duflo, Emmanuel Kieffer, Matthias R Brust, Grégoire Danoy, and Pascal Bouvry. 2019. A GP hyper-heuristic approach for generating TSP heuristics. In 2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). IEEE, 521--529.Google ScholarCross Ref
- John H Holland. 1975. Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press.Google Scholar
- Ahmed Kheiri and Ed Keedwell. 2017. A hidden markov model approach to the problem of heuristic selection in hyper-heuristics with a case study in high school timetabling problems. Evolutionary computation 25, 3 (2017), 473--501.Google Scholar
- John R. Koza. 1992. Genetic Programming.Google Scholar
- Shen Lin. 1965. Computer solutions of the traveling salesman problem. Bell System Technical Journal 44, 10 (1965), 2245--2269.Google ScholarCross Ref
- Su Nguyen, Mengjie Zhang, and Mark Johnston. 2011. A genetic programming based hyper-heuristic approach for combinatorial optimisation. In Proceedings of the 13th annual conference on Genetic and evolutionary computation. 1299--1306.Google ScholarDigital Library
- Patricia Ryser-Welch, Julian F Miller, Jerry Swan, and Martin A Trefzer. 2016. Iterative Cartesian genetic programming: creating general algorithms for solving travelling salesman problems. In Genetic Programming: 19th European Conference, EuroGP 2016, Porto, Portugal, March 30-April 1, 2016, Proceedings 19. Springer, 294--310.Google ScholarCross Ref
- Chee Kiong Soh and Yaowen Yang. 2000. Genetic programming-based approach for structural optimization. Journal of Computing in Civil Engineering 14, 1 (2000), 31--37.Google ScholarCross Ref
- Joc Cing Tay and Nhu Binh Ho. 2008. Evolving dispatching rules using genetic programming for solving multi-objective flexible job-shop problems. Computers & Industrial Engineering 54, 3 (2008), 453--473.Google ScholarDigital Library
Index Terms
- Phased Genetic Programming for Application to the Traveling Salesman Problem
Recommendations
Genetic algorithm for Traveling Salesman Problem
CIIS '22: Proceedings of the 2022 5th International Conference on Computational Intelligence and Intelligent SystemsTraveling Salesman Problem (TSP) is one of the most famous NP-hard problems which is hard to find an optimal solution. Many heuristic algorithms are applied to find a suboptimal solution in a limited time. In this paper, we employ a Genetic Algorithm (...
An Improved Greedy Genetic Algorithm for Solving Travelling Salesman Problem
ICNC '09: Proceedings of the 2009 Fifth International Conference on Natural Computation - Volume 05Genetic algorithm (GA) is too dependent on the initial population and a lack of local search ability. In this paper, an improved greedy genetic algorithm (IGAA) is proposed to overcome the above-mentioned limitations. This novel type of greedy genetic ...
Evolving Construction Heuristics for the Symmetric Travelling Salesman Problem
SAICSIT '16: Proceedings of the Annual Conference of the South African Institute of Computer Scientists and Information TechnologistsThe symmetric travelling salesman problem is a real world combinatorial optimization problem and a well researched domain. When solving combinatorial optimization problems such as the travelling salesman problem a low-level construction heuristic is ...
Comments