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Article

A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem

by
Shuli Hu
1,
Huan Liu
1,
Xiaoli Wu
1,
Ruizhi Li
2,*,
Junping Zhou
1,* and
Jianan Wang
1,*
1
School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China
2
School of Management Science and Information Engineering, Jilin University of Finance and Economics, Changchun 130117, China
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(4), 359; https://doi.org/10.3390/math7040359
Submission received: 29 March 2019 / Revised: 11 April 2019 / Accepted: 11 April 2019 / Published: 19 April 2019
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Abstract

Given an undirected, connected and edge-weighted graph, the dominating tree problem consists of finding a tree with minimum total edge weight such that for each vertex is either in the tree or adjacent to a vertex in the tree. In this paper, we propose a hybrid framework combining genetic algorithm with iterated local search (GAITLS) for solving the dominating tree problem. The main components of our framework are as follows: (1) the score functions D s c o r e and W s c o r e applied in the initialization and local search phase; (2) the initialization procedure with restricted candidate list (RCL) by controlling the parameter to balance the greediness and randomness; (3) the iterated local search with three phases, which is used to intensify the individuals; (4) the mutation with high diversity proposed to perturb the population. The experimental results on the classical instances show that our method performs much better than the-state-of-art algorithms.
Keywords: dominating tree; genetic algorithm; iterated local search; score functions dominating tree; genetic algorithm; iterated local search; score functions

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MDPI and ACS Style

Hu, S.; Liu, H.; Wu, X.; Li, R.; Zhou, J.; Wang, J. A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem. Mathematics 2019, 7, 359. https://doi.org/10.3390/math7040359

AMA Style

Hu S, Liu H, Wu X, Li R, Zhou J, Wang J. A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem. Mathematics. 2019; 7(4):359. https://doi.org/10.3390/math7040359

Chicago/Turabian Style

Hu, Shuli, Huan Liu, Xiaoli Wu, Ruizhi Li, Junping Zhou, and Jianan Wang. 2019. "A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem" Mathematics 7, no. 4: 359. https://doi.org/10.3390/math7040359

APA Style

Hu, S., Liu, H., Wu, X., Li, R., Zhou, J., & Wang, J. (2019). A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem. Mathematics, 7(4), 359. https://doi.org/10.3390/math7040359

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