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

Shuli Hu,Xiaoli Wu,Junping Zhou,Ruizhi Li,Jianan Wang,Huan Liu

doi:10.3390/math7040359

Shuli Hu, Xiaoli Wu + Show 4 more

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https://doi.org/10.3390/math7040359

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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.

Highlights

Let G = (V, E, W ) be an undirected, connected and edge-weighted graph, where V is the set of vertexes, E is the set of edges, and W is a non-negative weight function E → R+ associated with edges.We shall use wuv to represent a non-negative weight of each edge (u, v) ∈ E
We propose an effective hybrid framework combining genetic algorithm with iterated local search for dominating tree problem (DTP)
We focus on the framework proposed for solving the DTP, which is a hybrid framework by combining the genetic algorithm with iterated local search

Summary

Introduction

We shall use wuv to represent a non-negative weight of each edge (u, v) ∈ E. The dominating tree problem (DTP) aims to find a dominating tree DT of G with the minimum total edge weight. If the edge weight represents the energy to transfer message from one server to another, the total edge weight in DT equals the total cost of transferring message for multicasting. Another example is that DTP can be modelled using for routing the virtual backbone [4]. Minimizing the energy cost of the routing must be considered

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