Estimation of Distribution Algorithms for the Firefighter Problem
The firefighter problem is a graph-based optimization problem in which the goal is to effectively prevent the spread of a threat in a graph using a limited supply of resources. Recently, metaheuristic approaches to this problem have been proposed, including ant colony optimization and evolutionary algorithms.
In this paper Estimation of Distribution Algorithms (EDAs) are used to solve the FFP. A new EDA is proposed in this paper, based on a model that represents the relationship between the state of the graph and positions that become defended during the simulation of the fire spreading. Another method that is tested in this paper, named EH-PBIL, uses an edge histogram matrix model with the learning mechanism used in the Population-based Incremental Learning (PBIL) algorithm with some modifications introduced in order to make it work better with the FFP. Apart from these two EDAs the paper presents results obtained using two versions of the Mallows model, which is a probabilistic model often used for permutation-based problems. For comparison, results obtained on the same test instances using an Ant Colony Optimization (ACO) algorithm, an Evolutionary Algorithm (EA) and a Variable Neighbourhood Search (VNS) are presented.
The state-position model proposed in this paper works best for graphs with 1000 vertices and more, outperforming the comparison methods. For smaller graphs (with less than 1000 vertices) the VNS works best.
KeywordsEstimation of distribution algorithms Graph-based optimization Firefighter problem
Calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl), grant No. 407.
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