Discrete Applied Mathematics
Resolvability in graphs and the metric dimension of a graph
Discrete Applied Mathematics
Swarm intelligence
Tabu Search
A Memetic Algorithm for Minimum-Cost Vertex-Biconnectivity Augmentation of Graphs
Journal of Heuristics
Ant Colony Optimization
Advanced fitness landscape analysis and the performance of memetic algorithms
Evolutionary Computation - Special issue on magnetic algorithms
A tabu search algorithm for the quadratic assignment problem
Computational Optimization and Applications
Many hard examples in exact phase transitions
Theoretical Computer Science
On the Metric Dimension of Cartesian Products of Graphs
SIAM Journal on Discrete Mathematics
Improving graph colouring algorithms and heuristics using a novel representation
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
The core concept for the multidimensional knapsack problem
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
Computing minimal doubly resolving sets of graphs
Computers and Operations Research
An ILP formulation and genetic algorithm for the Maximum Degree-Bounded Connected Subgraph problem
Computers & Mathematics with Applications
An evolutionary-based approach for solving a capacitated hub location problem
Applied Soft Computing
On the metric dimension of infinite graphs
Discrete Applied Mathematics
Discrete Applied Mathematics
| Hi-index | 0.00 |
In this paper we consider the NP-hard problem of determining the metric dimension of graphs. We propose a genetic algorithm (GA) that uses the binary encoding and the standard genetic operators adapted to the problem. The feasibility is enforced by repairing the individuals. The overall performance of the GA implementation is improved by a caching technique. Since the metric dimension problem up to now has been considered only theoretically, standard test instances for this problem do not exist. For that reason, we present the results of the computational experience on several sets of test instances for other NP-hard problems: pseudo boolean, crew scheduling and graph coloring. Testing on instances with up to 1534 nodes shows that GA relatively quickly obtains approximate solutions. For smaller instances, GA solutions are compared with CPLEX results. We have also modified our implementation to handle theoretically challenging large-scale classes of hypercubes and Hamming graphs. In this case the presented approach reaches optimal or best known solutions for hypercubes up to 131072 nodes and Hamming graphs up to 4913 nodes.