Representation issue in graph coloring

Linear Linkage Encoding (LLE) is a powerful encoding scheme utilized when genetic algorithms (GAs) are applied to grouping problems. It discards the redundancy of other traditional encoding schemes. However, some genetic operators are quite costly in terms of computational time when LLE is utilized. In this study, two supplementary encoding schemes Linear Linkage Encoding with Ending Node Links (LLE-e) and Linear Linkage Encoding with Backward Links (LLE-b) are designed and used together with LLE. When a genetic operator is costly in LLE, the operation is carried out on one of the supplementary encodings and the result is reflected back to LLE. The algorithm is implemented in a Multi Objective Genetic Algorithm (MOGA) framework and various tests are carried out on Graph coloring Problem (GCP) instances obtained from DIMACS Challenge Suite. A performance improvement has been obtained when both supplementary encoding schemes are included in the algorithm.