Improved multi-objective particle swarm optimization algorithm for optimizing watermark strength in color image watermarking

A variant of Multi-Objective Particle Swarm Optimization (MOPSO), named as MOPSOtridist, is proposed in this paper. To improve the performance of existing MOPSO algorithms, new leader selection strategy and personal best (pbest) replacement scheme is introduced in this variant. In existing MOPSO algorithms, selection of leader is done only on the basis of particle’s current position and particle movement history is not taken into account. In MOPSOtridist, this information is used by selecting the most appropriate leader from the archive which has minimum distance from the region where the particle had visited recently. The proposed leader selection strategy efficiently explores the whole Pareto front by attracting the distinct regions explored by different particles. Additionally, a pbest replacement scheme is introduced to handle its stagnation at local optimal solutions by replacing the stagnated pbest of the particle with a new archive member, which is at maximum distance from the particle’s local optimal solutions. This will add diversity and forces those particles to explore other regions. For measuring the distance between particle’s regions and archive member, triangular distance (tridist) is used. The proposed MOPSOtridist algorithm along with other widely known variants of MOPSO, are tested exhaustively over two series of benchmark functions ZDT and DTLZ. The experiment results show that the proposed algorithm outperforms other MOPSO algorithms significantly in terms of standard performance metrics. Further, the proposed variant MOPSOtridist is applied to digital image watermarking problem for colour images in RGB colour space. Results demonstrate that MOPSOtridist efficiently produce optimal values of watermark strength to achieve good trade-offs between imperceptibility and robustness objectives.