New multi-objective genetic algorithms for diversity and convergence enhancement

We have developed new multi-objective evolutionary algorithms to improve convergence and diversity of Pareto front surface for multi-objective optimization. With Fonseca and Fleming's Multi-Objective Genetic Algorithms (MOGA) as a baseline algorithm, we propose an elite-preserving MOGA (EP-MOGA). In addition, we suggest a new sharing function coupled with an index-based priority for better diversity and convergence properties than the standard sharing function approach. In order to further enhance convergence to the Pareto front, a novel directional operator is developed, comprising selection of search direction and local one-dimensional search. The directional method drives design solutions normal to the plane passing extreme solutions as the NBI (Normal Boundary Interaction) method does. The proposed algorithms are named EP-MOGAS (Elite Preserving MOGA with a new Sharing function) and EP-MOGAS-D with the directional operator added. The new methods are applied to several standard test functions and a multi-objective compressor rotor design problem. In the test problems, comparisons are made for EP-MOGA, EP-MOGAS, EP-MOGAS-D and NSGA-II. Results show the new sharing function remarkably improves convergence and diversity of Pareto solutions. The new directional operator is found to enhance the convergence greatly while maintaining the diversity of solutions except for ZDT4, a test function with many local optimal Pareto fronts. Finally, a multi-objective shape design of compressor rotor blades confirms applicability and effectiveness of the present algorithms to real world constrained multi-disciplinary design optimization problems.