A novel multi-objective compass search

Direct search method has been widely used for solving single-objective optimization problems. In this paper, a proposal to extend the direct search method “compass search” to deal with multi-objective optimization problems, which we called as MOCS, is introduced. The concept of Pareto dominance is used to generate the Pareto optimal solutions. To handle constraints, different weights are calculated based on the violation situation of directions and are assigned to each candidate direction correspondingly. Roulette is then performed to select the search direction. In addition, a kernel density estimator is used to keep diversity. And a dynamic step length is adopted to enhance the speed of convergence. Simulation results and comparisons demonstrated the effectiveness, efficiency and robustness of MOCS which is highly competitive with current evolutionary multi-objective optimization techniques.