Multiple trajectory search for unconstrained/constrained multi-objective optimization

Many real-world optimization problems involve multiple conflicting objectives. Therefore, multi-objective optimization has attracted much attention of researchers and many algorithms have been developed for solving multi-objective optimization problems in the last decade. In this paper the multiple trajectory search (MTS) is presented and successfully applied to thirteen unconstrained and ten constrained multi-objective optimization problems. These problems constitute a test suite provided for competition in the special session & competition on performance assessment of constrained/bound constrained multi-objective optimization algorithms in CEC 2009. In the multiple trajectory search, a set of uniformly distributed solutions is first generated. These solutions will be separated into foreground solutions and background solutions. The search is focuses mainly on foreground solutions and partly on background solutions. The MTS chooses and applies one of the three local search methods on solutions iteratively. The three local search methods begin their search in a very large ldquoneighborhoodrdquo. Then the neighborhood contracts step by step until it reaches a pre-defined tiny size, after then, it is reset to its original size. By utilizing such size-varied neighborhood searches, the MTS effectively solves the multi-objective optimization problems.