A Hybrid Algorithm for the Simple Cell Mapping Method in Multi-objective Optimization

This paper presents a hybrid gradient free-gradient (GFG) algorithm for the simple cell mapping (SCM) method for multi-objective optimization problems (MOPs). The SCM method is briefly reviewed in the context of the multi-objective optimization problems (MOPs). We present a mixed application of gradient free directed search and gradient search algorithms for the SCM method and discuss its potentials for higher dimensional MOPs. We present several numerical exmaples to demonstrate the effectiveness of the proposed hybrid algorithm. The examples include two simple geometric MOPs, an example with five design parameters, and a proportional-integral-derivative (PID) control design for a second order linear system.