2012 Volume 132 Issue 1 Pages 42-52
This paper proposes a general methodology of multi-objective optimization based on the combined use of scalarization and evolutionary computation approaches. Mathematically, it is guaranteed that a Pareto optimal solution of a multi-objective optimization problem (MOP) can be found by minimizing the corresponding augmented Tchebysheff scalarized function. In this way, different Pareto optimal solutions can be obtained by solving different single-objective optimization problems (SOPs) with different weight for scalarization. Aiming at knowing the global structure of Pareto optimal set and/or Pareto frontier of a MOP with simple computation, we propose the basic concept that, (a) the SOPs with different weight should be solved independently by some evolutionary computation algorithms; and, (b) previously obtained useful solutions should be partly reused for the optimization of another SOP. In particular, for continuous-variable MOPs, we also propose a practical computation method based on the concept, which uses Particle Swarm Optimization (PSO) with effective reinitialization mechanism. The usefulness of the proposed methodology is demonstrated through numerical experiments with the proposed computation method.