Multi-objective differential evolution - algorithm, convergence analysis, and applications

The revival of multi-objective optimization (MOO) is mostly due to the recent development of evolutionary multiobjective optimization that allows the generation of the whole Pareto optimal front. Several evolutionary algorithms have been developed for this purpose. This paper focuses on the recent development of differential evolution (DE) algorithms for the multi-objective optimization purposes. Although there are a few other papers on the extension of DE concept to the MOO domain, this paper is intended to provide an overall picture of one specific multi-objective differential evolution (MODE) algorithm. In the MODE, the DE concept for the continuous single-objective optimization is extended to MOO for both continuous and discrete problems (C-MODE and D-MODE, respectively). The MODE is modeled in the context of Markov framework and global random search. Convergence properties are developed for both C-MODE and D-MODE. In particular, a set of parameter-setting guidelines for the C-MODE is derived based on the mathematical analysis. An application of the D-MODE to the planning of design, supply, and manufacturing resources in product development is also reported in this paper.