Multi-objective differential evolution

Differential evolution (DE) is a branch of evolutionary algorithms developed by Storn and Price (1997) for optimization problems over continuous domains. DE is characterized by representing the variables by real numbers and by its three-parents crossover. At the selection stage, 

MODE was used by Babu et al. (2005) to optimize the operation of an adiabatic styrene reactor. This work concerns a comparative study between the performance of MODE and the results of NSGA reported in a previous paper (Yee et al, 2003). This application is described in Section 3.7.3. Eor comparative purposes, this study adopts the same formulation used by Yee et al (2003). That is to say, the objectives are productivity, selectivity and yield of styrene the variables are ethyl benzene feed temperature, pressure, steam-over-reactant ratio and initial ethyl benzene flow rate. Two constraints are also considered. On the one hand, the results obtained by MODE agreed with those obtained by NSGA, in particular the behavior of the variables in the Pareto optimal set. On the other hand, based on visual inspections, it was revealed that, in some cases, the Pareto fronts obtained by MODE were better than those obtained by NSGA, while in other cases the Pareto fronts seemed nearly identical (no performance indicators were adopted in this case). 

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Multi-objective differential evolution (MODE) The work Babu et al. (2005) is very similar to that of Yee etal. (2003) except for different values for some model parameters (which affect the results). Babu et al. (2005)... 

I-MODE Improved Multi-objective Differential Evolution... 

Sharma, S. and Rangaiah, G.R (2013b) An improved multi-objective differential evolution with a termination criterion for optimizing chemical processes. Computers Chemical Engineering, 56, 155-173. 

Multi-Objective Differential Evolution (MODE). This is a custom multiobjective variant (with elitism) of Differential Evolution (DE) [24], that simply combines with the classic DE mutation/crossover operators the non-dominated sorting and crowding distance mechanisms used in NSGA2 (see below). We set crossover rate Cr = 0.3 and scale factor F = 0.5. 

Babu, B. and Jeban, M. M. L. (2003). Differential evolution for multi-objective optimization, in Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), Vol.4 (IEEE Press, Canberra, Australia), pp. 2696-2703. 

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