Modeling and Optimization of Cement Raw Materials Blending Process

Table 2

G-NLTV dynamic optimization models of the cement raw material blending process.

Optimization models		Optimization objective functions	Constraints
Single-objective; optimization	Model.1	min𝐽1=min(𝐶^𝑇𝑥)	(3.1)–(3.12), (3.13)–(3.17)
	Model.2	min𝐽2=min(𝑃^𝑇𝑥)	(3.1)–(3.12), (3.13)–(3.17)
	Model.3	min𝐽3=min𝑤1(Δ𝛼)^2+𝑤2Δ𝛽^2+𝑤3(ΔΩ)^2	(3.1)–(3.12), (3.13)–(3.17)
		(Notes: Δ𝛼=𝛼−𝛼𝑑0,Δ𝛽=𝛽−𝛽𝑑0,ΔΩ=Ω−Ω𝑑0)
Multiple-objective; optimization	Model.4	min(𝐽1,𝐽2)= min{Ψ1𝐽1+Ψ2𝐽2}	(3.1)–(3.12), (3.13)–(3.17)
	Model.5	min(𝐽1,𝐽3)= min{Ψ1𝐽1+Ψ2𝐽3}	(3.1)–(3.12), (3.13)–(3.17)
	Model.6	min(𝐽2,𝐽3)= min{Ψ1𝐽2+Ψ2𝐽3}	(3.1)–(3.12), (3.13)–(3.17)
	Model.7	min(𝐽1,𝐽2,𝐽3)= min{Ψ1𝐽1+Ψ2𝐽2+Ψ3𝐽3}	(3.1)–(3.12), (3.13)–(3.17)