Research on Zero-Wait Scheduling Problems in Multiproduct Processes with Due Dates - Intelligent Computing for Sustainable Energy and Environment - page 325

The concept of fuzzy α -cuts is extended in this paper. It is also called the level of
probability. The fuzzy scheduling objective can be transformed into the two different
programming function based on the concept of the fuzzy cut-set.
The α -level optimal programming model,

[

( ) ( )

]   

  

N

(4)


=

L L L

min P = h max 0 , e − C + w max 0 , C − t

α i i iM i iM i

α α

i 1

L L L

s . . C = C + O , ∀ j > 1

( )

i j i j − 1 i j

α α α

k k k

L L L L

C ≥ C + d + O , ∈ N , j ∈ M

( ) ( )

i j i − 1 j i − 1 i i j k

α α α α

k k k k k

L L L

C = S + O

i j i j i j

α α α

k k k

L

S ≥ 0

ij

α

The α -level worst programming model,

[ ]   

N

( ) ( )

  


=

(5)

R R

R

min P = h max 0 , e − C + w max 0 , C − t

α i i iM α i iM α i

i 1

R R R

s . . C = C + O , ∀ j > 1

( )

i j i j − 1 i j

α α α

k k k

R R R R

C ≥ C + d + O , ∈ N , j ∈ M

( ) ( )

i j i − 1 j i − 1 i i j k

α α α α

k k k k k

R R R

C = S + O

i j i j i j

α α α

k k k

S

R

≥ 0

ij

α

,P of the penalty objective ~ at the α -level
set, which may help decision-makers gain the variable range of the optimal objective
under a certain possible extent.

[ ]

L R

α α P

It can be got that an interval

3 The Improved Shuffled Frog-Leaping Algorithm (ISFLA)

3.1 Shuffled Frog-Leaping Algorithm in General

The shuffled frog-leaping algorithm (SFLA) is a meta-heuristic optimization method
that mimics the memetic evolution of a group of frogs when seeking for the location
that has the maximum amount of available food. It is based on evolution of memes
carried by the interactive individuals, and a global exchange of information among
themselves [9]. A number of researchers have studied on the SFLA and its
application.