Design of plant layout having passages and inner structural wall using particle swarm optimization

Abstract

The FLP has applications in both manufacturing and the service industry. The FLP is a common industrial problem of allocating facilities to either maximize adjacency requirement or minimize the cost of transporting materials between them. The “maximizing adjacency” objective uses a relationship chart that qualitatively specifies a closeness rating for each facility pair. This is then used to determine an overall adjacency measure for a given layout. The “minimizing of transportation cost” objective uses a value that is calculated by multiplying together the flow, distance, and unit transportation cost per distance for each facility pair. The resulting values for all facility pairs are then added. Most of the published research work for facilities layout design deals with equal-area facilities. By disregarding the actual shapes and sizes of the facilities, the problem is generally formulated as a quadratic assignment problem (QAP) of assigning equal area facilities to discrete locations on a grid with the objective of minimizing a given cost function. Heuristic techniques such as simulated annealing, simulated evolution, and various genetic algorithms developed for this purpose have also been applied for layout optimization of unequal area facilities by first subdividing the area of each facility in a number of “unit cells”. The particle swarm optimization(PSO) technique has developed by Eberhart and Kennedy in 1995 and it is a simple evolutionary algorithm, which differs from other evolutionary computation techniques in that it is motivated from the simulation of social behavior. PSO exhibits good performance in finding solutions to static optimization problems. Particle swarm optimization is a swarm intelligence method that roughly models the social behavior of swarms. PSO is characterized by its simplicity and straightforward applicability, and it has proved to be efficient on a plethora of problems in science and engineering. Several studies have been recently performed with PSO on multi objective optimization problems, and new variants of the method, which are more suitable for such problems, have been developed. PSO has been recognized as an evolutionary computation technique and has features of both genetic algorithms (GA) and Evolution strategies (ES). It is similar to a GA in that the System is initialized with a population of random solutions. However, unlike a GA each population individual is also assigned a randomized velocity, in effect, flying them through the solution hyperspace. As is obvious, it is possible to simultaneously search for an optimum solution in multiple dimensions. In this project we have utilized the advantages of the PSO algorithm and the results are compared with the existing GA. Need Statement of Thesis: To Find the best facility Layout or to determine the best sequence and area of facilities to be allocated and location of passages for minimum material handling cost using particle swarm optimization and taking a case study. The criteria for the optimization are minimum material cost and adjacency ratios.
Minimize F = ∑∑ . ……………………………………………... (1)
= =
M
i
M
j
ij
f
ij
d
1 1
*
g1= αi
min
– αi ≤ 0,………………………………………………………… (2)
g2= αi
- αi
max
≤ 0, ……………………………………………………… (3)
g3= ai
min
– ai ≤ 0,…………………………………………………………. (4)
g4= ∑ - A
=
M
i
ai
1
available ≤ 0,…………………………………………………... (5)
g5= αi
min
– αi ≤ 0,………………………………………………………… (6)
g6= αi
min
– αi ≤ 0,………………………………………………………… (7)
g7 = (xi
r
- xi
i.s.w
) (xi
i
.
s.w
- xi
l
) ≤ 0,…………………………………………... (8)
Where i, j= 1, 2, 3…….M, S= 1, 2, 3…P
fij
: Material flow between the facility i and j,
dij
: Distance between centroids of the facility i and j,
M: Number of the facilities,
αi
: Aspect ratio of the facility i,
αi
min
and αi
max
: Lower and upper bounds of the aspect ratio αi

ai :
Assigned area of the facility i,
ai
min
and ai
max
: Lower and upper bounds of the assigned area ai
Aavailable : Available area,
P: Number of the inner structure walls,
Since large number of different combination are possible, so we can’t interpret each to find the best one. For this we have used particle swarm optimization Techniques. The way we have used is different way of PSO. The most interesting facts that the program in C that we has been made is its “Generalized form”. In this generalized form we can find out the optimum layout configuration by varying:
ƒDifferent area of layout
ƒTotal number of facilitates to be allocated.
Number of rows
Number of facilities in each row
Area of each Facility
ƒDimension of each passage
Now we have compared it with some other heuristic method like Genetic algorithm, simulated annealing and tried to include Maximum adjacency criteria and taking a case study.