Castell 1998 Computers & Chemical Engineering

8/11/2019 Castell 1998 Computers & Chemical Engineering

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Computers them Engng

Vol. 22, Suppl., pp. S993-S996, 1998

0 1998 Elsevier Science Ltd. All rights reserved

PII: s0098-1354 98)00198-7

Printed in &at Britain

0098-1354/98 19.00 + 0.00

Optimisation of Process Plant Layout

using Genetic Algorithms

C. M. L. Castell, R. Lakshmanan, J. M. Skilling, R. Baiiares-Alcdntara

Department of Chemical Engineering, University of Edinburgh, Edinburgh EH9 3JL, UK

Abstract

The layout of chemical facilities is an activity that is largely carrie d out by the human designer. Few meth ods

exist for optimising layout. Difficulties in formulating the problem a s a mathem atical progr am stem from

non- convexities as well as from non-differentiable cost functions. Recent attemp ts (Pentea do and Ciric,

1996 ) have succee ded in only implicitly including land costs, resulting in layouts which can be excessively

conservative from the point of view of safety. The use of stochastic optimisation techniques, though not-

guaranteed to find the global optimum , has proved to be effective in obtaining good , practical solutions and

perm its th e incorporation of mor e realistic cost functions and constraints. In this resea rch, experiments wer e

carried out using various genetic algorithm formulations, and the resulting p rogram , which includes a useful

graphica l interactive compone nt, is presented here. 0 1 998 Elsevier Science Ltd . All rights reserve d.

Keyzuo rds: Proc ess Plant, Layout, Safety, Optimisation, Genetic Algorithms

INTRODUCTION

The process plant layout pro blem is concerned with

finding the optimal spatial arrangem ent of a collec-

tion of facilities on a site. Hereby a balance needs

to be achieved between safety, land area usage and

pipework costs. The problem belongs to the class

of special allocation problem s that have been previ-

ously studied in the contexts of manufacturing cells

layout and V LSI. In general, the area of each unit

and the interconnection cost of each unit pair is

provided by the process/project engineer. Safety

costs may also be included, and generally com pete

with the cost of pipework and land.

Computer-aided system layout packages exist,

based on adjacency (SPIRAL: Goetschalckx, 1992)

and distance (CRAFT: Armour and Buffa, 1963;

SHAP E: Hassan, et al., 1986). However, the lay-

out o f process plant is more complex in that one is

trying to minimise a number of different ob jective

functions simultaneously (e.g. pipe-length, safety

cost, etc.), whilst still satisfying a number of con-

straints. The standard techniques quoted in the lit-

erature are theref ore not suitable for the realistic

layout of proce ss plant.

Recent research into the process plant layout prob-

lem includes Suzuki and Fuchino (1991 ), who use

a facilities-interchange proce dure based on a cost

function calculated from unit separation distances

and a set of heuristics; Pentead o and Ciric (1996) ,

who take a mixed integer non-linear program ming

(MIN LP) approach to optimise a layout of circu-

lar or elliptical proce ss units for cost and safety;

and Georgiadis and Macchietto (1997), who invest-

igate the layout of a multifloor production facility

of equally sized units.

In our approach, we use a more realistic representa-

tion of a proc ess layout, taking aspec t r atio and ori-

entation of proc ess units into account. Land costs

are formulated as being proportional to the area

of the rectangle bounding the units. This mor e

complex m odel of the process plant presents diffi-

culties to conventional m athematical program ming

appr oach es owing to the non- differentiability of the

objective function. This motivated the use of a

stochas tic optimisation technique, for which there

is essentially no restriction on the form of the ob-

jective function.

GENETIC ALGORITHM OPTIMISATION

The traditional appro ach to using genetic al-

gorithm s (GA S) to solve a given problem involves

devising a means f or encoding potential solutions

as strings and using conventional opera tors, typic-

ally crosso ver and mutation, to perfor m the evolu-

tionary searc h. The succ ess of a GA application,

however, depends on whether or not distinct seg-

ments of the string representation represen t logical

building blocks (sche ma) which represent partial

encodings of good solutions (Michalewicz, 1992).

Recent resea rch in evolutionary compu tation (Surry

and Radcliffe, 1996) has shown that the represent-

ation used is key to the success of the GA applica-

tion. How ever, using a problem specific represent-

ation instead of a simple string usually means that

conventional genetic operators are no longer appro-

priate, and novel, more appropriate, operators must

be defined.

In our work, we have drawn on the experience of

resea rcher s in the area of evolutionary computation

to define special-purp ose opera tors to manipulate a

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s994 European Symposium on Computer Aided Process Engineering-8

very natural representation of a layout, conceptually

modelling the units and pipes as nodes and edg es in

a graph. Both tournament and roulette wheel se-

lection w ere used in the trials, with the form er be-

ing consistently mor e effective. Our results indicate

that the approach taken here has been a profitable

one for the layout optimisation problem.

LAYOUT PROBLEM FORMULATION

The representation used here encodes all the inform-

ation of a particular unit into the genetic c ode: the

x and y co-ordinates, length, w idth, orientation and

the Mond safety index (Lewis, 1979). In addition,

the interconnections between the units are recor ded

along with the cost associated with the pipework for

each link.

W ij

= cost of pipe between units E/m)

O TQj

= rectilinear

distance between centre of

units m)

= lx+ -

j l + l Yc , i Ye, j l

(b) Miiimising the area taken up by a rectangle

enclosing all the process plant (plant area) .

{min(((xi+ Wdmaz Xjcj)min)

X((Yi+ G7w z (Yjhnin)))

xwl

W

= cost of land E/m2)

(c) Minimising the infringement of Mon d safety dis-

tances.

{min C C max(0, (mom& j - dsij))} x wm

Figure 1: Proc ess unit representation

In Figure 1 (x, y) are the co-o rdinates of the top left

hand corner and (xc,ye) are the co-ordinates of the

centre of the proce ss unit. The length and width

are denoted by 1 and w , respectively. The ori-

entation of the unit is described by the variable o ,

which is 0 for the normal orientation and 1, when ro-

tated by 90. (Note: For all following formulae it is

assum ed that units are in their normal orientation.)

Safety is mode lled by the M ond fire and safety in-

dex, which was chosen as it is relatively simple to

calculate and, more importantly, is available at the

early stag es of a project when the layout design is

being performed. The index specifies the preferred

minimum distances between p lots of proce ss units.

The extent to which these constraints are violated

determines the safety cos t of the layout.

Objective Functions

Among

the more important characteristics of a good

layout are a low pipework cost, a small plant area

and a safe design (Mecklenburgh, 1985). We have

therefore adopted these characteristics as the ob-

jectives of our optimisation proce ss.

(a) Minimising the sum of weigh ted pipe lengths

between units.

We have assum ed that all pipes can only run in

north/south or east/w est directions and that all

pipes run from the centre point of a proc ess unit.

i

2om =

daij =

mond


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European S ymposium on Computer Aided P rocess Engineering-8

S9 X

Blocks must be placed within the designated

site area

Blocks must not overlap with one another.

Figure 2: Exam ple of x-projection overlapping

Two blocks will only overlap if they a re both x-

projection overlapping (Figure 2) and y-projection

overlapping. Mathem atically, this implies:

Zj - Zi + Wi)) Zj + Wj) - 2;)

2

0

(Yj -

Yi

+

h)) Yj

+ a,) -

Yi) 2

0

The location an d orientation information is manip-

ulated by the genetic code to optimise the process

plant layout, while a repair algorithm ensures that

the two conditions above hold.

GR PHIC L USER INTERF CE

The Graphical User Interface (GUI) is designed not

just to make the optimisation program more user

friendly, but is an integral part of the system design

as it perm its the process engineer to interact with

the optimisation proce ss, tailoring it to his/her own

needs. After the details o f the process units/plots

have been loaded up by the progra m the user initi-

ates the GA optimisation process. This produces a

layout in the user window, with all the named pro-

cess units re presente d by blocks, with connections

shown by lines routed between the blocks. In future

wor k, it is intended that additional constraints may

be placed on the formulation by the user as he or

she monitors the progress of the algorithm through

the graphica l interface.

On the right hand side of the display three scores

are given. One for pipework cost, one for land area

usage and one for safety. A combined total score

is given in the top right of the w indow. By click-

ing and dragging on one of the proc ess units/plots

on the screen, the process engineer can see how the

individual ratings for cost, land and safety change,

and also observe any change to the overall score.

The process engineer can therefore modify the lay-

out to his or her particular requirements while main-

taining a view of the eff ects of those changes on the

three objective functions. Weightings can be as-

signed to each objective function as deem ed fit by

the operator to produce the overall score for the

process plant layout.

A suggested approach to the use of the tool is to

begin w ith a set of Mon d indices calculated in the

prescribed manner and to use a low safety weight-

ing factor. The p rogram is likely to evolve a solution

that has a significant amount of overlap. By look-

ing at the graphical display o f the layout, the user

can then use his or her process-specific knowledge

to refine the Mond indices (either by recommending

the installation of additional protective devices on

critical units o r simply on the basis that a particular

value was overly conservative). Throu gh successive

runs, the safety factor is systematically increased to

a high va lue until the violations in the inter-unit

spacing recomm endations are negligible. Fine tun-

ing of this solution can be done either using the

hill-climbing algorithm included in the progra m or

manually through the graphical user interface.

RESULTS

Detailed below are the results of experiments carried

out to determine the effectiveness of the optimisa-

tion procedure. Figures 3 and 4 show the results

of the optimisation progra m tested on the Ethyl-

ene Oxide (EO ) Plant case study presented by Pen-

teado and Ciric (1996). Hereby the safety weight-

ing (wm) has been set at high and low levels to

demonstrate the flexibility of the GA approach to

optimisation. The dash ed circles around the haz-

ardous process units represent the Mond separation

distance requirements to adjacent units.

I

cm

i

I

\ I

\

/

--______A

\

\

Figure 3: EO layout (high safety factor)

As can be seen from these diagrams, far more com-

pact layouts are possible than if the same pro cess


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European Sym posium on C omputer A ided Process Engineering-8

units were modelled as circles or equal area squares.

Figure 4: EO layout (low safety factor)

Figure 5 represe nts a layout gen erated by the pro-

gram for a set of 20 randomly sized and shaped

units, with a random set of connections. This il-

lustrates that the program can handle larger prob-

lems, although the runtime is increased to about one

minute.

L

Figure 5: Twenty proc ess unit plant layout

CONCLUSIONS

The appro ach taken, applying stochastic op timisa-

tion techniques to chem ical plant layout, ha s resul-

ted in a useful and practical design aid. The soft-

war e provides useful graphical interactive comm u-

nication between the designer and the optimiser,

and the array o f formulations available to the user

allows for testing of a range of assumptions. Most

importantly, the formulation chosen and the imple-

mentation of the softw are hav e resulted in a single

tool that can handle a much larger s et of layout

problem s than was possible in the existing s tate of

the art.

fiture wor k will provide facilities to (a) tailor the

objective function to suit the preferences of a par-

ticular designer and (b) perm it on-line addition of

constraints by the user, and will incorporate integer

choice variables relating to the installation of addi-

tional protective devices which allow more compact

layout and hence reduce land costs.

ACKNOW LEDGEM ENT: The authors gratefully

acknow ledge the financial suppo rt provided by Elf

UK in the form of a Scho larship in Safety Engineer-

ing.

REFERENCES

Armour, G. C., and E. S. Buffa, 1963, A Heuristic

Algorithm and Simulation Appr oach to the Relat-

ive Location of Facilities, Manag ement Science, v9,

n2, pp294-309.

Georgiadis, M. C. and Macchietto, S., 1997, Lay-

out of Process Plants: A Novel Approach, Comp.

Chem. Eng., ~21, nS, ~~337-342.

Goetschalckx, M., 1992, SPIRAL: An Efficient and

Interactive Adjacency G raph Heuristic for Rapid

Prototyping of Facilities,

Design

European

Journal

of Operational Research, ~~304-321.

Hassan, M.M .D., et al., 1986, SHAPE: A Con-

struction Algorithm for Area Placem ent Evalu-

ation, International Journal of Production Re-

search ~24, pp1283-1295.

Lewis, D.J., 1979, The M ond fire, explosion and

toxicity index: a developm ent of the Dow Index,

AIChE Loss Prevention Symposium, Houston.

Mecklenburgh, J.C., 1985, Process Plant Layout,

Pub: George Goodwin.

Michalewicz, Z., 1992, Genetic Algorithms + Data

Structure s = Evolution Program s, Pub: Springer-

Verlag, 2ed.

Penteado, F. D. and Ciric, A. Ft., 1996, An MINLP

approach for safe process plant layout, Ind. Eng.

Chem. Res. ~35, ~~13541361.

Surry, P.D. and Radcliffe, N., 1996, Formal

Algorithms + Formal Representations = Search

Strategies, Department of Mathematics, Uni-

versity of Edinburgh, Scotland..

Suzuki, A. and Fuchino, T., 199 1, An Evolution-

ary Method of Arranging the Plot Plan for Process

Plant Layout, J. Chem. Eng. Jap. ~24 n2, pp

226-231.

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Castell 1998 Computers & Chemical Engineering