Industrial Plant Pipe-Route Optimisation

with Genetic Algorithms

Dae Gyu Kim

1

, David Corne

2

1

School of Cognitive and Computing Sciences,

University of Sussex at Brighton, Falmer, Brighton, BN1 9QH, UK

dgkim@cogs.susx.ac.uk

2

Parallel, Emergent, and Distributed Architectures Laboratory (PEDAL),

Department of Computer Science, University of Reading,

Whiteknights, Reading RG6 2AY, UK

D.W.Corne@reading.ac.uk

Abstract. The pipe-route design problem for heavy industrial plant

concerns minimising pipe material cost while satisfying constraints on

required interconnections and obstacle avoidance. This process is invari-

ably done by human experts, but modern stochastic iterative search tech-

niques allow the opportunity to automate this process. This study ex-

plores the possibility of automated industrial pipe-route design on three

test problems, using stochastic hillclimbing, simulated annealing, and ge-

netic algorithms. The representation strategy is explained and discussed,

and results are presented which show great promise for genetic algorithms

in particular in this application area.

1 Introduction

Hard pipe route design problems arise when equipment (such as pumps, boilers,

and so on) need to be multiply interconnected by uid or gas-carrying pipes in

such a way as to satisfy various constraints and objectives, such as to avoid ob-

stacles, avoid undue pressure variations, enable easy maintenance, and minimise

material cost, while of course satisfying the required interconnections. Pipe route

design is one of the most important steps involved in the design of large-scale

engineering plant such as ships, power plants, chemical plants, and so on. In

practice, the process mainly relies on human experts and their associated ex-

perience, since the range and complexity of the constraints tends to dissuade

attempts at automation.

In most industrial design practice, the locations of the various pieces of equip-

ment involved are determined in advance. Given these locations, a Piping and

Instrumentation Diagram (P&ID) is prepared, which species the connections

which must be made. For example, gure 1, in combination with a list of required

connections (such as E1-nozzle1 connects to E2-nozzle7, E4-nozzle5 connects to

E4nozzle7, and so on . . . ), constitutes a P&ID.

A designer is then given the job of laying out the pipe routes in accordance

with the P&ID, while meeting several other constraints and objectives as men-

tioned above. Designers' skill and experience tends to lead to routing designs

01

23

45

67

89

10

0 1 2 3 4 5 6 7 8 9 10

E1

E3TANK

E2RESERVOIRE4

TANK

1 2 3

4

56789

10

11

1 2 3

6 5 4789

12

3

45

6

7

89

1 2 34

5

610

11

9 8 7

PUMPE5

O3 O4 O5 O6 O7

O9 O10

O11 O12

O15

O16 O17 O18

O19

CONTROL ROOMO20

O1 O2

O14

O13O8

Fig. 1. A Piping & Instrumentation Diagram

which generally work well, but the greatly time-consuming nature of the design

process [1] makes it practically impossible to explore alternatives or seriously

attempt to optimise the design. Modern methods for tackling awkward prob-

lems, such as genetic algorithms (GAs) and simulated annealing (SA), introduce

the opportunity to greatly speed up and perhaps improve design practice and

quality in this area. The work reported here hence explored the potential for

GAs and other stochastic methods on this problem.

Many routing problems have been addressed with GAs . For example, [2] use

a GA to optimise the routing between chips on multi-chip modules, while [3]

describe three forms of pipe-network optimisation problem: pipe-sizing, layout

design, and pressure-regulation. The problem described here, however, diers

in certain key respects from others we have so far found in the literature. For

example, pipe-layout problems studied tend to concern nding the best way to

arrange connections between multiple demand and supply stations, however in

our case the interconnections are all pre-specied and the problem is instead to

minimise overall pipe-length taking obstacles into account. Connections which

need to be made are also pre-specied in electrical routing examples such as

[2], however, unlike in our case, such cases also typically involve designing the

relative layout of the items being interconnected, while having no analogue of

the potential to merge connections (see below).

Overview The remainder of this paper is set out as follows. Section 2 describes

the pipe routing design problem in more detail, and sets out the chromosome

representation used. Test problems, experiments, and results are then presented

in section 3, and then a concluding discussion appears in section 4.

2 Representing Pipe Routes

The problem we address here can be partly (but see later) viewed as optimis-

ing separately each of a collection of individual pipe connections. The essential

requirement for such a connection is that it be made in such a way as to avoid

obstacles. Taking pipe cost and manufacturing considerations into account, we

can be justied in considering only rectilinear connections, and we therefore can

conveniently view the problem in terms of choices of Steiner points [4]. Figure 2

illustrates this; we wish to make a rectilinear connection between the pump and

the storage tank, that is, between points A and B. Such a connection can take

one of two `basic routes', going either via Steiner point 0, or Steiner point 1.

A

Steiner Point 1

Pump

Tank

B

SteinerPoint 0

Fig. 2. Illustrating Steiner Points

In order to avoid obstacles, however, the basic routes must be diverted some-

how. There are essentially two possible diversions, termed `escape graphs' [5],

around each obstacle. This is illustrated in gure 3. Hence, a single basic route

(ie: a route involving a particular choice of Steiner point) gives rise to 2

k

dierent

possible routes when there are k obstacles in the way.

Associated with every connection which has to be made, then, is a collection

of potential routes derived from the two (in two dimensions) possible Steiner

points, and the appropriate obstacles in the P&ID. Figure 4 illustrates a general

case, in which the connection between `Start' and `End' must be made around

three obstacles (left hand side of the gure), giving rise to 6 possible routes as

detailed in the right hand side of the gure. As can be seen, Routes A and B are

the two that arise from the rst basic route (involving Steiner point 0) and the

Start

End

Route 1_1

Route 1_2

Route 2_2

Route 2_1

Route 3_2 Route 3_1

Obstacle 9Obstacle 4

Obstacle 1

Fig. 3. The construction of possible routes around obstacles

single obstacle. The two obstacles obstructing the second basic route (involving

Steiner point 1) give rise to the four potential routes C,D,E and F.

Steiner 0

Steiner 1Start

End

Possible routes

Route C

Route D

Route F

Route E

Route A

Route B

Fig. 4. Examples of possible routes around obstacles

Given the complete set of connections which need to be made and the lo-

cations of all equipment and obstacles { hence, given the P&ID { our strategy

is to preprocess the information to produce the choice of all possible routes for

each individual connection (Eg: as illustrated for the single example connection

in gure 4). A simple chromosome representation strategy is then to provide a

gene for each connection, alleles of each gene indexing the set of possible routes

for that particular connection.

Following preliminary experimentation on small test cases, the representa-

tion strategy we chose as most promising for the main work reported here was

one in which each gene (connection) had only two alleles, 0 or 1, representing re-

spectively the two choices of basic route (eg: either via Steiner point 0 or Steiner

point 1). Interpretation of the chromosome then automatically determined and

used the minimal length route around obstacles along the chosen basic route

(choosing deterministically between ties). We were hence able to represent 2D

rectilinear pipe-network optimisation as a binary chromosome problem.

Evaluation

The rst step in interpreting a chromosome simply uses preprocessed information

to determine which potential route is represented in the chromosome for each

gene. That is, if gene i displays allele 0 (1), then the route to be taken for the ith

connection is the one via Steiner point 0 (1) which, taking obstacle avoidance

into account, has minimal length.

Three operations are now applied in order to interpret the chromosome as a

complete pipe route. These are: Merging, Simplication, and Equivalent-length

calculation. Each is discussed briey next.

Merging Total pipe length is calculated as the sum of each pipe connection

minus the amount of duplicate pipe length. Duplicate pipe length is the total

length of spatially coincident pipe sections that can in practice be run as a

single pipe. This typically occurs when pipe routes for dierent connections rep-

resented in the chromosome coincide in direction of ow in addition to location.

For example, in Figure 5, a combination of routes B and C is preferred to other

combinations, since this will reduce the total pipe length most. Note that the

fact that pipes can be merged in this way is what stops the pipe-route design

problem addressed here from being able to be trivially decomposed into optimis-

ing individual connections. Such pipe-merging becomes more and more necessary

with larger installations.

A

D

B

C

Equipment 1

Equipment 2

Equipment 3

Conn

ection

2

Connection 1

Fig. 5. Merging duplicate pipe routes

Simplication At this stage, it may be possible to make several simplications

in the pipe route so far, as a result of opportunities which may have arisen mainly

from obstacle avoidance. Certain common example candidates for simplication

are shown in gure 6. The pipe-route is checked for such opportunities and the

simplications are made.

==>

3

Channel reduction

==>

Bay reduction

==>

Point reduction

1 2

3 4

5 6 1 2 5 6

1 2

3 4

5 61 2

7

5 6

1 2 3 1

Fig. 6. Cases for pipe-route simplication

Equivalent-Length Calculation Finally, each corner in the pipe network is

converted into its equivalent length. This is a way of taking corners into consider-

ation, whereby each corner is converted into a straight pipe with a certain length

which gives the same uid pressure drop as the corner [6], and the amount is

added to the total pipe length of the system.

Remarks Mainly owing to the merging and simplication processes, pipe-route

interpretation gives rise to a complex and time-consuming evaluation function.

To avoid undue complexity, the interpretation process as described above is

therefore `incomplete' in certain respects { for example, simplication may lead

to new opportunities for merging, but there is no extra merging step following

the simplication step. Also, simplication should ideally be iterated until no

more opportunities exist, but this would be particularly time-consuming. Also,

of course, it is built in to the interpretation function that, for each of the two (or

occasionaly one) Steiner points relevant to a connection, only one of the several

choices for potential routes around obstacles is allowed to be chosen. Allowing

more possible routes to be encoded may of course lead to better opportunity for

merging and simplication, leading to better overall solutions. This is yet to be

investigated fully, but preliminary experiments suggested that the representation

employed here struck a generally more robust balance between time complexity

and solution quality.

3 Experiments

We investigated the use of GAs [7], SA [8], and stochastic hillclimbing (SH) on

each of the test problems. In the following subsections we briey overview the

experimental setup, and summarise the results.

Test Problems Three moderately sized test problems were developed, con-

sisting of 20, 30, and 40 connections respectively. Figure 1 has already shown

the layout for the 20-connection problem, and 7 shows the optimal pipe route,

which we know since the solution space in this case was small enough to allow an

exhaustive search. Full details of all test problems are freely available from the

authors, and a web-site is currently being prepared to disseminate these details

more accessibly.

Fig. 7. The global minimum case with the 20-connection problem

Exhaustive search of the 20-connections problem results in the landscape

displayed in gure 8. The horizontal axis represents the numerical value of the

binary chromosome (in millions), from chromosome 0000::: on the left-hand side

to chromosome 1111::: on the far right, while the vertical axis displays total

pipe length for each chromosome. Though ne structure is essentially hidden,

the gure suggests that the landscape is deeply infected with local optima. For

example, one can imagine a hillclimber, perhaps being trapped in the far left

region of the landscape (mainly 0's) unable to escape to the global optimum far

towards the right (rather Hamming distant from it, in a mainly 1's area).

Fig. 8. Solution space for the 20-connection problem

Search space size for the 30 and 40 connection problems was more realistic

with respect to real problem cases, and also (of course) not feasibly amenable to

exhaustive search.

Experimental Setup Unless otherwise stated, each individual trial of an algo-

rithm ran for a maximum of 5,000 evaluations. This is a rather modest gure, but

we felt it important to seek good performance in such a relatively small space of

time since pipe-route design optimisation problems can necessitate rather com-

plex evaluation functions, as noted in section 2.

Standard SH was employed (random starting point; continually seek new

mutants, replace current with new only if new is better or equal to current),

using simple single-gene mutation as the neighbourhood operator. That is, a

mutation step consisted of choosing a gene at random, and ipping its value.

SA used the same neighbourhood operator, and a simple geometric cooling

schedule with starting temperature, number of iterations per temperature step,

and nal temperature set respectively at 30 the number of connections in the

problem, 50, and 0.001. These parameters arose as a fairly robust set following

much time consuming preliminary experimentation with dierent SA setups.

The GA used steady-sate reproduction, rank-based selection (as in [9], uni-

form crossover, a population size of 50, and the same mutation operator as SH

and SA.

Results Table 1 summarises results for trials on the 20, 30, and 40 connections

test problems. 10 trials each were made with each method, and the table records,

in column order, the best (minimum) result over the 10 trials, the worst result,

the mean result over the trials, and the number of trials (out of 10) in which an

optimal (known, in the 20-connections case) pipe-route design was found. In the

30 and 40 connections cases, number of optimal trials refers to the best-known

result for the problem.

The 20-Connections test problem

Best Result Worst Result Average Result Number of Optimal Trials

SH 202.0 218.6 207.4 0

SA 194.4 195.7 195.2 0

GA 192.5 194.4 192.6 8

The 30-Connections test problem

SH 308.6 308.6 308.6 10

SA 316.2 320.5 317.4 0

GA 308.6 308.6 308.6 10

The 40-Connections test problem

SH 392.9 402.3 396.2 0

SA 397.9 406.8 404.9 0

GA 354.3 354.3 354.3 10

Table 1. Summary of Results on test problems

On the 20-connections problem, SH performance was rather poor in relation

to both SA and GA, with SH and GA competing relatively closely, although the

GA seems clearly superior.

In the 30-connections case, SA seemed to have trouble, losing out to SH and

GA, both of which found the same best-known result in every trial. We can only

conjecture that this example may have sported a tness landscape with few or

no hard-to-escape local optima, enabling SH and GA to be steered quickly to a

result, leaving SA to unwisely, in this case, explore less promising avenues.

In the 40-connections case, the GA is clearly far superior to the other meth-

ods, with SH second-best, and SA a close third.

In each case, T-tests report the GA superior to SA with 95% condence. In

the 20-connections and 40-connections case, T-tests also nd GA superior to SH

with 95% condence.

4 Discussion

This initial foray into the use of GAs on pipe-route design problems appears

to show great promise. Commercial security considerations unfortunately made

it prohibitively hard to compare GA results with human expert results on real

problem examples as yet. However, we can at least report here the fact that a GA

was able to fairly reliably nd the global optimum solution in a case where the

global optimum was known (the 20-connections case), and that the GA appears

signicantly superior to either SA or SH on this problem in larger test cases.

Extensions of this work therefore seems warranted, in particular extending

the technique to handle three-dimensional pipe-route design. In 3D, for example,

there are typically 6 Steiner points giving rise to 6 basic routes, with four main

potential escape routes around any obstacle. This leads to an obvious extension

of our representation towards dealing with the 3D case. Choosing pipe-route

diameters in conjunction with other aspects of the problem is a further necessary

extension towards real-world examples. Evidently, there is also much scope to

design problem specic operators which should further improve results.

In summary, this study has suggested that industrial plant pipe-route opti-

misation can be feasibly done using genetic algorithms. We demonstrate a nat-

ural and eective representation for the problem, and also demonstrate results

that suggest genetic algorithms are superior to either hill-climbing or simulated

annealing on these problems (at least with the representation and standard op-

erators used here). Results point towards the potential success of extending

the technique to deal with realindustrial plant pipe-route design problems, thus

strongly supporting the work of human experts in this area.

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