Multi-objective Genetic Algorithms
for Pipe Arrangement Design
Satoshi Ikehira

Hajime KimuraDept. of Maritime Engineering
Graduate school of Engineering
Kyushu University
Fukuoka, Japan

Dept. of Marine Systems Engineering
Faculty of Engineering
Kyushu University
Fukuoka, Japanikehira@system.nams.kyushu-u.ac.jp

kimura@nams.kyushu-u.ac.jp

ABSTRACTThis paper presents an automatic design method for piping
arrangement. A pipe arrangement design problem is proposed fora space in which many pipes and objects co-exist. This problem
includes large-scale numerical optimization and combinatorial
optimization problems, as well as two criteria. For these reasons,
it is difficult to optimize the problem using usual optimization
techniques such as Random Search. Therefore, multi-objective
genetic algorithms suitable for this problem are developed. The
proposed method for optimizing a pipe arrangement efficiently isdemonstrated through several experiments.

Categories and Subject Descriptors
Real World Applications

General Terms
Algorithms, Design

Keywords
pipe

arrangement, multi-objective optimization, genetic algorithm

1. INTRODUCTION
Recently, the shipbuilding industry has been able to integratedesign and manufacturing systems due to advances in dataprocessing technology. This integration promotes automation andreduces labor requirements, which have become necessary due tothe lack of skilled workers. The design, analysis, and productionof a given system can all be completed using three-dimensional
data by employing CAD (Computer-Aided Design) software. It isquite difficult to visualize a complex pipe arrangement using a
two-dimensional blueprint. For this reason, pipe arrangement
designs have been generated using trial and error methods. Even
now, a large part of a design relies upon the designer's experience,
because the automation of pipe arrangements has not yet beenachieved. A reason for this may be the underreporting of researchon the automatic design of pipe arrangements.
This paper formulates a pipe arrangement design problem where
many pipes co-exist in a close space and some obstacles must beavoided. This problem includes large-scale numerical optimizationand combinatorial optimization problems, and has two criteria.
Copyright is held by the author/owner(s).
GECCO'06, July 8・2, 2006, Seattle, Washington, USA.
ACM 1-59593-186-4/06/0007.

Therefore, it is difficult to optimize the objective using usual
optimization techniques such as Random Search.
Therefore, multi-objective genetic algorithms suitable for thisproblem are proposed. It is demonstrated that the proposed
method can optimize a pipe arrangement efficiently, and someremarks are provided on applying this method to a practical pipearrangement design.

2. FORMURATING PIPE ARRANGEMENTDESIGN PROBLEM
2.1 Generating Piping RouteIn this paper, piping route is automatically designed when bothorigin and endpoint coordinates and the directions in which thepipes expand (direction vectors) are provided.
There is an infinite number of piping routes that could be used toconnect a given origin and endpoint. Therefore, a limit is imposedon the degrees-of-freedom for the route. A piping route is designedthat essentially specifies the bending points (nodes). First, a routeis designated as pattern-1, pattern-2, or pattern-3. Next, a shape isset according to the number of nodes and the relative position
between the origin and the end-point, as shown in Figs. 1, 2 and 3.
A pipe is characterized by both a pattern of generation and three
numerical parameters that describe the length of the straight parts.

Figure 1: pattern-1

Figure 2: pattern-2 Figure 3: pattern-3.

2.2 The cost functions
2.2.1 The cost function for materials cost
The cost function for materials cost is defined as the total sum of
the length of pipes.

2.2.2 The cost functions for obstacle
The evaluation values are worse when a pipe passes through thecenter of an obstacle and the length of the intersection is long.
nonpl =1k =1

f _ obstacle = å å (bkl - akl + Al )

Here, k and l are the index of each obstacle and pipe,respectively. n o and n p are the number of obstacles and pipes,respectively. bkl is the length of the intersection when a pipe kintersects an obstacle l . a kl is the averaged length between thecenter of the gravity of the obstacle l and the part divided by eachnode of the pipe k . Al is the length between the center of thegravity and the top of the obstacle l .

3.4 Result
To confirm the effectiveness of the proposed method, it wasapplied to a 15 pipes arrangement problem.

3. DESIGNING MULTI-OBJECTIVEGENETIC ALGORITHMS
3.1 Representation and Crossover
A combination of both a pattern of generation and numericalparameters are used as the representation and is called generation
gene.
A Crossover with Two Gene (XTG) is proposed. The XTG
generates one child from two parents using a gene named theobstacle gene, which contains the obstacle interference
information, as shown in Fig. 4.

Figure 6: Result of 15 pipes arrangement.

4. CONCLUSIONS
Figure 4: An example of the Crossover with Two Gene (XTG).

3.2 Generation-Alternation Model
A generation-alternation model based on the Pareto optimal
selection strategy, as shown in Fig. 5(Yoshida [2]), is employed.

In this paper, a design problem for pipe arrangement in a small
space where many pipes and obstacles co-exist was formulated,
and a multi-objective Genetic Algorithm suitable for this problem
was developed.
In the future, the work efficiency for installing a pipe and doing
maintenance should be considered, and the design should be
integrated with the production process. Moreover, fluid resistance,vibration or strength of structure should be considered as a costfunction. Because the search time increases as the number of pipes
increases, improvements to the proposed algorithms should becontinued.

5. ACKNOWLEDGMENTS
The authors thank Mr. Eisuke Ikezaki at Fukuoka Shipbuilding
Co., Ltd for introducing the practical problem on pipe arrangement
design kindly.
Figure 5: Generation-alternation model.

3.3 Modification Operator
to Avoid Contact with pipes
In this paper, a solution candidate is regarded as infeasible whenpipes interfere with each other. When initial solution candidates
are generated and new solution candidates are created, theprobability of pipes avoiding interference with each other rapidly
decreases as the number of pipes increases. To overcome thisproblem, a modification operator is proposed that makes infeasible
solutions candidates feasible, which changes the properties of theoriginal solution candidates as little as possible.

6. REFERENCES[1] S.Kobayashi, K.Yoshida, and M.Yamamura. Generatingpareto optimal decision trees by genetic algorithms. TheJapanese Society for Artificial Intelligence, 11(5):778--785,
1996.
[2] I.Ono. Genetic Algorithms for Optimization Taking Accountof Characteristics Preservation. Ph.D. dissertation, Tokyo
Institute of Technology, 1997.