shape grammar in generating concepts for a new Coca-Cola bottle design. The Bees Algorithm was found to outperform the evolutionary algorithm in this ...
Innovative Production Machines and Systems D.T. Pham, E.E. Eldukhri and A.J. Soroka (Eds.) © 2008 Cardiff University, Cardiff, UK.
Generating Branded Product Concepts: Comparing the Bees Algorithm and an Evolutionary Algorithm D.T. Pham, M.C. Ang, K.W. Ng, S. Otri, A. Haj Darwish Manufacturing Engineering Centre, Cardiff University, Cardiff CF24 3AA, UK
Abstract The task to generate product design concepts to maintain a particular brand identity whilst meeting functional requirements is challenging to designers. Shape grammars have been shown to be able formally to describe the creation of branded product shapes using a set of shape rules. These shape rules are applied manually to generate a family of new design concepts that maintain the brand identity of the product. However, shape grammars are not meant to evaluate whether the generated product concepts can meet specified functional requirements. When a shape grammar is combined with an optimisation technique such as an evolutionary algorithm, a computational procedure for generating branded design concepts that can meet functional requirements is established. This procedure evolves the set of shape rules whilst evaluating how well the outcome of the new design concepts meet a specified functional requirement. A new optimisation technique, the Bees Algorithm, was reported to perform better than many existing techniques. This paper compares the Bees Algorithm with an evolutionary algorithm when they are combined with a shape grammar in generating concepts for a new Coca-Cola bottle design. The Bees Algorithm was found to outperform the evolutionary algorithm in this investigation. Keywords: Bees Algorithm, branded product design, evolutionary algorithms, shape grammars
1. Introduction A product is an artefact developed for selling to customers by an enterprise [1]. A competitive enterprise is able to identify customer’s needs and customise products to meet those needs quickly at required quality. As a consumer market develops, competition arises, and technology matures. Technology is taken for granted [2]. Enterprise and its competitors will have products that have similar technology claims. The consumer market is soon filled with products that are nearly similar.. For example, all shampoo products claim to be very good for your hair. This leads consumers to look at other differentiating elements. One of the important differentiating elements
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is brand [3, 4]. In response, the enterprises have to brand their products distinctively and promote their product brand identity to gain market share [5, 6]. In developing a new improved product from an existing product, there is a need to gain benefits additional to those established by the existing product [7]. Such establishment benefits include the brand image depicted by the existing product shape and its design parameters. The importance of generating product concepts which consider product shape whilst meeting all functional requirements has been recognised by a number of researchers [8-10]. A branded product shape must be used to portray or reflect the identity of a brand. It is crucial that a branded product shape is considered and developed
during the product development stage. This branding strategy applied to product shape is transformed into branding requirements in product specification. Thus, product specification for a branded product has both functional and branding requirements. The task of generating product concepts depends on the experience, creativity and the knowledge of designers [8]. The ultimate aim of the product concept generating process is to derive solution concepts that meet the requirements identified in product specifications. Generating product design concepts to conform to a particular product brand identity and at the same time to fulfil functional requirements is a challenging task [9]. Therefore, there is a need to provide a support for the designer so that they may generate branded product shape/form better during product development process. 2. Shape grammars Shape grammars were first introduced by Stiny and Gips in 1972 [11]. Shape grammars are generative design systems that allow users to produce shapes syntactically [11, 12]. It is a formal method to generate shapes through a sequence of rule applications [12]. Shape grammars are used in architecture, arts and recently in product design to generate a family of shapes that conform to certain styles and brand identities [13-16]. They have been used to design the shape of consumer products. The first example in the literature was a coffeemaker grammar [17]. The coffeemaker grammar was able to generate four existing branded models of coffeemaker. Other examples are the Dove soap bar grammar [16], HarleyDavidson Motorcycle grammar [14] and Buick automobile grammar [13], and Cola-Cola bottle grammar [18]. Shape grammars are able to produce potentially a large number of shapes to be used during the early product concept development process. However, shape grammars are not meant to assess whether the generated shapes are meeting functional requirements. In order to assist a designer to produce potentially viable solutions, a number of researchers combined adaptive and evolutionary computing, such as genetic algorithms and simulated annealing, with shape grammars to generate 2D shapes and 3D structures to fulfil structural [19, 20] and functional requirements [21]. For a branded product design problem, Ang [22, 23] has combined an evolutionary algorithm with the Coca-Cola shape grammar to generate and explore solution concepts to meet a specified bottle volume
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(functional requirement) and branding requirements. However, the work has not been compared with any other optimisation techniques. 3. The Bees Algorithm Recently, an advanced adaptive computing technique, the Bees Algorithm [24] has been introduced and it shows promise. A number of successful applications using the Bees Algorithm have been reported. The Bees Algorithm has been used to solve continuous problems [24] and also on combinatorial ones [25]. In all the reported works, the quality of the results is shown to be better than the results generated by genetic algorithms. The Bees Algorithm is also used to solve a multi-objective optimisation problem [26]. These applications showed the strength of Bees Algorithm and pose an intriguing reason for further investigation. In this paper, a CocaCola grammar combined with the Bees Algorithm and the results are to be compared with earlier work using an evolutionary algorithm [23]. Similar volume requirements are used in this investigation. 4. Coca-Cola bottle case study The Coca-Cola shape grammar was produced to capture the contours of the trademark Coca-Cola bottle across different timelines [18]. The Coca-Cola bottle shape grammar provides information on specific bottle sections, characteristics of the shape and contour in each section, and the relationships between sections. There are no specific rules to generate values for different diameters and heights. Each bottle section is parameterised using diameters and heights. Diameters and heights provide the start point and end point of each connecting curve. Curves in bottle sections are formed by at least three points. In the implementation, the diameters and heights of each section are set within finite ranges. These parameters were used in the calculation of the volume for the bottle shapes produced by the prototype system. There are a total of seven rule groups in the CocaCola bottle grammar (Fig. 1). Starting from the rules for building the main body, there are other rules for construction of the upper part, modification of the main body, construction of the bottom, construction of the lower part, construction of the label region and construction of the cap. A rule group may contain more than one rule, for example, the construction of the upper part contains three separate rules that produce different shapes on top of the main body.
Based on the shape rules of the Coca-Cola bottle grammar, there is more than one rule in each rule group but only one rule can be selected for execution in a given computation step. In the construction of a bottle, the use of a rule from groups RG1, RG2, RG3 and RG4 is compulsory to produce a valid bottle design because every bottle must have a body, an upper part, a bottom and a cap. The rules in groups RG5, RG6 and RG7 are executed to produce variation in the bottle designs and their use is optional. Thus, the Bees Algorithm can randomly select shape rules within the same group to alter the bottle shape. Associate parameters are used to describe the heights and diameters of each bottle section (refer Fig. 2). For example, three parameters are used to describe the upper part section: bottom diameter (Φ1,2), top diameter (Φ2,2) and height (H3,2). These associated parameters, diameters and heights were set in the range of [minwidth, maxwidth] and [minheight, maxheight]. With the arrangement as shown in Fig.3, a total number of 16 associate parameters are used to define diameters and heights in each bottle part. To reduce the dimension of parameters, only the main body diameter and height was being generated by the Bees Algorithm. The remaining associate parameters are computed individually, based on ratio relationships between the main body and each respective bottle section.
Cap
Fig. 1. Coca-Cola bottle shape grammar (adapted from [18]) .
Φ1,4 Φ2,2
Upper part
H3,2
Φ1,2 Φ1,1 Body
Label Region Φ1,6 H2,6
H3,5
Φ1,5 Φ1,7 Φ 2,7
Lower part Φ1,3
H4,7
H2,1 H2,5
H3,7
Bottom Fig. 2. Parameterisation of Coca-Cola bottle (reproduced from Ang [23])
The resulting shape of bottle sections after each execution of a shape rule is varied. They were approximated excluding the bottom and cap to facilitate the calculation of the total volume. In this
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particular case study, the Bees Algorithm was used to generate rule sequences and associated parameters to achieve the total volume. The objective of this study is to minimise the difference between the bottle
volume and target volume of 500 ml. RG1
RG2
RG3
RG4
RG5
RG6
RG7
Φ1,1 H2,1
Φ1,2 Φ2,2 H3,2
Φ1,3
Φ1,4
Φ1,5 H2,5 H3,5
Φ1,6 H2,6
Φ1,7 Φ 2,7 H3,7 H4,7
Fig. 3. Rule group and their associate parameters (adapted from [23]).
5. Results A sample of different combinations of parameters was used by the Bees Algorithms and the results are shown in Table 1. The results demonstrate that the Bees Algorithm is able to find optimal solutions that achieve a 500 ml target volume within a 0.1 ml tolerance. The bottle shapes were generated using parameters and shape rules optimised by the Bees Algorithm. The contour of this family of bottles has a similar style to the existing trademark Coca-Cola bottle shape. An evolutionary algorithm was also applied to generate bottle shape using Coca-Cola shape rules and associated parameters [23]. The genotype was a 5x7 matrix similar to that shown in the table Fig.3. Single point crossover was performed on a pair of selected parents and followed by an intermediate recombination operator of Breeder Genetic Algorithm to recombine the diameters and height at the crossover point. Mutation was allowed to be same performed on either, altering the shape rule within the
rule or altering the parameter value in specified range in a random manner. Recombination and mutation were executed with the respective recombination probability (Pr) and mutation probability (Pm). Further details of the evolutionary algorithm implementation can be found in Ang’s work [23]. Different population size, maximum generation, recombination probability, mutation probability were tested for evolutionary algorithm implementation. The population size of 200 and the maximum generation of 200 were selected and the results are shown in Table 2. These settings allowed the evolutionary algorithm to achieve the bottle volume within 0.1 ml tolerance and did not consume high computation cost. Further investigations were conducted to obtain the best parameters combination for evolutionary algorithm and used to compare the performance with the Bees algorithm. It is found that the Bees algorithm can achieve bottle volume in less number of evaluations. The diagram in Fig 4 shows a comparison between the Bees Algorithm and the evolutionary algorithm. The Bees Algorithm parameters were: swarm size (n) = 100, elites (e) = 2, selected (m) =10, number of bees around elite site, N2= 10, number of bees around other selected site, N1 = 4, and initial patch size (ngh) = 0.01.The evolutionary algorithm parameters were: population size (Sp) = 200, maximum generation (Gm) = 200, recombination probability (Pr) = 0.9, mutation probability (Pm) = 0.1.
Table 1 Generating bottle volume and shape using the Bees Algorithm Swarm size (n) Elites (e) Selected (m) N2 N1 Initial patch size (Ngh) Best volume Bottle shape
401
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
10
10
10
10
20
10
30
20
20
30
100
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
5
5
10
10
10
10
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
10 4
0.5
0.1
0.025
0.01
0.01
0.1
0.05
0.1
0.05
0.1
0.01
500.00
499.98
500.01
499.99
500.05
500.02
499.99
499.99
500.10
500.00
500.00
Table 2 Generating bottle volume and shape using an evolutionary algorithm when 200 population size and 200 maximum generation Pr Pm Best volume
(a) 0.05 0.05
(b) 0.05 0.1
(c) 0.05 0.5
(d) 0.1 0.01
(e) 0.1 0.1
(f) 0.1 0.05
(g) 0.5 0.01
(h) 0.5 0.05
(i) 0.5 0.1
(j) 0.9 0.1
(k) 0.9 0.05
500.10
499.95
499.99
499.90
500.00
500.04
500.01
500.02
500.09
500.01
499.98
Bottle shape
Pr = Recombination probability, Pm = Mutation probability 50 Bees
|Best volume - target volume|
45
EA
40 35 30 25 20 15 10 5 0 0
5000
10000
15000
20000
25000
Num ber of Evaluations
Fig. 4. The Bees algorithm vs. evolutionary algorithm
6. Conclusions Both the Bees Algorithm and the evolutionary algorithm are found to be able to generate bottle shapes that have similar style with the existing Coca-Cola trademark bottle shape. The Bees Algorithm outperforms the evolutionary algorithm in that it was able to achieve the target volume in a smaller number of evaluations. This may due to the fact that the evolutionary algorithm is mimicking the Darwinian evolution process and that this process is a slow one. On the other hand, the Bees Algorithm is mimicking the foraging process of the bees and it is a relatively more aggressive process. Previous work [23] and this current work shows that optimisation techniques can be used with shape grammar rules to produce designs that
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conform to a particular brand and fulfil functional requirements. Acknowledgements The authors are members of the EU-funded FP6 Network of Excellence for Innovative Production Machines and System (I*PROMS). References [1] Ulrich KT and Eppinger SD. Product Design And Development. McGraw-Hill, Boston, 2003.
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