An integrated approach to achieving optimal design of computer games

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An integrated approach to achieving optimal design of computer games

Shang Hwa Hsu *, Feng-Liang Lee, Muh-Cherng Wu

Department of Industrial Engineering and Management, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan, ROC

Abstract

In a time-to-market environment, designers may not be able to incorporate all the design features in a computer game. For each feature, there are several levels of implementation, which is corresponded to different levels of benefit as well as cost. Therefore, a trade-off decision for determining appropriate levels of implementation is very important, yet has been rarely studied in literature. This paper presents an approach to solve the trade-off decision problem. This approach applies the neural network technique and develops a genetic algorithm to optimize the design of computer games. By this approach, a near-optimal design alternative can be identified in a timely fashion.

Keywords: Neural networks; Genetic algorithms; Optimization; Computer game

1. Introduction

Computer game is a promising industry (Bethke, 2003) and much research on the effective design of computer games has been published in the last two decades. Most of these studies focused on the identification of design factors to make a game fun.Malone and Lepper (1987)argued that a fun game has to involve four characteristics: challenge, fantasy, curiosity and control, which can intrinsically motivate game-players. Based on these characteristics, Fabricatore, Nussbaum, and Rosas (2002)developed a set of detailed design guidelines for action games. A recent study further identified 39 design features that contribute to the fun of an action game (Hsu, Lee, & Wu, 2004).

Attempting to incorporate all the design features in a computer game is infeasible for several reasons. First, time-to-market in this industry is a critical factor for product success because the life cycle of a computer game is quite short. Therefore, incorporating all the design features is generally impossible in a limited time frame. Second, the benefit function of a design feature has a marginal-diminishing effect. That is, the incremental benefit decreases as total investment on implementing a design feature increases. Therefore, it may not be cost-effective to implement every design feature up to its maximum level. Third, most companies in this industry tend to

adopt a risk-pooling product strategy, which leads to the development of several games at the same time. The resources allocated to a particular game are rather limited. How to effectively design a computer game in limited time and budget is therefore a very important issue, yet has rarely been investigated in previous literature.

The issue of designing a computer game within time and budget constraint is essentially a selection problem; that is, selecting a design alternative out of a large solution space. For example, a game involves 39 design features. Each feature can be implemented in six levels; the higher the implementation level, the higher the performance as well as the cost. Consequently, the solution space of designing such a game can involve 639alternatives—a formidable task if an optimal design is to be identified by applying an exhaustive search.

This paper proposes an approach to efficiently identifying a near-optimal design alternative out of the enormous solution space. This approach involves the use of artificial neural network (ANN) technique (Rumelhart, Hinton, & Williams, 1986) and genetic algorithm (GA) (Michalewicz, 1992) to select the design alternative. Specifically, a neural network is established to evaluate the perceived fun of a design alternative. A genetic algorithm is developed to identify a near-optimal design alternative. The identified design alterna-tive suggests the appropriate implementation level of each design feature and facilitates designers to properly allocate their efforts to various design features.

The technique of integrating ANN and GA has been successfully applied in some optimization problems such as engineering design (Marcelin, 2004; Mok, Kwong, & Lau, 2001; Qiu & Li, 2004; Shi, Lou, Lu, & Zhang, 2003; Su, Kao, & Tarng, 2004), management decision (Kuo & Chen, 2004;

www.elsevier.com/locate/eswa

* Corresponding author. Tel.: C886 3 5726731; fax: C886 3 5722392. E-mail addresses: shhsu@mail.nctu.edu.tw (S.H. Hsu), fengl@cc.fec.edu. tw (F.-L. Lee).

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Lee, Lee, Lee, Choi, & Lee, 2001; Li, Wu, & Pang, 2004; Yuan & Chen, 2001), and financial planning (Chen & Huang, 2003; Kim & Han, 2000, 2003; Shin & Han, 2000; Versace, Bhatt, Hinds, & Shiffer, 2004). In this study, we attempt to apply the techniques to tackle the problem of designing computer games. The remainder of this paper is organized as follows. Section 2 describes the modeling of a design alternative, which involves its implementation levels of design features and perceived fun. Section 3 describes how to apply neural network technique to evaluate the perceived fun of a design alternative. Section 4 formulates the research problem. Section 5 presents the genetic algorithm to search for a near-optimal solution. A numerical example is illustrated in Section 6 and concluding remarks are given in Section 7.

2. Modeling of design alternatives

Hsu et al. (2004)conducted a study to identify the design features contributing to fun, which involves 28 action games and the overall perceived fun of each game was rated at one of five levels, ranging from 1 to 5.

The procedure for the identification of design features consisted of three steps. First, experienced game-players were asked to classify the 28 games into three groups according to their perceived fun. Second, each game in the ‘fun’ group was contrasted with a game in the ‘no-fun’ group in order to identify the design features that make a game fun. Third, each design feature of a game was rated in terms of its implementation level, ranging from 0 to 5. Their experiment results indicated that an action game is composed of 39 design features.

An action game is essentially a design alternative before completion of a design process. This study models ith design alternative by vector xiZ ½xij, 1%j%39, where xij2[0, 5] represents the implementation level of jth design feature in the design alternative. The overall perceived fun of ith design alternative is represented by yi2[1,5].

According to the modeling, the solution space of the optimal

design of interest can be represented by

SZ f xj xZ ½xj; xj2½0; 5; xj2ZC; 1%j%39g, also called the Design Space. The space of the perceived fun can be represented by Y Z fyjy 2R; 1% y% 5g, briefly called Fun Space.

3. Evaluation of perceived fun for design alternatives To find an optimal design of interest, a general mapping function between Design Space S and Fun Space Y has to be established. Such a mapping function is constructed by a neural network.

The architecture of the neural network is described below. The network is composed of three layers: an input layer, an intermediate hidden layer, and an output layer. Each node in the input layer represents the implementation level of a design feature and the single node in the output layer represents the overall perceived fun. Given a design alternative x in Design

Space S, the neural network is intended to compute the overall perceived fun of the alternative.

The construction of the neural network involves two stages: network training and verification. InFig. 1, each of the lines connecting the nodes in distinct layers represents a weighting to be determined by the network training process. Of the sampled data sets, some are used to train the neural network and the others are used to verify the effectiveness of the network. A well-trained network has to ensure the validity of input/output mapping. That is, for an input vector xh with a corresponding output yh, the network will estimate an output

Ohwith tolerable error; namely, ðjOhKyhj=yhÞ% 3 where 3 is a very small value. The network if well trained can appropriately evaluate the perceived fun of a design alternative. Detailed procedure of the training algorithms can be referred to

Rumelhart et al. (1986).

With the constructed network, we can quickly determine the perceived fun of any design alternative in Design Space S. To facilitate the following presentation, the mapping provided by the neural network is represented by yZ Gð xÞ.

4. Problem formulation

The research problem for selecting an optimal design alternative of a computer game can be formulated as follows: Minimize Tð xÞ ZX N jZ1 f ðxjÞ Subject to: x 2S (1) y Z Gð xÞ (2) yR PFmin (3)

The objective function indicates that the total design time is to be minimized, where f(xj) represents the design time

required to achieve a particular implementation level xj for

jth design feature. Constraint (1) indicates that we need to Fig. 1. Architecture of the neural network.

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select a design alternative from Design Space S. Constraint (2) represents the neural network mapping between Design Space S and Fun Space F. Constraint (3) denotes that the perceived fun of the selected design alternative should meet the minimum requirement PFmin, which is demanded by users.

In the above formulation, Design space S consists of mN design alternatives, where N denotes the number of design features and m denotes the number of implementation levels. The design space can easily become quite huge (639z2.23! 1030) when several tens of design features (NZ39) and a few implementation levels (mZ6) are involved. Applying an exhaustive search method is almost impossible. Therefore, this research develops a genetic algorithm to efficiently find a near-optimal solution from such a huge space.

5. Searching for optimal design alternative

We develop a GA to solve the formulated problem. Each aspect of the proposed GA is described below.

5.1. Chromosome representation

A solution (a design alternative) is modeled by vector x (called a chromosome), which is composed of N features (called genes). Each feature has m implementation levels. 5.2. Initial population

An initial population P(0) is created by randomly generating M chromosomes. In generating a chromosome, the value of each gene xj, an integer, is randomly chosen from the interval

[0, 5].

5.3. Fitness function

By referring toChen and Huang (2003) and Marcelin (2004)

, the fitness function is defined below. The higher the Fð xÞ, the lower is the fitness value of x. The chromosome with a small fitness value is less likely to survive during the evolution of the population and tends to be finally excluded from the population. Fð_{xÞ ZK Tð xÞ C Z} PFmin y K1 Z Z 0; if PFmin% y;

a large positive number; otherwise (

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5.4. Crossover

The crossover operator is designed to create M!Pcrnew

chromosomes, where Pcr is the crossover probability. The

creation procedure is as follows. Randomly sample M!Pcr

chromosomes from P(t) and group them into (M!Pcr)/2 pairs.

Two new chromosomes are created by exchanging a portion of the two original chromosomes in a particular pair.

5.5. Mutation

The mutation operator is designed to create M!Pmu new

chromosomes from P(t), where Pmuis the mutation probability.

This operator creates a new chromosome by randomly selecting a chromosome from P(t) and replaces the value of one of its genes. The mutation procedure is repeated until M! Pmuhas been created.

5.6. Evolution of population

Put the original chromosomes in P(t) as well as the newly created ones into a set W, from which M chromosomes are to be selected to from the next population P(tC1). The evolution procedure is as follows (Goldberg & Deb, 1991). Randomly sample nR2 chromosomes from W and evaluate their fitness values. Select the one with maximum fitness value and put it into P(tC1). Iterate the above steps until P(tC1) is formed.

Table 1

Design features identified in example (Hsu et al., 2004) DF1: Scenario is unpredictable DF2: Scenario is varying DF3: Scenario is dramatic DF4: Scene is creative DF5: Scene is looking-real DF6: Scene is colorful DF7: Scene is complex DF8: Scene is varying DF9: Scene transmits smoothly DF10: Character is creative

DF11: Character looks like a real person DF12: Character’s style is similar to mine DF13: More than one player can participate DF14: Opponent is competitive

DF15: Opponent is unpredictable DF16: Weapons are creative DF17: Weapons are powerful

DF18: Background music suits the scene DF19: Background music is varying DF20: Music tempo suits the plot DF21: Sound effect varies with events DF22: Sound effect suits the event DF23: Sound effect is loud enough DF24: Sound effect is varying

DF25: Level difficulty is flexible to choose DF26: New skills are acquired at every level DF27: Level difficulty increases progressively DF28: Levels can be skipped

DF29: Beginning levels are easy DF30: Final levels are difficult DF31: Pace is fast enough DF32: Pace is varying

DF33: Input device is easy to control DF34: Game can be saved for continuity DF35: High score board can be viewed DF36: Game scores can be accumulated DF37: Virtual token can be won DF38: Instruction is clear

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5.7. Termination condition

The evolution stops either when the number of evolution tO T or when a particular chromosome keeps being the best solution in the population for over Q generations.

6. Numerical example

The proposed method of integrating ANN and GA to optimally design an action game is implemented by using the result ofHsu et al. (2004). The 39 design features identified are shown in Table 1. The implementation is coded with CCC program language.

In the research problem, we aim to identify a design alternative that minimizes total design time Tð xÞ and meets the minimum fun requirement PFminZ4.5. Design times required

to achieve various implementation levels for each design feature are shown inTable 2.

Of the 28 design alternatives inHsu et al. (2004)study , the data sets of 21 alternatives are used to train a neural network and that of the other seven alternatives are used to evaluate the effectiveness of the neural network. The trained neural network seems an effective one because the output error of the network is less than 0.2%.

The proposed GA is then used to identify a near-optimal design alternative from Design Space S. The parameters of the GA are given as follows: MZ100, PcrZ0.80, PmuZ0.05, TZ

99,999, QZ1000. We run the GA program with 100 replications. For the 100 replications, the mean design time is 514.83 time units and its standard deviation is 19.396 time units. Of the 100 replications, the best design alternative is shown inTable 3. The small standard deviation indicates that a few replications will be sufficient to identify a near-the-best solution of the GA. The computation time required for a replication is about 5 min, by a personal computer with 1.8 GHz CPU. This approach can provide a timely solution and therefore serve as an effective aid for game design.

7. Conclusions

This study proposes an approach to solving a trade-off decision problem for game design. Making a trade-off among design features is very important in the design process, but can be very complex. A computer game involves a large number of design features, and each feature can be implemented in various levels. The number of design alternatives can therefore be quite huge due to the combinatorial explosion of implementation levels. Due to the pressure of time-to-market, the time available to designers is relatively limited. Therefore, developing a method that allows to efficiently identifying a design alternative is critical to game design.

This study uses ANN and GA to optimize the design of a computer game. This issue is resolved in two-fold. First, the constructed ANN, using a few expensive experiment data, can evaluate the overall perceived fun of a design alternative. Second, the proposed GA can efficiently identify a near-optimal design alternative out of the enormous solution space. The suggested design alternative facilitates game designers to properly allocate their efforts to various design features.

Although this approach has been successfully applied to action games, the applicability of other types of digital contents remains to be investigated. At the present time, we are Table 2

Design time required to achieve various implementation levels for each design feature Implementation level 0 1 2 3 4 5 DF1 0 10 30 50 70 90 DF2 0 10 20 40 80 160 DF3 0 10 30 90 190 330 DF4 0 10 20 40 80 160 DF5 0 10 20 30 40 50 DF6 0 5 6 10 12 15 DF7 0 5 7 8 9 10 DF8 0 5 10 15 18 20 DF9 0 5 7 10 12 20 DF10 0 10 20 30 40 50 DF11 0 10 30 60 90 120 DF12 0 10 20 40 80 160 DF13 0 10 12 20 22 24 DF14 0 10 20 40 80 160 DF15 0 10 20 30 40 50 DF16 0 10 20 40 80 120 DF17 0 10 20 40 80 100 DF18 0 10 20 40 60 80 DF19 0 5 7 19 20 25 DF20 0 5 7 8 9 10 DF21 0 5 7 10 15 20 DF22 0 10 20 30 40 50 DF23 0 5 7 10 12 14 DF24 0 5 8 10 12 20 DF25 0 5 6 10 12 15 DF26 0 10 20 40 60 80 DF27 0 10 20 30 40 50 DF28 0 10 12 15 18 20 DF29 0 5 8 10 15 20 DF30 0 5 8 10 12 15 DF31 0 10 12 15 18 20 DF32 0 10 12 15 18 20 DF33 0 10 20 30 40 50 DF34 0 5 15 25 35 45 DF35 0 5 10 15 20 25 DF36 0 5 10 15 20 25 DF37 0 10 20 40 60 80 DF38 0 5 10 15 20 25 DF39 0 10 20 30 40 50 Table 3

The best design alternative of the 100 replications Total design time required Tð xÞ 483

Overall perceived fun (y) 4.5483 Implementation level of each

design feature x1Z0 x2Z1 x3Z1 x4Z2 x5Z2 x6Z3 x7Z2 x8Z0 x9Z5 x10Z0 x11Z1 x12Z0 x13Z0 x14Z0 x15Z1 x16Z0 x17Z2 x18Z4 x19Z4 x20Z0 x21Z4 x22Z0 x23Z5 x24Z3 x25Z4 x26Z2 x27Z1 x28Z5 x29Z0 x30Z5 x31Z5 x32Z1 x33Z1 x34Z5 x35Z3 x36Z1 x37Z0 x38Z3 x39Z3

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investigating the possibility of extending this approach to some other digital contents such as other types of computer games, multi-media, movies, e-learning, and man–machine interfaces of mobile devices.

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