Elsevier

Computers in Human Behavior

Volume 27, Issue 5, September 2011, Pages 1482-1492
Computers in Human Behavior

Interactive genetic algorithms with individual’s fuzzy fitness

https://doi.org/10.1016/j.chb.2010.10.012Get rights and content

Abstract

Interactive genetic algorithms are effective methods to solve an optimization problem with implicit or fuzzy indices, and have been successfully applied to many real-world optimization problems in recent years. In traditional interactive genetic algorithms, many researchers adopt an accurate number to express an individual’s fitness assigned by a user. But it is difficult for this expression to reasonably reflect a user’s fuzzy and gradual cognitive to an individual. We present an interactive genetic algorithm with an individual’s fuzzy fitness in this paper. Firstly, we adopt a fuzzy number described with a Gaussian membership function to express an individual’s fitness. Then, in order to compare different individuals, we generate a fitness interval based on α-cut set, and obtain the probability of individual dominance by use of the probability of interval dominance. Finally, we determine the superior individual in tournament selection with size two based on the probability of individual dominance, and perform the subsequent evolutions. We apply the proposed algorithm to a fashion evolutionary design system, a typical optimization problem with an implicit index, and compare it with two interactive genetic algorithms, i.e., an interactive genetic algorithm with an individual’s accurate fitness and an interactive genetic algorithm with an individual’s interval fitness. The experimental results show that the proposed algorithm is advantageous in alleviating user fatigue and looking for user’s satisfactory individuals.

Introduction

Optimization problems are very common in real-world applications, e.g., the traveling salesman problem (TSP) (Lin & Kernighan, 1973), job-shop scheduling (Adams, Balas, & Zawack, 1986), product design (Li & Azarm, 2000). For an optimization problem whose objective functions are differential and whose scale is small or medium, some traditional optimization methods, e.g., the Newton method (Xie, Li, & Tang, 2003), are suitable to solve it. Whereas for an optimization problem whose objective functions are not differential, or even not continuous, or for one whose objective functions are differential but whose scale is very large, many traditional optimization methods are no longer applicable.

Genetic algorithms (GAs), proposed in the 1960s, are a kind of global and stochastic optimization method inspired from nature evolution (Holland, 1975). In GAs, a solution to a problem being solved is encoded as an individual and often with a binary string. GAs contain a number of individuals that collectively form a population of solutions. Initially each individual is randomly generated. An evaluation process is then applied to assign an individual’s fitness. Individuals that are better in terms of their objective function are assigned high fitness, and those with high fitness are more likely to be selected to generate individuals in the next generation. A new generation of individuals is generated either by copying members without alteration or by modifying them in an attempt to increase their fitness. A typical operator that is applied to modify members is called crossover, which combines information from two selected parent individuals to generate new ones. The main search power of crossover operation is based on the exploration of existing solutions. Searching for optimal solutions, however also needs to explore those parts of a solution space that have not been represented in current solutions. Mutation operation accomplishes this task by randomly modifying a portion of individuals in the current generation to yield new solutions. The new generation of individuals is then re-evaluated using the same objective function and the process repeats until predefined termination rule is met (Zhang, Chung, & Lo, 2007).

Since GAs do not require continuous and differential objective functions of an optimization problem, and can effectively look for satisfactory solutions for a large scale problem, they have gained broad attention in the optimization community and fruitful achievements have been obtained.

But the performance of the canonical genetic algorithm, a genetic algorithm proposed early, is not satisfactory. For example, it often finds local optimal solutions of an optimization problem. In order to further enhance its performance, many researchers have proposed some improved ones, including efficient adaptive genetic algorithms (Gong & Pan, 2003), co-evolutionary genetic algorithms for high dimensional complicated optimization problems (Wiegand, 2003), as well as multi-objective genetic algorithms for simultaneously optimizing several objective functions (Deb, Pratap, Agarwal, & Meyarivan, 2002). In addition, the implementation of genetic algorithms also expands from a PC to a cluster as well as a network. To distinguish them from interactive genetic algorithms (IGAs) which will be introduced later in this section, we name them traditional genetic algorithms (TGAs).

Although traditional genetic algorithms do not require continuous and differential objective functions, they do require well-defined objective functions in order to calculate an individual’s fitness. But it is difficult or even impossible for many complicated optimization problems to have one or several well-defined objective functions because of their implicit or fuzzy indices. Therefore traditional genetic algorithms are not applicable to such optimization problems.

Interactive genetic algorithms, proposed in mid-1980s, are effective methods to solve an optimization problem with implicit or fuzzy indices (Dawkins, 1986). These algorithms combine traditional evolution mechanism with a user’s intelligent evaluation, and the user assigns an individual’s fitness rather than a function that is difficult or even impossible to explicitly express. Up to now, they have been successfully applied in many fields, e.g., face identification (Caldwell & Johnston, 1991), music composition (Tokui & Iba, 2000), micro-machine design (Kamalian, Zhang, Takagi, & Agogino, 2005), fashion design (Gong, Hao, Zhou, & Sun, 2007), hearing aid fitting (Takagi & Ohsaki, 2007), plant layout design (Brintrup, Ramsden, & Tiwari, 2007) and ergonomic chair design (Brintrup, Ramsden, & Tiwari, 2008).

The obvious characteristic of IGAs, compared with TGAs, is that a user assigns an individual’s fitness. The user compares different individuals in the same generation and assigns fitness based on their phenotype through a human–computer interface. The frequent interaction results in user fatigue. Therefore IGAs often have small population size and a small number of evolutionary generations (Takagi, 2001), which influences these algorithms’ performance to some degree and restricts their applications in complicated optimization problems. Accordingly how to evaluate an individual and express its fitness becomes one of the key problems in IGAs.

Since user fatigue results from the user’s evaluation on an individual and expression of its fitness, in order to alleviate user fatigue, a possible alternative is to change the approach to express an individual’s fitness. The goal of this paper is to alleviate user fatigue by adopting an appropriate approach to express an individual’s fitness.

Up to now, there have been two approaches to express an individual’s fitness, i.e., an accurate number and an interval. As is well known, a user’s cognitive is fuzzy and gradual, therefore the evaluation of an individual by the user and the expression of its fitness should also be fuzzy and gradual. It is difficult to reflect the above character if we adopt an accurate number to express an individual’s fitness. We ever adopted an interval, a kind of uncertain number, to express an individual’s fitness (Gong & Guo, 2007), further, we presented an adaptive interactive genetic algorithm in which the probabilities of crossover and mutation change along with the evolution (Gong, Guo, Lu, & Ma, 2008). Although this method alleviates user fatigue to some degree, it requires two numbers, i.e., the lower limit and the upper limit, in order to express an individual’s fitness, which increases time of human–computer interaction.

Besides an interval, a fuzzy number is another kind of uncertain number. In this paper, we adopt a fuzzy number described with a Gaussian membership function to express an individual’s fitness. Then, in order to compare different individuals, we generate a fitness interval based on α-cut set, and obtain the probability of individual dominance by use of the probability of interval dominance. Finally, we determine the superior individual in tournament selection with size two based on the probability of individual dominance, and perform the subsequent evolutions. We name the algorithm an interactive genetic algorithm with an individual’s fuzzy fitness (IGA-IFF).

Our contributions in this paper mainly embody in the following two aspects. Firstly, we adopt a novel expression of an individual’s fitness, which much accords with a user’s fuzzy cognitive to the evaluated object. Secondly, we present an effective method to compare different individuals when an individual’s fitness is expressed with a fuzzy number, which is necessary for a population to evolve. These contributions can improve the performance of existing IGAs in alleviating user fatigue and looking for the optimal solutions of an optimization problem, therefore it is beneficial to solve complicated problems with implicit or fuzzy indices.

In the next section, we will review some related work on methods to alleviate user fatigue and fuzzy numbers. The emphasis of this paper is Section 3, in which we will describe ideas of IGA-IFF, an individual’s fuzzy fitness, comparison of two individuals, and steps of IGA-IFF in detail. We will present the proposed algorithm’s application in a fashion evolutionary design system and some experimental results in Section 4. Finally, we will draw some conclusions and provide opportunities for future research in Section 5.

Section snippets

Related work

Generally speaking, there are two approaches to evaluate an individual. One is that a user directly evaluates an individual based on his or her preference. For example, Takagi and Ohya (1996) proposed a fitness assignment method which combines a continuous fitness with a discrete one. The other is that surrogate-assisted models evaluate a part of or even all individuals in some generations. For example, Sugimoto and Yoneyama (2001) presented a method to estimate an individual’s fitness using

Interactive genetic algorithm with individual’s fuzzy fitness

An interactive genetic algorithm with an individual’s fuzzy fitness is an IGA which expresses the result of a user evaluating an individual with a fuzzy number, and adopts traditional genetic operations. Some new problems will result from the fuzzy expression of an individual’s fitness, in which the primary one is how to compare different individuals in the same generation. It will directly influence selection operation adopted in the algorithm. In addition, it will also influence the

Backgrounds

Fashion design is a very popular vocation, for everyone likes to wear satisfactory fashions but few can design a satisfactory one. In fact, fashion design is a very complicated process and often completed by designers who have been systematically trained. Although there are some softwares available for fashion design, they are often too professional for an ordinary person to use. With the development of society pursuing personality becomes a fad. That is to say, people often like to wear

Conclusion

User fatigue problem, resulted from evaluation on an individual and expression of its fitness by a user, is very important and hard to solve in IGAs. It is key for IGAs to improve performance in case of successfully solving user fatigue problem.

It is easy to understand that user fatigue can alleviate to some degree if we adopt an appropriate approach to express an individual’s fitness. Based on this, we proposed a novel interactive genetic algorithm, i.e., IGA-IFF in this paper. We adopted a

Acknowledgments

This work was completed when Dun-wei Gong was visiting CERCIA, School of Computer Science, the University of Birmingham. It was supported by NSFC with Grant No. 60775044 and Program for New Century Excellent Talents in University with Grant No. NCET-07-0802.

References (30)

  • D.W. Gong et al.

    Theory and applications of adaptive genetic algorithms

    (2003)
  • D.W. Gong et al.

    Theory and applications of interactive genetic algorithms

    (2007)
  • D.W. Gong et al.

    Interactive genetic algorithms with multiple approximate models

    Control Theory and Applications

    (2008)
  • G.S. Hao et al.

    Method of replacing the user with machine in interactive genetic algorithm

    Pattern Recognition and Artificial Intelligence

    (2006)
  • J.H. Holland

    Adaptation in natural and artificial systems

    (1975)
  • Cited by (0)

    View full text