Keywords

1 Introduction

Nature offers solutions to engineering problems. Nowadays, many engineering solutions mimic those that nature has built through evolution [1]. Evolution is the system that nature uses to adapt to its environment. It is a complex system, but has phases and processes that can be emulated with computation [2]. Genetic evolution is the most widely used tool by nature. Today we better know the processes that control genetics [3], and to the extent that we can emulate it with computational algorithms.

Genetic algorithms (GAs) emulate the process that characterizes genetic evolution using genetic operators [4]. These operators apply to a population from one generation to another. Each generation is evaluated according to the fitness function [5]. In this way, the evolutionary system perfects the solution in each generation.

The engineering design process can have different levels of complexity. In industrial design, the desired solution optimizes quality values. However, the design process can involve many parameters that complicate optimization, and the design can contain many non-linear parameters. When the goal function has many local extremes, problems can appear [6]. In these cases, GA can solve the problem [7].

The most widely used optimization methods have problems [8]. The gradient method optimizes only local extremes [9], and the stochastic search method only disturbs the solution of the gradient method [10]. However, GA keep and evolve solutions in a search space.

GAs have been used in many optimization applications. We can see the application of GAs as: image processing [11], numerical optimization [12], programming [13], machine learning [14] or data structures [15]. This optimization method evolves solutions in a search space to obtain the desired result. Using GA as computer tools was introduced by Fraiser [16].

In this bibliographic review, we introduce a GA framework, and then see the relationship between GA and design. Next we see some examples of applying GA in industrial design.

2 Genetic Algorithms: Framework

A GA algorithm contains a search space formed by a population of individuals. Each subject, the so-called specimen, is composed of chromosomes. The so-called genotype forms the information contained in chromosomes. The so-called phenotype is the chromosome appearance. For each subject, the fitness function associates and evaluates an aptitude. From one generation to another, the population is submitted to the so-called genetic operators: crossing, mutation and cloning. Therefore, this process is evolutionary multiobjective optimization (EMO). We can establish a relationship between elements of nature and computation (Table 1).

Table 1. Relationship between nature and evolutionary computation
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GA have the following stages (Fig. 1). First, the initial population is set up. In stage 2, the fitness function evaluates each specimen. If the evaluation is positive, the subject moves to the next generation through cloning. If the evaluation is negative, the subject is selected according to its level of adaptation. In stage 3, genetic operators create new specimens to form the next generation. Stage 2 is repeated until the satisfaction criterion is met.

Fig. 1.
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GA schema

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Each specimen represents a solution that needs to evolve from the beginning to reach the final specifications. To build the solutions space, we can use a complex or a simple representation. When we work in design, two problems can appear [17]. On the one hand, if we use a simple representation, GA spends a lot of time searching irrelevant regions. If, on the other hand, chromosomes representation is complex, the next generation can evolve without reaching the point of equilibrium. Zhao et al. [18] has worked in the gene theory to simply the design process.

2.1 Genetic Operators

In each step from one generation to another, GA apply genetic operators. There are three genetic operators: crossing, mutation and cloning. GA performance depends on the choice of crossing and mutation operators [17]. Cloning operator is a save/recover operator. Cloning consists in copying the solutions that adapt well to the final specifications. The crossover operator creates a new specimen from two other individuals. To make the crossover, GA use one crossing point or more by recombining chromosomes to form a new genotype. A recent survey [19] suggests that the geometric crossover operator (or the topological crossover operator) is well-defined when the solution is defined with distance (geometrically). Mutation creates a new specimen by making changes in its genotype. Modifications consist in changing part of the genotype or adding/removing chromosomes.

2.2 Fitness Function

As with nature, the survival of a specimen depends on its adaptation to the environment. In GA, the fitness function evaluates the fitness of each specimen. This fitness function must contain the requirements and specifications desired in the final solution. In this way, the degree each specimen’s adaptation represents its distance to the final solution. The fitness function is considered the search core of GA. In design optimization, the fitness function is considerably important. An experimental study [20] establishes that an improved fitness function (IGA) has better convergence than traditional GA.

3 Involving GA in Design

Design generates solutions to cover products and specifications, and must contain information needed to manufacture them. Manufacturing imposes additional restrictions to design. Therefore, design is a task that involves a search to fulfill specifications and requirements. In 1962, a study by Asimov [21] showed the organization while solving a design task without taking into account the role that knowledge plays. It is a huge simplification, but the bases of this model are used in CAD-CAM systems.

Another model that enable knowledge of the design process is the so-called cognitive model [22]. This model can describe the designer’s reasoning and decision making in design stages. However, this model is very difficult to translate into computational terms without using a broad simplification [23]. Here the design process is assimilated into parametric design thinking (PDT). PDT englobes the parametric design, the cognitive model and the computer-aided design. In short, the thinking process, involved in design, can be divided into two aspects: creative thinking and the pre-knowledge-based design (e.g. parametric design or configuration design [24]). We can see how GA can be used in these two contexts: creative design and configuration design.

3.1 Creative Design

Computerizing the creative design is a challenging task. In the creative design, there are two research lines: assisting human creativity and solving creative problems. In the former, users evaluate the population. So it is not necessary to define a fitness function. However, this causes a limited iteration speed because users cannot evaluate large populations. Frazer [25] concludes that a computer system´s creativity is attributed to the originator of the method.

A method to expand the search space is to reduce the number of the fitness function’s restrictions. In this way, the system can change the initial representation. Then the system can build solutions beyond the optimization problem. The creative problem could have been solved by searching a solution that was not initially represented. This theory has been defended by Boden [26].

Another method is the so-called embryogenesis theory [27]. Here the fitness function evaluates the phenotype. Embryos are used to explore the search space. In this way, search parameters are not fixed.

Other studies have attempted to transform the creative process into an algorithm. Yang et al. [28] proposed dividing the search space into three: design flow space, knowledge inspiration space and solution operating space. In this way, GA acquire a certain level of creativity. Shieh et al. [29] propose three hybrid representations to obtain creative design alternatives. Golberg David [30] explains how to design creative GAs based on human comprehension.

3.2 Configuration Design

While the creative design is based on creative thinking, we can see modeling methods based on the problem’s pre-knowledge. The configuration design [31] is based on the selection and assembly of components to build the final solution. The relationship between specifications and configurations is known. Therefore, it is a search to acquire an optimal configuration [32].

We can set a clear analogy between the configuration design and GA: configurable elements are encoded as genes with chromosomes. These elements evolve by GA (Fig. 2).

Fig. 2.
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Relationship between GA and the configuration design

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In the configuration design, the configurable elements set the search space. The efficiency of GA is excellent due to the intensive exploring and exploitation that the genetic operators allow. Zou et al. [33] built the airspace grid design with configuration design-based GA. The search space, in this case, is formed by different grid configurations. GA evolve the grid testing alternatives configuration for each grid element. Da et al. [34] evaluated an evolutionary design composed of composite parts with different configurations. Andres-Perez et al. [35] used an enhanced mutation operator to generate different configurations in the search space. Chandrasekaran and Banerjee [36] resorted to a multiobjective evolutionary algorithm to offer an efficient and effective means to obtain a Pareto near-optimal set of solutions.

4 Applications of GA in Industrial Design

The potential use of GA in industrial design is remarkably high as they apply to most engineering fields: mechanical, electrical, aerospace and civil engineering. We analyze their application in three tools used in industrial design:

  • Conceptual design

  • Parametric design

  • Reverse engineering

4.1 Conceptual Design

In conceptual design, either new components are used, or old components are combined in a novel way. There is no fixed method. Goldberg [37] presents a structure with four components: a problem to solve (the design challenge), someone to solve it (the designer), one conceptual design or more, and one method to compare alternative designs. This author presents GA as “a lower limit in the capacity of a designer in the processes of recombination and selection”.

In conceptual design, GA are used as the method to compare and to search for alternative designs. This search can be guided by the designer, or the GA guide to the designer, to choose alternatives. Zhu et al. [38] used a GA-based selection method to accomplish an optimum multi-link transmission mechanism design. These authors adopted a polygon model into the iterative optimization process to describe the domination relationships of the individuals on the Pareto front. Mueller and Ochsendorf [39] proposed a computational approach for designing space exploration, which extends existing interactive evolutionary algorithms to enhance the inclusion of designer preferences. Zhang and Mueller [40] used GA to balance conflicting requirements in a conceptual structures design. Skiborowski et al. [41] introduced an interesting hybrid evolutionary-deterministic optimization approach for a conceptual design. They used successively relaxed mixed-integer nonlinear programming (SR-MINLP) to reduce the search time. Another approach to conceptual design optimization is shown by Zhang et al. [42], who followed an improved concurrent subspace optimization strategy (CSSO) and an improved differential evolution (DE) algorithm to solve the system-level and discipline-level optimization problems in conceptual design.

4.2 Parametric Design

In industry the shape of a component is important. Technical specifications and manufacturing costs depend on component shape (weight, torque, strength, etc.). In shape optimization, a parameter value must be found. The dependence function between the objective parameter with the shape variables can be non-linear or discontinuous. GA can assimilate this dependence function. Constraints can be determined by using a differential evolution algorithm in which the parameters are intermediate design variables [43].

The application of GA to parametric design has been successful in different studies. Gunpinar and Gunpinar [44] used GA to change the position of the points in parametric design. Particles are placed at points in the shape space by optimizing the fitness of the particle positions with a permutation GA (Fig. 3). Mostofizadeh et al. [45] performed the parametric design of a row of cylindrical film cooling holes to use GA in the optimization of gas turbines. In this case, the use of parameters improved the artificial neural network (ANN). Dandy et al. [46] compared the use of parameters in two GA: a traditional GA and a modified GA with improved operators. Renzi [47] utilized nonlinear constraints to test individuals within each generation with geometric bounds and related parameters in an integrated design environment (IDe). Zhu et al. [38] compared the use of different model parameters in GA by choosing between the deterministic optimal design point and the robust optimal design point. Sekulski [48] selected the genotype by testing phenotype parameters.

Fig. 3.
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Car hood models generated by parametric GA [44]

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4.3 Reverse Engineering

A reverse engineering process begins by recording existing points by matching the model represented with the physically existing model. The next step is to establish a topology in the unstructured points cloud that reflects the mirror relations between the model and the real object. The rebuilding phase is based on belonging to subsets of the extracted elements.

For all these phases, GA have been investigated by different authors. Zhang et al. [49] applied Euclidean distance to duplicate the position of atoms in a material structure. Brunnstro and Stoddart [50] built mirror relations for points of correspondence in GA. The chromosomes of this model represent a correspondence between two sets of points (model point—real object point). The fitness function reflects the correspondence quality by calculating the distance between a pair of points. Its genetic code is composed of the transformation matrix parameters and the fitness function that minimizes the distance between each pair of points.

5 Results

The bibliographic review has introduced improvements into GA applications in industrial design. We describe the characteristics of different GA examples in several industrial design fields (Table 2). The design tool and case studies show that multiple GA applications are possible with different GA specifications.

Table 2. Comparison between the GA applications reported in the literature
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We can see priority GA specifications to improve industrial design using GA. These parameters could be: a constrained fitness function, a chromosome substring, a good selection of genetic operators. In [47], we predict that a constrained fitness function is better than a nondeterministic function. In [43] and [48], we observe that a constrained representation improves evolution. In [38], we discover that modified genetic operators are decisive to accomplish the final design specifications.

6 Conclusions and Future Work

GA can be successfully applied to industrial design. By even considering the creative factor in design, GAs can show the designer additional solutions.

In this bibliographic review, we study the definitions of the elements that compose a GA. We link these elements with the design process, which we see at both the creative and strictly procedural levels. Finally, we describe the characteristics of different GAs examples in several industrial design fields.

With all this, we see how GA have difficulties in creative and conceptual designs. However, we can verify how the fields of parametric design and configurations design have a high potential when applying GA. This is where our path is discovered by developing an optimization method in industrial design.