# Product Image Generation Method Based on Morphological Optimization and Image Style Transfer
## 3 Optimization Design Model of Product Form Based on Genetic Algorithm and Esthetic Evaluation  
### A Morphological Optimization Design Model Based on the Genetic Algorithm  
The process of product form design involves the concrete realization of stages such as user demand exploration and scheme presentation by designers. From the perspective of knowledge flow theory, it constitutes a micro-process entailing the deconstruction and reconstruction of knowledge information. The standard genetic algorithm is goal-oriented and constructs fitness functions to evaluate the population. Through processes such as initial population evaluation and genetic operations, it selects individuals possessing optimization fitness function values, which are deemed as the optimal solutions to the problem [28]. The single-parent genetic algorithm represents a special instance of the standard genetic algorithm, wherein genetic operations are solely performed on a single individual, namely the target product sample that is to be optimized. In this study, an esthetic comprehensive evaluation model is employed to compute the fitness of individuals within the population. The flowchart illustrating the morphological optimization design process is depicted in Figure 1.  
Gene encoding involves analyzing the styling elements and key control points of superior product samples and subsequently decomposing them into morphological components. The key morphological components of the product specimen delineate the target region. The coordinates of these key control points represent the product's form and offer a quantitative description of the product sample. The design parameter set for the product sample is defined as \(C=\left\{c_{1},c_{2}...,c_{g}\right\}\), where each design parameter cg has a value range of \(C_{g}\in\left[U_{g},V_{g}\right]\) (\(U_{g}\) denoting the maximum value and \(V_{g}\) denoting the minimum value of the design parameter). Subsequently, binary encoding is employed to encode the product sample. In order to realize the optimization of the genetic algorithm, this study uses a binary coding scheme to discretize continuous parameters within predefined boundaries, mainly based on the following reasons:  
1. Compatibility: Binary encoding, as a classical implementation of the genetic algorithm, can directly apply standard crossover and mutation operators;
2. Scalability: The coordinate values of each control point are mapped from bounded continuous intervals (e.g., \(X\in\left[X_{\min},X_{\max}\right],Y\in\left[Y_{\min},Y_{\max}\right]\) ) to binary segments, which supports high-precision parameter optimization;3. Efficiency advantage: Binary coding can effectively balance the scale of the bounded discrete search space and computational efficiency in morphological optimization. Based on this coding scheme, the initial population is first generated in the discrete parameter space within the defined boundaries by random sampling, and then a new design scheme is generated by iterative optimization in the bounded discrete search space through genetic operations such as selection, crossover, and mutation. System parameter initialization involves the setting of parameters for morphological optimization design, including the initial population size, number of iterations, crossover probability, and mutation probability. The initial population pertains to the quantity of product samples during the first iteration. For morphological optimization problems, the size of the initial population primarily hinges on the complexity of the morphological design features or parameter sets. Typically, the population size falls within a range of 10 to 160. The determination of the number of iterations is generally based on the convergence curve obtained through numerous experimental trials. The crossover probability and mutation probability are often set according to the diversity of product solutions.