A new metaheuristic algorithm called CDDO was developed. In 2021[11], Tarik A. Rashid and Sabat Abdulhameed created the algorithm. The golden ratio is used in this algorithm, which optimizes the aesthetic value of the child's artwork depending on their cognitive development and learning behavior. The eminent mathematician Fibonacci is credited with discovering the golden ratio. The golden ratio that is common in art, nature, design, and architecture, is comparable to ratio of 2 successive numbers in the Fibonacci sequence. The stages of a child's drawing development—from scribbling stage to pattern-based level of sophistication—are simulated by CDDO, together with cognitive learning. To improve outcomes, changes are made to a child's hand pressure's length, width, and golden ratio. CDDO is broken down into the following phases.

A. The First Stage (The Scribble)

A child's initial attempts at drawing typically consist of random marks. The child learns to recognize movement and hand pressure at this period. Due to the child's observation that all other hand motions lead to curves and only linear movements produce lines, movement could be both curved and random. The hand pressure is excessive in this step; either too low or too high will be corrected through trial and error in later steps while considering a variety of other factors—initialization, for example. Xij for I = 1 to N solutions. In the case when numerous decision variables are taken into account, X represents the current solution reflecting a child's drawing with changeable choice variables like hand pressure, length, golden ratio, and width of the drawing. I stands for the number of the decision variables, and j for the number of parameters.

B. The Second Stage (Exploitation)

In this phase, the child develops the ability to control the movement and direction of their bodies in order to create shapes. Hand pressure is one of the classification criteria for a child's performance. Eq. (1) is used to compute the Initial Random Hand Pressure (RHP). In order to compare the hand pressure of the present solution with the current solution's hand pressure, RHP is a random number between the upper boundary of the solution (UP) and the lower boundary of the problem (LB). Eq. (2) will choose HP from a group of solution parameters where HP is hand pressure and j is a collection of solution parameters.

$$HP=X(i,rand(j\left)\right)$$

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C. Third Stage (Golden Ratio)

Now that the child has reached this stage, she or he can analyze the patterns in real pictures, try to interpret the drawings, practice drawing by copying, practicing, and showing enthusiasm (with trail), and employ the skills they have learned via feedback and experience. The child's level rate (LR) and skill rate (SR), which are two random integers initially between 0 and 1 and between 0.6 and 1 if the child has relevant hand pressure, are taken into account when comparing the current hand pressure to RHP. In the case when the current hand pressure is less than RHP, the solution is updated using Eq. (2). The child's competence and level of knowledge is likely accurate when LR and SR are set to high levels (0.6–1), but it could be made better by taking the GR component into account. Another element used to update and improve the performance regarding the solution is the Golden Ratio (GR). The width and length of a child's artwork are the two selected solution components, and GR is the ratio of these dimensions (see Eq. (3)). With the use of (Eq. (4)), one of these two elements is chosen at random from each of the problem's factors.

$${X}_{iGR}=\frac{{X}_{iL}+{X}_{iW}}{{X}_{iL}}$$

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$$W,L=rand\left(0,j\right)$$

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The GR can be defined as proportion between the length (L) and width (W) of a child's drawing, and it is used in Eq. (5) Xilbest for representing the best drawing of the child to date, which is the local best solution, and global best solution that has been noticed by the children in their surroundings.

$${X}_{i+1}= \text{G}\text{R}+\text{S}\text{R}. \text{*} \left({X}_{ilbest}-{X}_{i }\right)+LR. *({X}_{igbest}-{X}_{i })$$

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D. Fourth Stage (Creativity)

In this stage, the child mixes data to update solutions which have GR or are very close to it. The lack of meaningful hand pressure in the answer, yet, suggests that the child's talent is underdeveloped and need to be developed further using the creative factor and the GR. Every algorithmic solution generates a unique Pattern Memory (PM), whose size changes depending on the challenges. However, one method to boost algorithm's rate of convergence is to choose a random solution from PM array to be utilized to update the solutions which aren't doing well. In actuality, this quickens the pace of the child' learning. In Eq. (6), the updated solution and the ideal solution are reached using both PM and CR.

$${X}_{i+1}={X}_{iMP}+CR. *\left({X}_{igbest}\right)$$

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E. Fifth Stage (Pattern Memory)

Inches of detail are the main focus in this level. The algorithm incorporates the behavior as it has been displayed by agent's personal best-updating mechanism. It is also at this point that the population's best overall solution will be updated in the case when a better one becomes available. This will likewise be the case if the optimal global solution so far found in every one of the iterations is used to refresh the pattern memory. The CDDO algorithm's steps were shown in Fig. 1.